Chapter4 How We Got the Solutions

CHAPTER 4 Discounted Cash Flow Valuation Multiple Choice Questions: I.

DEFINITIONS

ANNUITY a 1. An annuity stream of cash flow payments is a set of: a. level cash flows occurring each time period for a fixed length of time. b. level cash flows occurring each time period forever. c. increasing cash flows occurring each time period for a fixed length of time. d. increasing cash flows occurring each time period forever. e. arbitrary cash flows occurring each time period for no more than 10 years. Difficulty level: Easy ANNUITIES DUE e 2. Annuities where the payments occur at the end of each time period are called _____ , whereas _____ refer to annuity streams with payments occurring at the beginning of each time period. a. ordinary annuities; early annuities b. late annuities; straight annuities c. straight annuities; late annuities d. annuities due; ordinary annuities e. ordinary annuities; annuities due Difficulty level: Easy PERPETUITY c 3. An annuity stream where the payments occur forever is called a(n): a. annuity due. b. indemnity. c. perpetuity. d. amortized cash flow stream. e. amortization table. Difficulty level: Easy STATED INTEREST RATES a 4. The interest rate expressed in terms of the interest payment made each period is called the _____ rate. a. stated annual interest b. compound annual interest c. effective annual interest d. periodic interest e. daily interest Difficulty level: Easy EFFECTIVE ANNUAL RATE c 5. The interest rate expressed as if it were compounded once per year is called the _____ rate.

a. b. c. d. e.

stated interest compound interest effective annual periodic interest daily interest

Difficulty level: Easy ANNUAL PERCENTAGE RATE b 6. The interest rate charged per period multiplied by the number of periods per year is called the _____ rate. a. effective annual b. annual percentage c. periodic interest d. compound interest e. daily interest Difficulty level: Easy II.

CONCEPTS

ORDINARY ANNUITY VERSUS ANNUITY DUE c 7. You are comparing two annuities which offer monthly payments for ten years. Both annuities are identical with the exception of the payment dates. Annuity A pays on the first of each month while annuity B pays on the last day of each month. Which one of the following statements is correct concerning these two annuities? a. Both annuities are of equal value today. b. Annuity B is an annuity due. c. Annuity A has a higher future value than annuity B. d. Annuity B has a higher present value than annuity A. e. Both annuities have the same future value as of ten years from today. Difficulty level: Medium UNEVEN CASH FLOWS AND PRESENT VALUE b 8. You are comparing two investment options. The cost to invest in either option is the same today. Both options will provide you with $20,000 of income. Option A pays five annual payments starting with $8,000 the first year followed by four annual payments of $3,000 each. Option B pays five annual payments of $4,000 each. Which one of the following statements is correct given these two investment options? a. Both options are of equal value given that they both provide $20,000 of income. b. Option A is the better choice of the two given any positive rate of return. c. Option B has a higher present value than option A given a positive rate of return. d. Option B has a lower future value at year 5 than option A given a zero rate of return. e. Option A is preferable because it is an annuity due. Difficulty level: Medium UNEVEN CASH FLOWS AND FUTURE VALUE

a

9.

You are considering two projects with the following cash flows: Project A Project B Year 1 $2,500 $4,000 Year 2 3,000 3,500 Year 3 3,500 3,000 Year 4 4,000 2,500 Which of the following statements are true concerning these two projects? I. Both projects have the same future value at the end of year 4, given a positive rate of return. II. Both projects have the same future value given a zero rate of return. III. Both projects have the same future value at any point in time, given a positive rate of return. IV. Project A has a higher future value than project B, given a positive rate of return. a. II only b. IV only c. I and III only d. II and IV only e. I, II, and III only Difficulty level: Medium

PERPETUITY VERSUS ANNUITY d 10. A perpetuity differs from an annuity because: a. perpetuity payments vary with the rate of inflation. b. perpetuity payments vary with the market rate of interest. c. perpetuity payments are variable while annuity payments are constant. d. perpetuity payments never cease. e. annuity payments never cease. Difficulty level: Easy ANNUAL PERCENTAGE RATE e 11. Which one of the following statements concerning the annual percentage rate is correct? a. The annual percentage rate considers interest on interest. b. The rate of interest you actually pay on a loan is called the annual percentage rate. c. The effective annual rate is lower than the annual percentage rate when an interest rate is compounded quarterly. d. When firms advertise the annual percentage rate they are violating U.S. truth-inlending laws. e. The annual percentage rate equals the effective annual rate when the rate on an account is designated as simple interest. Difficulty level: Easy INTEREST RATES b 12. Which one of the following statements concerning interest rates is correct? a. The stated rate is the same as the effective annual rate. b. An effective annual rate is the rate that applies if interest were charged annually. c. The annual percentage rate increases as the number of compounding periods per year increases.

d. e.

Banks prefer more frequent compounding on their savings accounts. For any positive rate of interest, the effective annual rate will always exceed the annual percentage rate.

Difficulty level: Easy EFFECTIVE ANNUAL RATE c 13. Which of the following statements concerning the effective annual rate are correct? I. When making financial decisions, you should compare effective annual rates rather than annual percentage rates. II. The more frequently interest is compounded, the higher the effective annual rate. III. A quoted rate of 6% compounded continuously has a higher effective annual rate than if the rate were compounded daily. IV. When borrowing and choosing which loan to accept, you should select the offer with the highest effective annual rate. a. I and II only b. I and IV only c. I, II, and III only d. II, III, and IV only e. I, II, III,and IV Difficulty level: Medium CONTINUOUS COMPOUNDING d 14. The highest effective annual rate that can be derived from an annual percentage rate of 9% is computed as: a. .09e -1. b. e.09 × q. c. e × (1 + .09). d. e.09 – 1. e. (1 + .09)q. Difficulty level: Easy TIME VALUE c 15. The time value of money concept can be defined as a. the relationship between the supply and demand of money. b. the relationship between money spent versus money received. c. the relationship between a dollar to be received in the future and a dollar today. d. the relationship of interest rate stated and amount paid. e. None of the above. Difficulty level: Easy CASH FLOWS d 16. Discounting cash flows involves a. discounting only those cash flows that occur at least 10 years in the future. b. estimating only the cash flows that occur in the first 4 years of a project. c. multiplying expected future cash flows by the cost of capital. d. discounting all expected future cash flows to reflect the time value of money. e. taking the cash discount offered on trade merchandise.

Difficulty level: Easy INTEREST a 17. Compound interest a. allows for the reinvestment of interest payments. b. does not allow for the reinvestment of interest payments. c. is the same as simple interest. d. provides a value that is less than simple interest. e. Both A and D. Difficulty level: Easy ANNUITY c 18. An annuity a. is a debt instrument that pays no interest. b. is a stream of payments that varies with current market interest. c. is a level stream of equal payments through time. d. has no value. e. None of the above. Difficulty level: Easy COMPOUNDING d 19. The stated rate of interest is 10%. Which form of compounding will give the highest effective rate of interest? a. annual compounding b. monthly compounding c. daily compounding d. continuous compounding e. It is impossible to tell without knowing the term of the loan. Difficulty level: Easy PRESENT VALUE b 20. The present value of future cash flows minus initial cost is called a. the future value of the project. b. the net present value of the project. c. the equivalent sum of the investment. d. the initial investment risk equivalent value. e. None of the above. Difficulty level: Easy III. PROBLEMS PRESENT VALUE – SINGLE SUM a 21. Find the present value of $5,325 to be received in one period if the rate is 6.5%. a. $5,000.00 b. $5,023.58

c. d. e.

$5,644.50 $5,671.13 None of the above.

Difficulty level: Easy SIMPLE & COMPOUND INTEREST b 22. If you have a choice to earn simple interest on $10,000 for three years at 8% or annually compound interest at 7.5% for three years which one will pay more and by how much? a. Simple interest by $50.00 b. Compound interest by $22.97 c. Compound interest by $150.75 d. Compound interest by $150.00 e. None of the above. Difficulty level: Easy FUTURE VALUE – SINGLE SUM d 23. Bradley Snapp has deposited $7,000 in a guaranteed investment account with a promised rate of 6% compounded annually. He plans to leave it there for 4 full years when he will make a down payment on a car after graduation. How much of a down payment will he be able to make? a. $1,960.00 b. $2,175.57 c. $8,960.00 d. $8,837.34 e. $9,175.57 Difficulty level: Easy ORDINARY ANNUITY AND PRESENT VALUE d 24. Your parents are giving you $100 a month for four years while you are in college. At a 6% discount rate, what are these payments worth to you when you first start college? a. $3,797.40 b. $4,167.09 c. $4,198.79 d. $4,258.03 e. $4,279.32 Difficulty level: Easy ORDINARY ANNUITY AND PRESENT VALUE b 25. You just won the lottery! As your prize you will receive $1,200 a month for 100 months. If you can earn 8% on your money, what is this prize worth to you today? a. $87,003.69 b. $87,380.23 c. $87,962.77 d. $88,104.26 e. $90,723.76 Difficulty level: Easy

