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Engineering Economics

Assignment 01

Shuja Irfan 11-EE-149 Section A Submitted to: Mr. Zaheer

Date Of Submission : 20th February, 2014.

MS-324

1. Annie buys a television set from a merchant who offers P25,000 at the end of 60 days. Annie wishes to pay immediately and the merchant offers to compute the required amount on the assumption that money is worth 14% simple interest. What is the required amount? SOLUTION Assuming the interest is annual =2 14% 0.14 = = 12 12 . . = 25,000 . . . .= 1+ ∗

=

25,000 = 24,430 0.14 1 + 12 ∗ 2

The amount required by Annie is P24,430 2. What is the principal amount if the amount of interest at the end of 2 ½ year is P4,500 for a simple interest of 6% per annum? SOLUTION = 2.5 ∗ 2 = 5 0.06 = 6% = = 0.03 2 = 4,500 4,500 . .= = = 30,000 ∗ 0.03 ∗ 5 3. Eric lends P6000 at 6% simple interest for 4 years. At the end of this time he invests the entire amount (principal plus interest) at 5% compounded annually for 12 years. How much will he have at the end of the 16 year period? SOLUTION =4 = 12 = 6% = 0.06 = 5% = 0.05 . . = 6,000 . . = . . = . . ∗ 1+ ∗ = 6,000 1 + 4 ∗ 0.06 = 7,440 . . = . . 1+ = 7,440 1 + 0.05 = 13,361 So Eric will have an amount of P13,361 at the end of period of 16 years.

4. The tag price of a certain commodity is for 100 days. If paid in 31 days, there is a 3% discount. What is the simple interest paid? SOLUTION = 100 3 0.03 = %= 31 31 = . .∗ ∗

=

0.03 ∗ 100 ∗ . . 31

5. How long will it take for an investment to double its amount if invested at an interest rate of 6% compounded bi-monthly? SOLUTION = 6% = 0.06 . ! "ℎ$ = 2 ∗ . . = 2 ∗ . . = . .∗ 1 + ln 2 = ∗ ln 1 + 0.06 => ! "ℎ$ = 12 ∗ 2 = 24

= 11.89 ≈ 12

Hence it will take 24 months to double the investment.

6. On his 6th birthday a boy is left an inheritance. The inheritance will be a lump sum of P10,000 on his 21st birthday. What is the present value of the inheritance as of the boy’s 6th birthday, if the interest is 4% compounded annually?

SOLUTION = 21 − 6 = 15 = 4% = 0.04 . . = 10,000 . . = 10,000 = . .∗ 1 + 0.04

,

=> 5,552.64 ≈ 5,553

Which means that the boy was left an inheritance of P5,553 on his 6th birthday.

7. Alexander owes 25,000.00 due in 1 year and 75,000.00 due in 4 years. He agrees to pay 50,000.00 today and the balance in 2 years. How much must he pay at the end of two years if money is worth 5% compounded semi-annually? SOLUTION = 5% ∗ 2 = 0.05 ∗ 2 = 0.1 -./. 01 = - = 25,000 + 75,000 − 50,000 = 50,000 2! 3 " 4.5.6/1 . "17 4 51.7$ = 50,000 ∗ 1 + 0.1 = 60,500 8. If 5000,000.00 is deposited at a rate of 11.25% compounded monthly, determine the compounded interest after 7 years and 9 months. SOLUTION = 7 ∗ 12 + 9 = 93 = 11.25 = 0.1125 . . = 50,00,000 . . = . .∗ 1 + = 50,00,000 ∗ 1 + 0.1125 = . . − . . = 10,11,27,59,63,000

89

= 10,11,28,09,63,000

9. A sum of 1000.00 is invested now and left for another eight years, at which time the principal is withdrawn. The interest has accrued is left for another eight years. If the effective annual interest rate is 5%, what will be the withdrawal amount at the end of the 16th year? SOLUTION Considering the interest is compounded annually, = = =8 = 5% = 0.05 . . = 1,000 . . = . . 1+ = 1,000 1 + 0.05 : = 1,478 . . = . . − 1,000 = 478 . . = . . ∗ 1+ = 478 1 + 0.05 : = 706 Hence the withdrawal amount at the end of 16 years is 706

10. 15,000.00 were deposited in a bank account 20 years ago. Today it is worth P 3,0000.00. Interest is paid semi-annually. Determine the nominal rate of interest paid on this account.

SOLUTION = 2 ∗ 20 = 40 . . = 15,000 . . = 30,000 . . = . .∗ 1 + = 1.75 $1! − .