ORDINARY ANNUITY AND PRESENT VALUE b 26. Todd is able to pay $160 a month for five years for a car. If the interest rate is 4.9 percent, how much can Todd afford to borrow to buy a car? a. $6,961.36 b. $8,499.13 c. $8,533.84 d. $8,686.82 e. $9,588.05 Difficulty level: Easy ORDINARY ANNUITY AND PRESENT VALUE a 27. You are the beneficiary of a life insurance policy. The insurance company informs you that you have two options for receiving the insurance proceeds. You can receive a lump sum of $50,000 today or receive payments of $641 a month for ten years. You can earn 6.5% on your money. Which option should you take and why? a. You should accept the payments because they are worth $56,451.91 today. b. You should accept the payments because they are worth $56,523.74 today. c. You should accept the payments because they are worth $56,737.08 today. d. You should accept the $50,000 because the payments are only worth $47,757.69 today. e. You should accept the $50,000 because the payments are only worth $47,808.17 today. Difficulty level: Medium ORDINARY ANNUITY AND PRESENT VALUE c 28. Your employer contributes $25 a week to your retirement plan. Assume that you work for your employer for another twenty years and that the applicable discount rate is 5 percent. Given these assumptions, what is this employee benefit worth to you today? a. $13,144.43 b. $15,920.55 c. $16,430.54 d. $16,446.34 e. $16,519.02 Difficulty level: Medium ORDINARY ANNUITY AND PRESENT VALUE a 29. You have a sub-contracting job with a local manufacturing firm. Your agreement calls for annual payments of $50,000 for the next five years. At a discount rate of 12 percent, what is this job worth to you today? a. $180,238.81 b. $201,867.47 c. $210,618.19 d. $223,162.58 e. $224,267.10 Difficulty level: Medium ANNUITY DUE AND PRESENT VALUE

b

30. The Ajax Co. just decided to save $1,500 a month for the next five years as a safety net for recessionary periods. The money will be set aside in a separate savings account which pays 3.25% interest compounded monthly. They deposit the first $1,500 today. If the company had wanted to deposit an equivalent lump sum today, how much would they have had to deposit? a. $82,964.59 b. $83,189.29 c. $83,428.87 d. $83,687.23 e. $84,998.01 Difficulty level: Medium

ANNUITY DUE AND PRESENT VALUE b 31. You need some money today and the only friend you have that has any is your ‘miserly’ friend. He agrees to loan you the money you need, if you make payments of $20 a month for the next six month. In keeping with his reputation, he requires that the first payment be paid today. He also charges you 1.5% interest per month. How much money are you borrowing? a. $113.94 b. $115.65 c. $119.34 d. $119.63 e. $119.96 Difficulty level: Medium ANNUITY DUE AND PRESENT VALUE c 32. You buy an annuity which will pay you $12,000 a year for ten years. The payments are paid on the first day of each year. What is the value of this annuity today at a 7% discount rate? a. $84,282.98 b. $87,138.04 c. $90,182.79 d. $96,191.91 e. $116,916.21 Difficulty level: Medium ORDINARY ANNUITY VERSUS ANNUITY DUE a 33. You are scheduled to receive annual payments of $10,000 for each of the next 25 years. Your discount rate is 8.5 percent. What is the difference in the present value if you receive these payments at the beginning of each year rather than at the end of each year? a. $8,699 b. $9,217 c. $9,706 d. $10,000 e. $10,850 Difficulty level: Medium ORDINARY ANNUITY VERSUS ANNUITY DUE

d

34. You are comparing two annuities with equal present values. The applicable discount rate is 7.5 percent. One annuity pays $5,000 on the first day of each year for twenty years. How much does the second annuity pay each year for twenty years if it pays at the end of each year? a. $4,651 b. $5,075 c. $5,000 d. $5,375 e. $5,405 Difficulty level: Medium

ORDINARY ANNUITY VERSUS ANNUITY DUE a 35. Martha receives $100 on the first of each month. Stewart receives $100 on the last day of each month. Both Martha and Stewart will receive payments for five years. At an 8% discount rate, what is the difference in the present value of these two sets of payments? a. $32.88 b. $40.00 c. $99.01 d. $108.00 e. $112.50 Difficulty level: Medium ORDINARY ANNUITY AND FUTURE VALUE c 36. What is the future value of $1,000 a year for five years at a 6% rate of interest? a. $4,212.36 b. $5,075.69 c. $5,637.09 d. $6,001.38 e. $6,801.91 Difficulty level: Easy ORDINARY ANNUITY AND FUTURE VALUE d 37. What is the future value of $2,400 a year for three years at an 8% rate of interest? a. $6,185.03 b. $6,847.26 c. $7,134.16 d. $7,791.36 e. $8,414.67 Difficulty level: Easy ORDINARY ANNUITY AND FUTURE VALUE c 38. Janet plans on saving $3,000 a year and expects to earn 8.5 percent. How much will Janet have at the end of twenty-five years if she earns what she expects? a. $219,317.82 b. $230,702.57 c. $236,003.38 d. $244,868.92 e. $256,063.66

Difficulty level: Easy ANNUITY DUE VERSUS ORDINARY ANNUITY b 39. Toni adds $3,000 to her savings on the first day of each year. Tim adds $3,000 to his savings on the last day of each year. They both earn a 9% rate of return. What is the difference in their savings account balances at the end of thirty years? a. $35,822.73 b. $36,803.03 c. $38,911.21 d. $39,803.04 e. $40,115.31 Difficulty level: Medium ORDINARY ANNUITY PAYMENTS d 40. You borrow $5,600 to buy a car. The terms of the loan call for monthly payments for four years at a 5.9% rate of interest. What is the amount of each payment? a. $103.22 b. $103.73 c. $130.62 d. $131.26 e. $133.04 Difficulty level: Easy ORDINARY ANNUITY PAYMENTS AND COST OF INTEREST c 41. You borrow $149,000 to buy a house. The mortgage rate is 7.5% and the loan period is 30 years. Payments are made monthly. If you pay for the house according to the loan agreement, how much total interest will you pay? a. $138,086 b. $218,161 c. $226,059 d. $287,086 e. $375,059 Difficulty level: Medium ORDINARY ANNUITY PAYMENTS AND FUTURE VALUE d 42. The Great Giant Corp. has a management contract with their newly hired president. The contract requires a lump sum payment of $25 million be paid to the president upon the completion of her first ten years of service. The company wants to set aside an equal amount of funds each year to cover this anticipated cash outflow. The company can earn 6.5% on these funds. How much must the company set aside each year for this purpose? a. $1,775,042.93 b. $1,798,346.17 c. $1,801,033.67 d. $1,852,617.25 e. $1,938,018.22

Difficulty level: Easy ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE e 43. You retire at age 60 and expect to live another 27 years. On the day you retire, you have $464,900 in your retirement savings account. You are conservative and expect to earn 4.5% on your money during your retirement. How much can you withdraw from your retirement savings each month if you plan to die on the day you spend your last penny? a. $2,001.96 b. $2,092.05 c. $2,398.17 d. $2,472.00 e. $2,481.27 Difficulty level: Medium ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE c 44. The McDonald Group purchased a piece of property for $1.2 million. They paid a down payment of 20% in cash and financed the balance. The loan terms require monthly payments for 15 years at an annual percentage rate of 7.75% compounded monthly. What is the amount of each mortgage payment? a. $7,440.01 b. $8,978.26 c. $9,036.25 d. $9,399.18 e. $9,413.67 Difficulty level: Medium ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE d 45. You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5 percent. If you want to have this debt paid in full within five years, how much must you pay each month? a. $471.30 b. $473.65 c. $476.79 d. $479.37 e. $480.40 Difficulty level: Medium ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE b 46. You are buying a previously owned car today at a price of $6,890. You are paying $500 down in cash and financing the balance for 36 months at 7.9 percent. What is the amount of each loan payment? a. $198.64 b. $199.94 c. $202.02 d. $214.78 e. $215.09 Difficulty level: Medium

ORDINARY ANNUITY PAYMENTS AND PRESENT VALUE b 47. The Good Life Insurance Co. wants to sell you an annuity which will pay you $500 per quarter for 25 years. You want to earn a minimum rate of return of 5.5 percent. What is the most you are willing to pay as a lump sum today to buy this annuity? a. $26,988.16 b. $27,082.94 c. $27,455.33 d. $28,450.67 e. $28,806.30 Difficulty level: Medium ANNUITY DUE PAYMENTS AND PRESENT VALUE c 48. Your car dealer is willing to lease you a new car for $299 a month for 60 months. Payments are due on the first day of each month starting with the day you sign the lease contract. If your cost of money is 4.9 percent, what is the current value of the lease? a. $15,882.75 b. $15,906.14 c. $15,947.61 d. $16,235.42 e. $16,289.54 Difficulty level: Medium ANNUITY DUE PAYMENTS AND PRESENT VALUE d 49. Your great-aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,500 on the first day of each year, starting immediately and continuing for fifty years. What is the value of this inheritance today if the applicable discount rate is 6.35 percent? a. $36,811.30 b. $37,557.52 c. $39,204.04 d. $39,942.42 e. $40,006.09 Difficulty level: Medium SIMPLE VERSUS COMPOUND INTEREST c 50. Beatrice invests $1,000 in an account that pays 4% simple interest. How much more could she have earned over a five-year period if the interest had compounded annually? a. $15.45 b. $15.97 c. $16.65 d. $17.09 e. $21.67 Difficulty level: Easy ANNUITY DUE PAYMENTS AND FUTURE VALUE

a

51. Your firm wants to save $250,000 to buy some new equipment three years from now. The plan is to set aside an equal amount of money on the first day of each year starting today. The firm can earn a 4.7% rate of return. How much does the firm have to save each year to achieve their goal? a. $75,966.14 b. $76,896.16 c. $78,004.67 d. $81.414.14 e. $83,333.33 Difficulty level: Medium

ANNUITY DUE PAYMENTS AND FUTURE VALUE e 52. Today is January 1. Starting today, Sam is going to contribute $140 on the first of each month to his retirement account. His employer contributes an additional 50% of the amount contributed by Sam. If both Sam and his employer continue to do this and Sam can earn a monthly rate of ½ of 1 percent, how much will he have in his retirement account 35 years from now? a. $199,45.944. b. $200,456.74 c. $249,981.21 d. $299,189.16 e. $300,685.11 Difficulty level: Medium ORDINARY ANNUITY TIME PERIODS AND PRESENT VALUE c 53. You are considering an annuity which costs $100,000 today. The annuity pays $6,000 a year. The rate of return is 4.5 percent. What is the length of the annuity time period? a. 24.96 years b. 29.48 years c. 31.49 years d. 33.08 years e. 38.00 years Difficulty level: Medium ORDINARY ANNUITY TIME PERIODS AND PRESENT VALUE d 54. Today, you signed loan papers agreeing to borrow $4,954.85 at 9% compounded monthly. The loan payment is $143.84 a month. How many loan payments must you make before the loan is paid in full? a. 29.89 b. 36.00 c. 38.88 d. 40.00 e. 41.03 Difficulty level: Medium ORDINARY ANNUITY TIME PERIODS AND FUTURE VALUE

a

55. Winston Enterprises would like to buy some additional land and build a new factory. The anticipated total cost is $136 million. The owner of the firm is quite conservative and will only do this when the company has sufficient funds to pay cash for the entire expansion project. Management has decided to save $450,000 a month for this purpose. The firm earns 6% compounded monthly on the funds it saves. How long does the company have to wait before expanding its operations? a. 184.61 months b. 199.97 months c. 234.34 months d. 284.61 months e. 299.97 months Difficulty level: Medium

ANNUITY DUE TIME PERIODS AND PRESENT VALUE b 56. Today, you are retiring. You have a total of $413,926 in your retirement savings and have the funds invested such that you expect to earn an average of 3 percent, compounded monthly, on this money throughout your retirement years. You want to withdraw $2,500 at the beginning of every month, starting today. How long will it be until you run out of money? a. 185.00 months b. 213.29 months c. 227.08 months d. 236.84 months e. 249.69 months Difficulty level: Medium ANNUITY DUE TIME PERIODS c 57. The Bad Guys Co. is notoriously known as a slow-payer. They currently need to borrow $25,000 and only one company will even deal with them. The terms of the loan call for daily payments of $30.76. The first payment is due today. The interest rate is 21% compounded daily. What is the time period of this loan? a. 2.88 years b. 2.94 years c. 3.00 years d. 3.13 years e. 3.25 years Difficulty level: Medium ORDINARY ANNUITY INTEREST RATE c 58. The Robertson Firm is considering a project which costs $123,900 to undertake. The project will yield cash flows of $4,894.35 monthly for 30 months. What is the rate of return on this project? a. 12.53% b. 13.44% c. 13.59% d. 14.02% e. 14.59% Difficulty level: Medium

ORDINARY ANNUITY INTEREST RATE a 59. Your insurance agent is trying to sell you an annuity that costs $100,000 today. By buying this annuity, your agent promises that you will receive payments of $384.40 a month for the next 40 years. What is the rate of return on this investment? a. 3.45% b. 3.47% c. 3.50% d. 3.52% e. 3.55% Difficulty level: Medium ORDINARY ANNUITY INTEREST RATE e 60. You have been investing $120 a month for the last 15 years. Today, your investment account is worth $47,341.19. What is your average rate of return on your investments? a. 9.34% b. 9.37% c. 9.40% d. 9.42% e. 9.46% Difficulty level: Medium ORDINARY ANNUITY INTEREST RATE c 61. Brinker, Inc. has been investing $136,000 a year for the past 4 years into a business venture. Today, Brinker sold that venture for $685,000. What is their rate of return on this venture? a. 9.43% b. 11.06% c. 15.59% d. 16.67% e. 18.71% Difficulty level: Easy ANNUITY DUE INTEREST RATE b 62. Your mother helped you start saving $25 a month beginning on your 10th birthday. She always made you make your deposit on the first day of each month just to “start the month out right”. Today, you turn 21 and have $4,482.66 in your account. What is your rate of return on your savings? a. 5.25% b. 5.29% c. 5.33% d. 5.36% e. 5.50% Difficulty level: Easy ANNUITY DUE INTEREST RATE a 63. Today, you turn 21. Your birthday wish is that you will be a millionaire by your 40th birthday. In an attempt to reach this goal, you decide to save $25 a day, every day until you turn 40. You

a. b. c. d. e.

open an investment account and deposit your first $25 today. What rate of return must you earn to achieve your goal? 15.07% 15.13% 15.17% 15.20% 15.24%

Difficulty level: Easy UNEVEN CASH FLOWS AND PRESENT VALUE b 64. Marko, Inc. is considering the purchase of ABC Co. Marko believes that ABC Co. can generate cash flows of $5,000, $9,000, and $15,000 over the next three years, respectively. After that time, they feel the business will be worthless. Marko has determined that a 14% rate of return is applicable to this potential purchase. What is Marko willing to pay today to buy ABC Co.? a. $19,201.76 b. $21,435.74 c. $23,457.96 d. $27,808.17 e. $31,758.00 Difficulty level: Easy UNEVEN CASH FLOWS AND PRESENT VALUE a 65. You are considering two savings options. Both options offer a 4% rate of return. The first option is to save $1,200, $1,500, and $2,000 a year over the next three years, respectively. The other option is to save one lump sum amount today. If you want to have the same balance in your savings at the end of the three years, regardless of the savings method you select, how much do you need to save today if you select the lump sum option? a. $4,318.67 b. $4,491.42 c. $4,551.78 d. $4,607.23 e. $4,857.92 Difficulty level: Easy UNEVEN CASH FLOWS AND PRESENT VALUE b 66. You are considering two insurance settlement offers. The first offer includes annual payments of $5,000, $7,500, and $10,000 over the next three years, respectively. The other offer is the payment of one lump sum amount today. You are trying to decide which offer to accept given the fact that your discount rate is 5 percent. What is the minimum amount that you will accept today if you are to select the lump sum offer? a. $19,877.67 b. $20,203.00 c. $21,213.15 d. $23,387.50 e. $24,556.88 Difficulty level: Easy

UNEVEN CASH FLOWS AND PRESENT VALUE d 67. You are considering a job offer. The job offers an annual salary of $52,000, $55,000, and $60,000 a year for the next three years, respectively. The offer also includes a starting bonus of $2,000 payable immediately. What is this offer worth to you today at a discount rate of 6 percent? a. $148,283.56 b. $148,383.56 c. $150,283.56 d. $150,383.56 e. $152,983.56 Difficulty level: Easy UNEVEN CASH FLOWS AND PRESENT VALUE b 68. You are considering a project with the following cash flows: Year 1 Year 2 Year 3 $1,200 $1,800 $2,900 What is the present value of these cash flows, given a 9% discount rate? a. $4,713.62 b. $4,855.27 c. $5,103.18 d. $5,292.25 e. $6,853.61 Difficulty level: Easy UNEVEN CASH FLOWS AND PRESENT VALUE d 69. You are considering a project with the following cash flows: Year 1 Year 2 Year 3 $5,600 $9,000 $2,000 What is the present value of these cash flows, given an 11% discount rate? a. $8,695.61 b. $8,700.89 c. $13,732.41 d. $13,812.03 e. $19,928.16 Difficulty level: Easy UNEVEN CASH FLOWS AND PRESENT VALUE a 70. You are considering a project with the following cash flows: Year 1 Year 2 Year 3 $4,200 $5,000 $5,400 What is the present value of these cash flows, given a 3% discount rate? a. $13,732.41 b. $13,812.03 c. $14,308.08 d. $14,941.76 e. $14,987.69 Difficulty level: Easy

UNEVEN CASH FLOWS AND PRESENT VALUE a 71. You have some property for sale and have received two offers. The first offer is for $189,000 today in cash. The second offer is the payment of $100,000 today and an additional $100,000 two years from today. If the applicable discount rate is 8.75 percent, which offer should you accept and why? a. You should accept the $189,000 today because it has the higher net present value. b. You should accept the $189,000 today because it has the lower future value. c. You should accept the second offer because you will receive $200,000 total. d. You should accept the second offer because you will receive an extra $11,000. e. You should accept the second offer because it has a present value of $194,555.42. Difficulty level: Medium UNEVEN CASH FLOWS AND PRESENT VALUE b 72. Your local travel agent is advertising an extravagant global vacation. The package deal requires that you pay $5,000 today, $15,000 one year from today, and a final payment of $25,000 on the day you leave two years from today. What is the cost of this vacation in today’s dollars if the discount rate is 6 percent? a. $39,057.41 b. $41,400.85 c. $43,082.39 d. $44,414.14 e. $46,518.00 Difficulty level: Medium UNEVEN CASH FLOWS AND FUTURE VALUE e 73. One year ago, the Jenkins Family Fun Center deposited $3,600 in an investment account for the purpose of buying new equipment four years from today. Today, they are adding another $5,000 to this account. They plan on making a final deposit of $7,500 to the account next year. How much will be available when they are ready to buy the equipment, assuming they earn a 7% rate of return? a. $18,159.65 b. $19,430.84 c. $19,683.25 d. $20,194.54 e. $20,790.99 Difficulty level: Medium UNEVEN CASH FLOWS AND FUTURE VALUE c 74. What is the future value of the following cash flows at the end of year 3 if the interest rate is 6 percent? The cash flows occur at the end of each year. Year 1 Year 2 Year 3 $5,180 $9,600 $2,250 a. $15,916.78 b. $18,109.08 c. $18,246.25 d. $19,341.02 e. $19,608.07