=> 30,000 = 15,000 1 + 3.//5

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Assignment 01

Shuja Irfan 11-EE-149 Section A Submitted to: Mr. Zaheer

Date Of Submission : 20th February, 2014.

MS-324

1. Annie buys a television set from a merchant who offers P25,000 at the end of 60 days. Annie wishes to pay immediately and the merchant offers to compute the required amount on the assumption that money is worth 14% simple interest. What is the required amount? SOLUTION Assuming the interest is annual =2 14% 0.14 = = 12 12 . . = 25,000 . . . .= 1+ ∗

=

25,000 = 24,430 0.14 1 + 12 ∗ 2

The amount required by Annie is P24,430 2. What is the principal amount if the amount of interest at the end of 2 ½ year is P4,500 for a simple interest of 6% per annum? SOLUTION = 2.5 ∗ 2 = 5 0.06 = 6% = = 0.03 2 = 4,500 4,500 . .= = = 30,000 ∗ 0.03 ∗ 5 3. Eric lends P6000 at 6% simple interest for 4 years. At the end of this time he invests the entire amount (principal plus interest) at 5% compounded annually for 12 years. How much will he have at the end of the 16 year period? SOLUTION =4 = 12 = 6% = 0.06 = 5% = 0.05 . . = 6,000 . . = . . = . . ∗ 1+ ∗ = 6,000 1 + 4 ∗ 0.06 = 7,440 . . = . . 1+ = 7,440 1 + 0.05 = 13,361 So Eric will have an amount of P13,361 at the end of period of 16 years.

4. The tag price of a certain commodity is for 100 days. If paid in 31 days, there is a 3% discount. What is the simple interest paid? SOLUTION = 100 3 0.03 = %= 31 31 = . .∗ ∗

=

0.03 ∗ 100 ∗ . . 31

5. How long will it take for an investment to double its amount if invested at an interest rate of 6% compounded bi-monthly? SOLUTION = 6% = 0.06 . ! "ℎ$ = 2 ∗ . . = 2 ∗ . . = . .∗ 1 + ln 2 = ∗ ln 1 + 0.06 => ! "ℎ$ = 12 ∗ 2 = 24

= 11.89 ≈ 12

Hence it will take 24 months to double the investment.

6. On his 6th birthday a boy is left an inheritance. The inheritance will be a lump sum of P10,000 on his 21st birthday. What is the present value of the inheritance as of the boy’s 6th birthday, if the interest is 4% compounded annually?

SOLUTION = 21 − 6 = 15 = 4% = 0.04 . . = 10,000 . . = 10,000 = . .∗ 1 + 0.04

,

=> 5,552.64 ≈ 5,553

Which means that the boy was left an inheritance of P5,553 on his 6th birthday.

7. Alexander owes 25,000.00 due in 1 year and 75,000.00 due in 4 years. He agrees to pay 50,000.00 today and the balance in 2 years. How much must he pay at the end of two years if money is worth 5% compounded semi-annually? SOLUTION = 5% ∗ 2 = 0.05 ∗ 2 = 0.1 -./. 01 = - = 25,000 + 75,000 − 50,000 = 50,000 2! 3 " 4.5.6/1 . "17 4 51.7$ = 50,000 ∗ 1 + 0.1 = 60,500 8. If 5000,000.00 is deposited at a rate of 11.25% compounded monthly, determine the compounded interest after 7 years and 9 months. SOLUTION = 7 ∗ 12 + 9 = 93 = 11.25 = 0.1125 . . = 50,00,000 . . = . .∗ 1 + = 50,00,000 ∗ 1 + 0.1125 = . . − . . = 10,11,27,59,63,000

89

= 10,11,28,09,63,000

9. A sum of 1000.00 is invested now and left for another eight years, at which time the principal is withdrawn. The interest has accrued is left for another eight years. If the effective annual interest rate is 5%, what will be the withdrawal amount at the end of the 16th year? SOLUTION Considering the interest is compounded annually, = = =8 = 5% = 0.05 . . = 1,000 . . = . . 1+ = 1,000 1 + 0.05 : = 1,478 . . = . . − 1,000 = 478 . . = . . ∗ 1+ = 478 1 + 0.05 : = 706 Hence the withdrawal amount at the end of 16 years is 706

10. 15,000.00 were deposited in a bank account 20 years ago. Today it is worth P 3,0000.00. Interest is paid semi-annually. Determine the nominal rate of interest paid on this account.

SOLUTION = 2 ∗ 20 = 40 . . = 15,000 . . = 30,000 . . = . .∗ 1 + = 1.75 $1! − .

=> 30,000 = 15,000 1 + 3.//5

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