Difficulty level: Medium UNEVEN CASH FLOWS AND FUTURE VALUE d 75. What is the future value of the following cash flows at the end of year 3 if the interest rate is 9 percent? The cash flows occur at the end of each year. Year 1 Year 2 Year 3 $9,820 $0 $4,510 a. $15,213.80 b. $15,619.70 c. $15,916.78 d. $16,177.14 e. $17,633.08 Difficulty level: Medium UNEVEN CASH FLOWS AND FUTURE VALUE c 76. What is the future value of the following cash flows at the end of year 3 if the interest rate is 7.25 percent? The cash flows occur at the end of each year. Year 1 Year 2 Year 3 $6,800 $2,100 $0 a. $8,758.04 b. $8,806.39 c. $10,073.99 d. $10,314.00 e. $10,804.36 Difficulty level: Medium UNEVEN CASH FLOWS AND FUTURE VALUE e 77. Suzette is going to receive $10,000 today as the result of an insurance settlement. In addition, she will receive $15,000 one year from today and $25,000 two years from today. She plans on saving all of this money and investing it for her retirement. If Suzette can earn an average of 11% on her investments, how much will she have in her account if she retires 25 years from today? a. $536,124.93 b. $541,414.14 c. $546,072.91 d. $570,008.77 e. $595,098.67 Difficulty level: Medium PRESENT VALUE, PAYMENTS AND FUTURE VALUE b 78. The Bluebird Company has a $10,000 liability they must pay three years from today. The company is opening a savings account so that the entire amount will be available when this debt needs to be paid. The plan is to make an initial deposit today and then deposit an additional $2,500 a year for the next three years, starting one year from today. The account pays a 3% rate of return. How much does the Bluebird Company need to deposit today? a. $1,867.74 b. $2,079.89

c. d. e.

$3,108.09 $4,276.34 $4,642.28

Difficulty level: Medium UNEVEN CASH FLOWS AND FUTURE VALUE c 79. The government has imposed a fine on the Not-So-Legal Company. The fine calls for annual payments of $100,000, $250,000, and $250,000, respectively over the next three years. The first payment is due one year from today. The government plans to invest the funds until the final payment is collected and then donate the entire amount, including investment earnings, to a national health center. The government will earn 3.5% on the funds held. How much will the national health center receive three years from today? a. $613,590.00 b. $614,622.50 c. $615,872.50 d. $616,006.00 e. $619,050.05 Difficulty level: Medium PERPETUITY PRESENT VALUE b 80. George Jefferson established a trust fund that provides $150,000 in scholarships each year for worthy students. The trust fund earns a 4.25% rate of return. How much money did Mr. Jefferson contribute to the fund assuming that only the interest income is distributed? a. $3,291,613.13 b. $3,529,411.77 c. $3,750,000.00 d. $4,328,970.44 e. $6,375,000.00 Difficulty level: Easy PERPETUITY PRESENT VALUE e 81. A 9% preferred stock pays an annual dividend of $4.50. What is one share of this stock worth today? a. $.41 b. $4.50 c. $5.00 d. $45.00 e. $50.00 Difficulty level: Easy PERPETUITY PRESENT VALUE e 82. You would like to establish a trust fund that will provide $50,000 a year forever for your heirs. The trust fund is going to be invested very conservatively so the expected rate of return is only 2.75 percent. How much money must you deposit today to fund this gift for your heirs? a. $1,333,333.33 b. $1,375,000.00 c. $1,425,000.00

d. e.

$1,666,666.67 $1,818,181.82

Difficulty level: Easy PERPETUITY DISCOUNT RATE c 83. You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy? a. 3.25% b. 3.33% c. 3.43% d. 3.50% e. 3.67% Difficulty level: Medium PERPETUITY DISCOUNT RATE d 84. The Eternal Gift Insurance Company is offering you a policy that will pay you and your heirs $10,000 a year forever. The cost of the policy is $285,000. What is the rate of return on this policy? a. 2.85% b. 3.25% c. 3.46% d. 3.51% e. 3.60% Difficulty level: Easy PERPETUITY PAYMENT e 85. Your rich uncle establishes a trust in your name and deposits $150,000 in it. The trust pays a guaranteed 4% rate of return. How much will you receive each year if the trust is required to pay you all of the interest earnings on an annual basis? a. $3,750 b. $4,000 c. $4,500 d. $5,400 e. $6,000 Difficulty level: Easy PERPETUITY PAYMENT b 86. The preferred stock of ABC Co. offers an 8.4% rate of return. The stock is currently priced at $50.00 per share. What is the amount of the annual dividend? a. $2.10 b. $4.20 c. $5.00 d. $6.40 e. $8.60 Difficulty level: Easy

ANNUAL PERCENTAGE RATE d 87. Your credit card company charges you 1.5% per month. What is the annual percentage rate on your account? a. 12.00% b. 15.00% c. 15.39% d. 18.00% e. 19.56% Difficulty level: Medium ANNUAL PERCENTAGE RATE d 88. What is the annual percentage rate on a loan with a stated rate of 2% per quarter? a. 2.00% b. 2.71% c. 4.04% d. 8.00% e. 8.24% Difficulty level: Medium ANNUAL PERCENTAGE RATE c 89. You are paying an effective annual rate of 13.8% on your credit card. The interest is compounded monthly. What is the annual percentage rate on your account? a. 11.50% b. 12.00% c. 13.00% d. 13.80% e. 14.71% Difficulty level: Medium EFFECTIVE ANNUAL RATE b 90. What is the effective annual rate if a bank charges you 7.64% compounded quarterly? a. 7.79% b. 7.86% c. 7.95% d. 7.98% e. 8.01% Difficulty level: Medium EFFECTIVE ANNUAL RATE d 91. Your credit card company quotes you a rate of 14.9 percent. Interest is billed monthly. What is the actual rate of interest you are paying? a. 13.97% b. 14.90% c. 15.48% d. 15.96% e. 16.10%

Difficulty level: Medium EFFECTIVE ANNUAL RATE d 92. Mr. Miser loans money at an annual rate of 21 percent. Interest is compounded daily. What is the actual rate Mr. Miser is charging on his loans? a. 22.97% b. 23.08% c. 23.21% d. 23.36% e. 23.43% Difficulty level: Medium EFFECTIVE ANNUAL RATE e 93. You are considering two loans. The terms of the two loans are equivalent with the exception of the interest rates. Loan A offers a rate of 7.45% compounded daily. Loan B offers a rate of 7.5% compounded semi-annually. Loan _____ is the better offer because______: a. A; you will pay less interest. b. A; the annual percentage rate is 7.45%. c. B; the annual percentage rate is 7.64%. d. B; the interest is compounded less frequently. e. B; the effective annual rate is 7.64%. Difficulty level: Medium EFFECTIVE ANNUAL RATE b 94. You have $2,500 that you want to use to open a savings account. You have found five different accounts that are acceptable to you. All you have to do now is determine which account you want to use such that you can earn the highest rate of interest possible. Which account should you use based upon the annual percentage rates quoted by each bank? Account A: 3.75%, compounded annually Account B: 3.70%, compounded monthly Account C: 3.70%, compounded semi-annually Account D: 3.65%, compounded continuously Account E: 3.66%, compounded quarterly a. Account A b. Account B c. Account C d. Account D e. Account E Difficulty level: Medium CONTINUOUS COMPOUNDING d 95. What is the effective annual rate of 14.9% compounded continuously? a. 15.96% b. 16.01% c. 16.05% d. 16.07% e. 16.17%

Difficulty level: Medium CONTINUOUS COMPOUNDING c 96. What is the effective annual rate of 9.75% compounded continuously? a. 9.99% b. 10.11% c. 10.24% d. 10.28% e. 10.30% Difficulty level: Medium CONTINUOUS COMPOUNDING d 97. The Smart Bank wants to appear competitive based on quoted loan rates and thus must offer a 7.9% annual percentage rate. What is the maximum rate the bank can actually earn based on the quoted rate? a. 7.90% b. 8.18% c. 8.20% d. 8.22% e. 8.39% Difficulty level: Medium CONTINUOUS COMPOUNDING VERSUS ANNUAL COMPOUNDING c 98. You are going to loan your friend $1,000 for one year at a 5% rate of interest. How much additional interest can you earn if you compound the rate continuously rather than annually? a. $.97 b. $1.09 c. $1.27 d. $1.36 e. $1.49 Difficulty level: Medium FUTURE VALUE c 99. Today you earn a salary of $28,500. What will be your annual salary fifteen years from now if you earn annual raises of 3.5 percent? a. $47,035.35 b. $47,522.89 c. $47,747.44 d. $48,091.91 e. $48,201.60 Difficulty level: Medium FUTURE VALUE e 100. You hope to buy your dream house six years from now. Today your dream house costs $189,900. You expect housing prices to rise by an average of 4.5% per year over the next six years. How much will your dream house cost by the time you are ready to

a. b. c. d. e.

buy it? $240,284.08 $246,019.67 $246,396.67 $246,831.94 $247,299.20

Difficulty level: Medium PRESENT VALUE b 101. Your grandmother invested one lump sum 17 years ago at 4.25% interest. Today, she gave you the proceeds of that investment which totaled $5,539.92. How much did your grandmother originally invest? a. $2,700.00 b. $2,730.30 c. $2,750.00 d. $2,768.40 e. $2,774.90 Difficulty level: Medium PRESENT VALUE c 102. You would like to give your daughter $40,000 towards her college education thirteen years from now. How much money must you set aside today for this purpose if you can earn 6.3% on your funds? a. $17,750.00 b. $17,989.28 c. $18,077.05 d. $18,213.69 e. $18,395.00 Difficulty level: Medium INTEREST RATE FOR A SINGLE PERIOD e 103. One year ago, you invested $3,000. Today it is worth $3,142.50. What rate of interest did you earn? a. 4.63% b. 4.68% c. 4.70% d. 4.73% e. 4.75% Difficulty level: Easy INTEREST RATE FOR MULTIPLE PERIODS d 104. Forty years ago, your father invested $2,500. Today that investment is worth $107,921. What is the average rate of return your father earned on his investment? a. 8.50% b. 9.33% c. 9.50% d. 9.87%

e.

9.99%

Difficulty level: Easy PRESENT VALUE AND RATE CHANGES a 105. You want to have $10,000 saved ten years from now. How much less do you have to deposit today to reach this goal if you can earn 6% rather than 5% on your savings? a. $555.18 b. $609.81 c. $615.48 d. $928.73 e. $1,046.22 Difficulty level: Medium FUTURE VALUE – SINGLE SUM c 106.You have deposited $1,500 in an account that promises to pay 8% compounded quarterly for the next five years. How much will you have in the account at the end? a. $1,598.33 b. $2,203.99 c. $2,228.92 d. $6,991.44 e. None of the above. Difficulty level: Easy FUTURE VALUE – SINGLE SUM d 107.What is the future value of investing $9,000 for 7 years at a continuously compounded rate of 11%? a. $15,930.00 b. $18,685.44 c. $19,369.83 d. $19,437.90 e. None of the above. Difficulty level: Easy FUTURE VALUE – CONTINUOUS COMPOUNDING b 108.What is the future value of investing $3,000 for 3/4 year at a continuously compounded rate of 12%? a. $3,163 b. $3,263 c. $3,283 d. $3,287 e. $3,317 Difficulty level: Challenge EAR & FUTURE VALUE d 109.Which of the following amounts is closest to the end value of investing $5,000 for 14 months at

a. b. c. d. e.

a stated annual interest rate of 6% compounded monthly? $5,293 $5,345 $5,352 $5,362 $6,183

Difficulty level: Medium EAR & FUTURE VALUE c 110.Which of the following amounts is closest to the end value of investing $10,000 for 18 months at a stated annual interest rate of 12% compounded quarterly? a. $11,800 b. $11,852 c. $11,940 d. $11,961 e. None of the above is within $100 of the correct answer. Difficulty level: Medium FUTURE VALUE e 111.Which of the following amounts is closest to the end value of investing $7,500 for 2.5 years at an effective annual interest rate of 12.36%. Interest is compounded semiannually. a. $ 7,531 b. $ 8,427 c. $ 9,469 d. $ 9,818 e. $10,037 Difficulty level: Medium EAR d 112.If the stated rate of interest is 12% and it is compounded monthly, what is the effective annual interest rate? a. 12.00% b. 12.25% c. 12.46% d. 12.68% e. 12.92% Difficulty level: Medium PRESENT VALUE – SINGLE SUM d 113.What is the present value of a payment of $21,000 three years from now if the effective annual interest rate is 4%? a. $17,951 b. $18,480 c. $18,658 d. $18,669 e. $19,218

Difficulty level: Easy PRESENT VALUE – FUTURE SUM a 114.Thorton will receive an inheritance of $500,000 three years from now. Thorton's discount rate is 10% interest rate compounded semiannually. Which of the following values is closest to the amount that Thorton should accept today for the right to his inheritance? a. $ 373,108. b. $ 375,657. c. $ 665,500. d. $ 670,048. e. None of the above is within $10 of the correct answer. Difficulty level: Medium PRESENT VALUE – FUTURE SUM d 115.A mortgage instrument pays $1.5 million at the end of each of the next two years. An investor has an alternative investment with the same amount of risk that will pay interest at 8% compounded semiannually. Which of the following amounts is closest to what the investor should pay for the mortgage instrument? a. $1,386,834 b. $1,388,889 c. $2,674,897 d. $2,669,041 e. $3,854,512 Difficulty level: Easy PERPETUITY d 116.You are to receive $75 per year indefinitely. The market rate of interest for these types of payments is 8%. The price you would pay for this stream is: a. $ 9.375 b. $ 81.00 c. $ 93.75. d. $937.50. e. None of the above. Difficulty level: Easy GROWING PERPETUITY c 117.Aunt Clarisse has promised to leave you an annuity that will pay $60 next year and grow at an annual rate of 4%. The payments are expected to go on indefinitely and the interest rate is 9%. What is the value of the growing perpetuity? a. $ 667 b. $ 693 c. $1,200 d. $1,248 e. None of the above. Difficulty level: Medium PRESENT VALUE - ANNUITY

c

118.A court settlement awarded an accident victim four payments of $50,000 to be paid at the end of each of the next four years. Using a discount rate of 4%, calculate the present value of the annuity. a. $173,255 b. $178,495 c. $181,495 d. $184,095 e. $200,000 Difficulty level: Medium

PRESENT VALUE - ANNUITY d 119.What is the present value of 10 annual payments of $500 at a discount rate of 12%? a. $1,332 b. $1,761 c. $1,840 d. $2,825 e. $3,040 Difficulty level: Medium PRESENT VALUE - ANNUITY b 120.An S&L provides a loan with 15 yearly repayments of $8,000 with the first payment beginning immediately. Which of the following amounts comes closest to the present value of the loan if the interest rate is 7%? a. $ 72,863 b. $ 77,964 c. $115,648 d. $120,000 e. Not enough information is given to determine the answer. Difficulty level: Medium FUTURE VALUE – SINGLE SUM e 121.The great, great grandparents of one of your classmates sold their factory to the government 104 years ago for $150,000. If these proceeds had been invested at 6%, how much would this legacy be worth today? Assume annual compounding. a. $ 936,000.00 b. $ 1,086,000.00 c. $60,467,131.54 d. $60,617,131.54 e. $64,254,159.44 Difficulty level: Medium IV. ESSAYS FUTURE VALUE 122. Mr. Miser, who is 35 years old, has just inherited $11,000 and decides to use the windfall towards his retirement. He places the money in a bank which promises a return of 6% per year until his

planned retirement in 30 years. If his funds earn 6% interest compounded annually, how much will he have at retirement? Repeat the analysis for both semi-annual and continuous compounding. $11,000(1.06)30 = $63,178.40 $11,000(1.03)60 = $64,867.63 $11,000 . e(.06)(30) = $66,546.12 PRESENT VALUE OF A PERPETUITY 123. Your aunt, in her will, left you the sum of $5,000 a year forever with payments starting immediately. However, the news is better. She has specified that the amount should grow at 5% per year to maintain purchasing power. Given an interest rate of 12%, what is the PV of the inheritance? $5,000 + $5,000(1.05)/(.12-.05) = $80,000 PRESENT VALUE OF AN ANNUITY 124. If you invest $100,000 today at 12% per year over the next 15 years, what is the most you can spend in equal amounts out of the fund each year over that time. $100,000 = Annuity Payment * Ann.Factor(.12,15)6.8109 = $14,682.42 or PV=$-100,000 I/YR=12 N=15 PMT=?=$14,682.42 EFFECTIVE ANNUAL RATE VERSUS ANNUAL PERCENTAGE RATE 125. Using the example of a savings account, explain the difference between the effective annual rate and the annual percentage rate. The effective annual rate is what you actually earn, the annual percentage rate is a quoted rate. If interest is compounded during the year, the ending balance of a savings account cannot be calculated directly using the annual percentage rate. Also, in the case of the savings account, the effective annual rate will always be higher than the annual percentage rate as long as the account is compounded more than once a year and the interest rate is greater than zero. PRESENT VALUE OF AN ANNUITY 126. There are three factors that affect the present value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the present value of the annuity. The factors are the interest rate, payment amount, and number of payments. An increase in the payment and number of payments will increase the present value, while an increase in the interest rate will decrease the present value. FUTURE VALUE OF AN ANNUITY 127. There are three factors that affect the future value of an annuity. Explain what these three factors are and discuss how an increase in each will impact the future value of the annuity. The factors are the interest rate, payment amount, and number of payments. An increase in any of these three will increase the future value of the annuity. PERPETUITY PAYMENTS 128. A friend who owns a perpetuity that promises to pay $1,000 at the end of each year, forever, comes to you and offers to sell you all of the payments to be received after the 25th year for a price of $1,000. At an interest rate of 10 percent, should you pay the $1,000 today to receive payment numbers 26 and onwards? What does this suggest to you about the value of perpetual payments?

The present value of the perpetuity is $10,000, and the present value of the first 25 payments is $9,077.04, thus you should be willing to pay only $922.96 for payments 26 and onwards. This suggests that the value of a perpetuity is derived primarily from the payments received early in its life, and the payments to be received later have little worth today.

SOLUTIONS TO TEST BANK PROBLEMS Chapter 4 21. Enter 22. 23.

24.

1 N

5325 PV PMT FV Solve for -5,000 Simple Interest = $10,000 (.08)(3) = $2,400; Compound Interest = $10,000((1.075)3 1) = $2,422.97; Difference = $2,422.97 - $2,400 = $22.97 $7,000 (1.06)4 = $8,837.34

  .06 4×12   1 − 1 /(1 + )    12  APV = $100 ×    = $100 × 42.5803 = $4,258.03 .06     12   Enter

4× 12 N

Solve for

25.

100 N

Solve for

FV

8/12 I/Y

1,200 PV PMT -87,380.23

FV

  .049 5×12   1 − 1 /(1 + )     12  APV = $160 ×   = $160 × 53.11957 = $8,499.13 .049     12   Enter

5× 12 N

Solve for

27.

6/12 100 I/Y PV PMT -4,258.03

  .08 100   1 − 1 /(1 + )     12  APV = $1,200 ×   = $1,200 × 72.816858 = $87,380.23 .08     12   Enter

26.

6.5 I/Y

4.9/12 I/Y PV 8,499.13

-160 PMT

FV

  .065 10 ×12   1 − 1 /(1 + )       12 APV = $641 ×   = $641 × 88.0685 = $56,451.91 .065     12   Enter

10× 12 N

6.5/12 I/Y PV

641 PMT

FV

Solve for

28.

-56,451.91

  .05 52 ×20   1 − 1 /(1 + )       52 APV = $25 ×   = $25 × 657.2215 = $16,430.54 .05     52   Enter

20× 52 N

5/52 I/Y

Solve for 29.

[

FV

]

1 − 1 /(1 + .12 )5  APV = $50 ,000 ×   = $50,000 × 3.6047762 = $180,238.81 .12   Enter

5 N

12 I/Y

Solve for

30.

25 PV PMT -16,430.54

50,000 PV PMT -180,238.81

FV

  .0325 5×12   1 − 1 /(1 + )     12   × 1 + .0325  Adue PV = $1,500 ×   = $1,500 × 55.30972726 ×   .0325 12       12   1.002708333 = $83,189.29 Enter Solve for

31.

5× 12 3.25/12 -1,500BGN N I/Y PV PMT FV 83,189.29

[

Enter

6 N

1.5 I/Y

Solve for 32.

]

1 − 1 /(1 + .015 ) 6  Adue PV = $20 ×   × (1 + .015 ) = $20 × 5.697187165 × 1.015 = .015   $115.65 PV 115.65

[

-20BGN PMT FV

]

1 − 1 /(1 + .07 )10  Adue PV = $12 ,000 ×   × (1 + .07 ) = $12,000 × 7.023582 × 1.07 = .07   $90,182.79 Enter Solve for

10 N

7 I/Y

12,000BGN PV PMT FV -90,182.79

33.

[

]

1 − 1 /(1 + .085 ) 25  APV = $10 ,000 ×   = $10,000 × 10.234191 = $102,341.91 .085   Enter

25 N

8.5 I/Y

Solve for

10,000 PV PMT -102,341.91

[

FV

]

1 − 1 /(1 + .085 ) 25  Adue PV = $10 ,000 ×   × (1 + .085 ) = $10,000 × 10.234191 × 1.085 = .085   $111,040.97 Enter

25 N

Solve for

8.5 I/Y

10,000BGN PV PMT FV -111,040.97

Difference = $111,040.97 - $102,341.91 = $8,699.06 = $8,699 (rounded) Note: The difference = .085 × $102,341.91 = $8,699.06 34.

[

]

1 − 1 /(1 + .075 ) 20  Adue PV = $5,000 ×   × (1 + .075 ) = $5,000 × 10.194491 .075   × 1.075 = $54,795.39 Enter

20 N

Solve for

7.5 5,000BGN I/Y PV PMT FV -54,795.39

[

]

1 − 1 /(1 + .075 ) 20  $54 ,795 .39 = C ×   ; C = $5,375 .075   Enter Solve for

20 N

7.5 54,795.39 I/Y PV PMT -5,375

FV

Because each payment is received one year later, then the cash flow has to equal: $5,000 × (1 + .075) = $5,375

35.

  08  1 − 1 /(1 + . )5×12     12   × 1 + .08  Adue PV = $100 ×    = $100 × 49.318409 × 1.006667 =   .08 12       12   $4,964.72 Enter Solve for

5× 12 8/12 100BGN N I/Y PV PMT FV -4,964.72

  .08 5×12   1 − 1 /(1 + )     12  APV = $100 ×   = $100 × 49.318409 = $4,931.84 .08     12   Enter Solve for

36.

5× 12 8/12 N I/Y PV -4,931.84

5 N

6 I/Y

PV

Solve for

AFV = $2,400 × Enter

3 N

AFV = $3,000 × Enter Solve for

25 N

1,000 PMT FV -5,637.09

(1 + .08 )3 −1 = $2,400 × 3.2464 = $7,791.36 .08 8 I/Y

PV

Solve for 38.

FV

Difference = $4,964.72 - $4,931.84= $32.88  .08   = $32 .88 Note: Difference = $4,931 .84 ×   12  (1 + .06 )5 −1 = $1,000 × 5.63709 = $5,637.09 AFV = $1,000 × .06 Enter

37.

100 PMT

2,400 PMT FV -7,791.36

(1 + .085 ) 25 −1 = $3,000 × 78.667792 = $236,003.38 .085 8.5 I/Y

PV

-3,000 PMT FV 236,003.38

39.

AFV = $3,000 × Enter

(1 + .09 ) 30 −1 = $3,000 × 136.3075385 = $408,922.62 .09

30 N

9 I/Y

PV

Solve for

Adue FV = $3,000 ×

-3,000 PMT FV 408,922.62

(1 + .09 )30 −1 × (1 + .09 ) = $3,000 × 136.3075385 × 1.09 = .09

$445,725.65 Enter

30 N

9 I/Y

PV

Solve for

-3,000BGN PMT FV 445,725.65

Difference = $445,725.65 - $408,922.62 = $36,803.03 Note: Difference = $408,922.62 × .09 = $36,803.03

40.

  .059 4×12   1 − 1 /(1 + )     12  $5,600 = C ×   ; $5,600 = C × 42.66356; C = $131.26 .059     12   Enter

4× 12 N

5.9/12 I/Y

Solve for

41.

5,600 PV

PMT -131.26

  .075 30 ×12   1 − 1 /(1 + )       12 $149 ,000 = C ×   ; $149,000 = C × 143.0176; C = $1,041.83 .075     12   Enter

30× 12 N

Solve for

7.5/12 149,000 I/Y PV PMT FV -1,041.83

Total interest = ($1,041.83 × 30 × 12) 42.

FV

$25 ,000 ,000 = C × Enter Solve for

10 N

- $149,000 = $226,058.80 = $226,059 (rounded)

(1 + .065 )10 −1 ; $25,000,000 = C × 13.49442254; C = $1,852,617.25 .065

6.5 I/Y

25,000,000 PV PMT FV -1,852,617.25

43.

  .045 27×12   1 − 1 /(1 + )       12 $464 ,900 = C ×   ; $464,900 = C × 187.3639893; C = .045     12   $2,481.27 Enter

27× 12 N

Solve for 44.

4.5/12 -464,900 I/Y PV PMT FV 2,481.27

Amount financed = $1,200,000 × (1 - .2) = $960,000

  .0775 15×12   1 − 1 /(1 + )       12 $960 ,000 = C ×   ; $960,000 = C × 106.2387933; .0775     12   C = $9,036.25 Enter Solve for

45.

15× 12 7.75/12 960,000 N I/Y PV PMT FV -9,036.25

  .065 5×12   1 − 1 /(1 + )     12  $24,500 = C ×   ; $24,500 = C × 51.10864813; C = $479.37 .065     12   Enter

5× 12 N

6.5/12 I/Y

Solve for 46.

24,500 PV PMT -479.37

FV

Amount financed = $6,890 - $500 = $6,390

  .079 36   1 − 1 /(1 + )     12  $6,390 = C ×   ; $6,390 = C × 31.95885; C = $199.94 .079     12   Enter Solve for

36 N

7.9/12 I/Y

6,390 PV

PMT -199.94

FV

47.

  055 25×4   1 − 1 /(1 + . )     4  APV = $500 ×   = $500 × 54.16588 = $27,082.94 .055     4   Enter

25× 4 N

Solve for

48.

5.5/4 500 I/Y PV PMT -27,082.94

FV

  .049 60   1 − 1 /(1 + . )     12   × 1 + .049  Adue PV = $299 ×   = $299 × 53.1195698 ×   .049 12       12   1.00408333 = $15,947.61 Enter

60 N

Solve for 49.

4.9/12 -299BGN I/Y PV PMT FV 15,947.61

[

]

1 − 1 /(1 + .0635 )50  Adue PV = $2,500 ×   × (1 + .0635 ) = $2,500 × 15.0230089 × 1.0635 .0635   = $39,942.42 Enter Solve for

50 N

6.35 2,500BGN I/Y PV PMT FV -39,942.42

50.

Ending value at 4% simple interest = $1,000 + ($1,000 × .04 × 5) = $1,200.00; Ending value at 4% compounded annually = $1,000 × (1 +.04)5 = $1,216.65; Difference = $1,216.65 - $1,200.00 = $16.65 Enter

5 N

4 I/Y

-1,000 PV

PMT

Solve for

51.

$250 ,000 = C ×

FV 1,216.65

(1 + .047 )3 −1 × (1 + .047 ) ; $250,000 = C × 3.143209 × 1.047 = .047

$75,966.14 Enter

3 N

4.7 I/Y

PV

Solve for 52.

Adue FV = ($ 140 ×1.50 ) ×

250,000 PMT FV -75,966.14

(1 + .005 )35 ×12 −1 × (1 + .005 ) = $210 × 1,424.710299 × .005

1.005 = $300,685.11 Enter

35× 12 N

Solve for 53.

.5 I/Y

-(140× 1.5)BGN PV PMT FV 300,685.11

[

]

1 − 1 /(1 + .045 )t  $100 ,000 = $6,000 ×   ; ln4 = t × ln1.045; t = 31.49 .045   Enter Solve for

N 31.49

4.5 -100,000 6,000 I/Y PV PMT

FV

54.

  .09 t   1 − 1 /(1 + )     12   $4,954 .85 = $143 .84 ×   ; ln1.3483489 = t × ln1.0075; t = 40 .09     12   Enter Solve for

55.

N 40

9/12 4,954.85 -143.84 I/Y PV PMT FV

$136 ,000 ,000 = $450 ,000 ×

(1 +

.06 t ) −1 12 ; ln 2.5111111 = t × ln1.005; t = 184.61 .06 12

Note: t is stated in the number of months. Enter Solve for

56.

6/12 N I/Y 184.61

PV

-450,000 136,000,000 PMT FV

  .0 t3   .   1 −  1/ 1(+ .1 )2   .0  3  ×  1+  $4 1,9 32= $62,5 0×  0   .0 3  1 2     .1 2   

; t × ln.00249688 = ln.532549498; t = 213.29

Note: t is expressed in months Enter N Solve for 213.29

57.

3/12 -413,926 2,500BGN I/Y PV PMT FV

  .21 t   1 − 1 /(1 + )  .21      365   $25,000 = $30 .76 ×   ; t × ln.000575177 = ln.629865908;  × 1 + .21    365    365   t = 1,095.08 days = 3 years Enter N

21/365 25,000 -30.76BGN I/Y PV PMT FV

Solve for 1095.08 1095.08 days ÷ 365 days = 3 years

58.

  r  1 − 1 /(1 + )30     12   $123,900 = $4,894 .35 ×    ; This can not be solved directly, so it’s r     12   easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that your answer is correct. Enter

30 N

Solve for

59.

/12 -123,900 4,894.35 I/Y PV PMT FV 13.59

  r  1 − 1 /(1 + ) 40 ×12     12  $100 ,000 = $384 .40 ×    ; This can not be solved directly, so it’s r     12   easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct. Enter

40× 12 N

Solve for

60.

/12 -100,000 384.40 I/Y PV PMT FV 3.45

$47 ,341 .19 = $120 ×

(1 +

r 15 ×12 ) −1 12 ; This can not be solved directly, so it’s easiest to r 12

just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct. Enter

15× 12 N

Solve for 61.

/12 I/Y 9.46

PV

-120 47,341.19 PMT FV

(1 + r ) 4 −1 ; This can not be solved directly, so it’s easiest to just r use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct. $685 ,000 = $136 ,000 ×

Enter Solve for

4 N

I/Y 15.59

PV

-136,000 685,000 PMT FV

62.

$4,482 .66 = $25 ×

(1 +

r ( 21 −10 ) ×12 ) −1 r   12 × 1 +  ; This can not be solved directly, so r  12  12

it’s easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct. Enter

(21-10)× 12 /12 -25BGN 4,482.66 N I/Y PV PMT FV Solve for 5.29 To more decimal places, the answer is 5.28632 percent.

63.

$1,000 ,000 = $25 ×

(1 +

r ( 40 −21 ) ×365 ) −1 r   365 × 1 +  ; This can not be solved directly, r 365   365

so it’s easiest to just use the calculator method to get an answer. You can then use the calculator answer as the rate in the formula just to verify that you answer is correct. Enter

(40-21)× 365 /365 -25BGN 1,000,000 N I/Y PV PMT FV Solve for 15.07 To more decimal places, the answer is 15.0697117 percent. 64.

      1 1 1 PV = $5,000 × + $9,000 × + $15,000 × 1 2  3  ; PV = (1 + .14 )   (1 + .14 )  (1 + .14 )    $21,435.74 Enter

1 N

14 I/Y PV -4,385.96

2 N

14 I/Y

3 N

14 I/Y

Solve for Enter Solve for Enter Solve for

PMT

PV PMT -6,925.21 PV PMT -10,124.57

5,000 FV 9,000 FV 15,000 FV

Present value = $4,385.96 + $6,925.21 + $10,124.57 = $21,435.74

65.

      1 1 1 PV = $1,200 × + $1,500 × + $2,000 × 1 2  3  ; PV = (1 + .04 )   (1 + .04 )  (1 + .04 )    $4,318.67 Enter

1 N

4 I/Y PV -1,153.85

2 N

4 I/Y

3 N

4 I/Y

Solve for Enter Solve for Enter Solve for

PMT

PV PMT -1,386.83 PV PMT -1,777.99

1,200 FV 1,500 FV 2,000 FV

Present value = $1,153.85 + $1,386.83 + $1,777.99 = $4,318.67 66.

      1 1 1 PV = $5,000 × + $7,500 × + $10 ,000 × 1 2  3  ; PV = (1 + .05 )   (1 + .05 )  (1 + .05 )    $20,203.00 Enter

1 N

5 I/Y PV -4,761.90

2 N

5 I/Y

3 N

5 I/Y

Solve for Enter Solve for Enter Solve for

PMT

PV PMT -6,802.72 PV PMT -8,638.38

5,000 FV 7,500 FV 10,000 FV

Present value = $4,761.90 + $6,802.72 + $8,638.38 = $20,203.00

67.

      1 1 1 PV = $2,000 + $52 ,000 × + $55,000 × + $60 ,000 × 1 2  3  (1 + .06 )   (1 + .06 )  (1 + .06 )    PV = $150,383.56 Enter

1 N

6 52,000 I/Y PV PMT FV -49,056.60

2 N

6 I/Y

3 N

6 I/Y

Solve for Enter Solve for Enter Solve for

PV PMT -48,949.80 PV PMT -50,377.16

55,000 FV 60,000 FV

Present value = $2,000 + $49,056.60 + $48,949.80 + $50,377.16 = $150,383.56 68.

      1 1 1 PV = $1,200 × + $1,800 × + $2,900 × 1 2  3  ; PV = (1 + .09 )   (1 + .09 )  (1 + .09 )    $4,855.27 Enter

1 N

9 I/Y PV -1,100.92

2 N

9 I/Y

3 N

9 I/Y

Solve for Enter Solve for Enter Solve for

PMT

PV PMT -1,515.02 PV PMT -2,239.33

1,200 FV 1,800 FV 2,900 FV

Present value = $1,100.92 + $1,515.02 + $2,239.33 = $4,855.27

69.

      1 1 1 PV = $5,600 × + $9,000 × + $2,000 × 1 2  3  ; PV = (1 + .11)   (1 + .11)  (1 + .11)    $13,812.03 Enter

1 N

11 I/Y PV -5,045.05

2 N

11 I/Y

3 N

11 I/Y

Solve for Enter Solve for Enter Solve for

PMT

PV PMT -7,304.60 PV PMT -1,462.38

5,600 FV 9,000 FV 2,000 FV

Present value = $5,045.05 + $7,304.60 + $1,462.38 = $13,812.03 70.

      1 1 1 PV = $4,200 × + $5,000 × + $5,400 × 1 2  3  ; PV = (1 + .03)   (1 + .03)  (1 + .03 )    $13,732.41 Enter

1 N

3 I/Y PV -4,077.67

2 N

3 I/Y

3 N

3 I/Y

Solve for Enter Solve for Enter Solve for

PMT

PV PMT -4,712.98 PV PMT -4,941.76

4,200 FV 5,000 FV 5,400 FV

Present value = $4,077.67 + $4,712.98 + $4,941.76 = $13,732.41 71.

  1 PV = $100 ,000 + $100 ,000 × 2  ; PV = $184,555.42 (1 + .0875 )  

Enter Solve for

2 N

8.75 100,000 I/Y PV PMT FV -84.555.42

Present value = $100,000 + $84,555.42 = $184,555.42 You should accept the $189,000 today since it is the higher net present value.

72.

    1 1 PV = $5,000 + $15 ,000 × + $25 ,000 × 1  2  (1 + .06 )   (1 + .06 )   PV = $41,400.85

Enter

1 N

6 I/Y

2 N

6 I/Y

Solve for Enter Solve for

PV PMT 14,150.94 PV 22,249.91

-15,000 FV

-25,000 PMT FV

Present value = $5,000.00 + $14,150.94 + $22,249.91 = $41,400.85 73.

[

] [

] [

]

FV = $3,600 × (1.07 )5 + $5,000 × (1.07 ) 4 + $7,500 × (1.07 )3 ; FV = $20,790.99 Enter

5 N

7 -3,600 I/Y PV

PMT

FV 5,049.19

4 N

7 I/Y

-5, 000 PV

PMT

FV 6,553.98

3 N

7 I/Y

-7,500 PV

PMT

FV 9,187.82

Solve for Enter Solve for Enter Solve for

Future value = $5,049.19 + $6,553.98 + $9,187.82 = $20,790.99 74.

[

] [

]

FV = $5,180 × (1.06 ) 2 + $9,600 × (1.06 )1 + $2,250 ; FV = $18,246.25 Enter

2 N

6 -5,180 I/Y PV

1 N

6 I/Y

Solve for Enter Solve for

-9,600 PV

PMT

FV 5,820.25

PMT FV 10,176.00

Future value = $5,820.25 + $10,176.00 + $2,250.00 = $18,246.25

75.

[

]

FV = $9,820 × (1.09 ) 2 + 0 + $4,510 ; FV = $16,177.14 Enter

2 N

9 -9,820 I/Y PV

PMT

Solve for

FV 11,667.14

Future value = $11,667.14 + $0 + $4,510.00 = $16,177.14 76.

[

] [

]

FV = $6,800 × (1.0725 ) 2 + $2,100 × (1.0725 )1 + $0 ; FV = $10,073.99 Enter

2 N

7.25 I/Y

-6,800 PV

1 N

7.25 I/Y

-2,100 PV PMT

PMT

Solve for Enter Solve for

FV 7,821.74 FV 2,252.25

Future value = $7,821.74 + $2,252.25 + $0 = $10,073.99 77.

[

] [

] [

FV = $10 ,000 × (1.11) 25 + $15 ,000 × (1.11) 24 + $25 ,000 × (1.11) 23 FV = $595,098.67 Enter

25 N

11 -10,000 I/Y PV

24 N

11 -15,000 I/Y PV

23 N

11 -25,000 I/Y PV

Solve for Enter Solve for Enter Solve for

]

PMT FV 135,854.64 PMT FV 183,587.35 PMT FV 275,656.68

Future value = $135,854.64 + $183,587.35 + $275,656.68 = $595,098.67 78.

[

] [

] [

]

$10 ,000 = C × (1.03 )3 + $2,500 × (1.03 ) 2 + $2,500 × (1.03 )1 + $2,500 ; C= $2,079.89 Enter Solve for

3 N

3 I/Y

PV 2,079.89

-2,500 10,000 PMT FV

79.

[

] [

]

FV = $100 ,000 × (1.035 ) 2 + $250 ,000 × (1.035 )1 + $250 ,000 ; C= $615,872.50 Enter

2 N

3.5 -100,000 I/Y PV PMT FV 107,122.50

1 N

3.5 -250,000 I/Y PV PMT FV 258,750.00

Solve for Enter Solve for

FV = $107,122.50 + $258,750.00 + $250,000 = $615,872.50 80.

PV =

150 ,000 ; PV = $3,529,411.77 .0425

81.

PV =

$4.50 ; PV = $50.00 .09

82.

PV =

50 ,000 ; PV = $1,818,181.82 .0275

83.

r=

$12 ,000 ; r = 3.43 percent $350 ,000

84.

r=

$10 ,000 ; r = 3.51 percent $285 ,000

85.

C = $150 ,000 ×.04 ; C = $6,000

86.

C = $50 .00 ×.084 ; C = $4.20

87.

APR = .015 × 12 = .18 = 18 percent

88.

APR = .02 × 4 = .08= 8 percent

89.

  APR  .138 = 1 +   − 1 ; APR = 13.00 percent   12 

12

Enter Solve for

13.8 NOM EFF 13.00

12 C/Y

90.

  .0764 EAR = 1 +    4 Enter Solve for

4

  − 1 ; EAR = 7.86 percent 

7.64 NOM EFF 7.86

4 C/Y

12

91.

  .149  EAR = 1 +   − 1 ; EAR = 15.96 percent   12  Enter Solve for

92.

  .21  EAR = 1 +     365  Enter Solve for

93.

14.9 NOM EFF 15.96 365

Solve for

− 1 ; APR = 23.36 percent

21 NOM EFF 23.36

  .0745 EAR A = 1 +    365 Enter

12 C/Y

  

365 C/Y

365

7.45 NOM EFF 7.73

− 1 ; APR = 7.73 percent 365 C/Y

2

  .075  EAR B = 1 +   − 1 ; APR = 7.64 percent   2  Enter Solve for

7.5 NOM EFF 7.64

2 C/Y

94.

EARA = 3.75 percent 12

  .037  EAR B = 1 +   − 1 ; EAR = 3.76 percent   12  Enter Solve for

3.7 NOM EFF 3.76

12 C/Y

2

  .037  EAR C = 1 +   − 1 ; EAR = 3.73 percent   2  Enter Solve for

3.7 NOM EFF 3.73

2 C/Y

EAR D = e.0365 − 1 = 2.71828 .0365 − 1 ; EAR = 3.72 percent Using ex on a financial calculator: EAR = 3.72 percent On the Texas Instruments BA II Plus, the input is: .0365, 2nd, ex, -1, = .0372 = 3.72 percent   .0366 EAR E = 1 +    4 Enter Solve for

4

  − 1 ; EAR = 3.71 percent 

3.66 NOM EFF 3.71

4 C/Y

Account B offers the highest effective annual rate at 3.76 percent. 95.

EAR

=e.149 −1 = 2.71828

.149

−1 ;

EAR = 16.07 percent

Using ex on a financial calculator: EAR = 16.07 percent On the Texas Instruments BA II Plus, the input is: .149, 2nd, ex, -1, = .1607 = 16.07 percent 96.

EAR

=e.0975 −1 = 2.71828

.0975

−1 ;

EAR = 10.24 percent

Using ex on a financial calculator: EAR = 10.24 percent On the Texas Instruments BA II Plus, the input is: .0975, 2nd, ex, -1, = .1024 = 10.24 percent

97.

EAR

=e.079 −1 = 2.71828

.079

−1 ;

EAR = 8.22 percent

Using ex on a financial calculator: EAR = 8.22 percent On the Texas Instruments BA II Plus, the input is: .079, 2nd, ex, -1, = .0822 = 8.22 percent 98.

EAR

=e.05 −1 = 2.71828

.05

−1 ;

EAR = 5.127 percent

Using ex on a financial calculator: EAR = 5.127 percent On the Texas Instruments BA II Plus, the input is: .05, 2nd, ex, -1, = .05127 = 5.127 percent

99.

Additional interest = $1,000 × (.05127 - .05) = $1.27 Future value = $28,500 × (1 + .035)15 = $47,747.44 Enter

15 N

3.5 -28,500 I/Y PV

Solve for 100.

Future value = $189,900 × (1 + .045)6 = $247,299.20 Enter

6 N

Solve for 101.

4.5 -189,900 I/Y PV PMT FV 247,299.20

Present value = $5,539.92 × [1 ÷ (1 + .0425)17] = $2,730.30 Enter

17 N

4.25 I/Y

Solve for 102.

13 N

Solve for

5,539.92 FV

6.3 I/Y

40,000 FV

PV PMT -18,077.05

$3,142.50 = $3,000 × (1 + r)1; r = 4.75 percent Enter

1 N

Solve for 104.

PV PMT -2,730.30

Present value = $40,000 × [1 ÷ (1 + .063)13] = $18,077.05 Enter

103.

PMT FV 47,747.44

I/Y 4.75

-3,000 PV

PMT

3,142.50 FV

$107,921 = $2,500 × (1 + r)40; r = 9.87 percent Enter Solve for

40 N

I/Y 9.87

-2,500 PV

PMT

107,921 FV

105.

Present value = $10,000 × [1 ÷ (1 + .06)10] = $5,583.95; Present value = $10,000 × [1 ÷ (1 + . 05)10] = $6,139.13; Difference = $6,139.13 - $5,583.95 = $555.18 Enter

10 N

6 I/Y

10 N

5 I/Y

Solve for Enter 106. 107. 108. 109. 110. 111. 112. 113. 114. 115. 116. 117. 118. 119. 120. 121.

PV PMT -5,583.95

10,000 FV

10,000 PMT FV

PV Solve for -6,139.13 $1,500(1.02)20 = $2,228.92 $9,000(e.11(7)) -1 = $9,000 (2.15976625) = $19,437.90 EAR=(er-1) = e.12-1 = 0.1275 (12.75%) End value after 3/4 year = $3000(1+0.1275)3/4 = $3,282.53 EAR=(1+r/m)m-1 = [1+(0.06/12)]12-1 = 0.06167781 End value = $5,000(1+0.06167781)14/12 = $5,361.61 EAR=(1+r/m)m-1 = [1+(0.12/4)]4-1 = 0.1255 End value = $10,000(1+0.1255)1.5 = $11,940.38 End value = $7,500(1+0.1236)2.5 = $10,036.69 (1 + .12/12)12 - 1 PV = FV/(1+r)n = $21,000/(1+.04)3 = $18,668.92 EAR = (1+r/m)m-1 = [1+(0.1/2)]2-1 = 0.1025 PV = $500,000/(1+0.0125)3 = $373,107.70 EAR = (1+r/m)m-1 = (1+0.08/2)2-1 = 0.0816 PV = $1.5/(1.0816)1 + $1.5/(1.0816)2 = $2,669,041 PVperpertuity = Pmt/r = $75/.08 = $937.50. PVgrowing perpetuity = Pmt/(r - g) = $60/(.09 - .04) = $1,200 PVannuity = PMT(PVIFA4%,4) = $50,000(3.6299) = $181,495 CALC: N=10 FV=0 PV=? I=12 PMT=$500; PV = $2,825 PV = Immediate Pmt + Pmt(PVIFA7%,14) = $8,000 + $8,000(8.7455) = $77,964 $150,000(1.06)104 = $64,254,159.44