Engineering Economy Sample Problem Solutions

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

ENGINEERING ECONOMY – SAMPLE PROBLEM SOLUTIONS SIMPLE INTEREST: 1. P8, 000 is borrowed for 75 days at 12% per annum simple interest. How much will be due at the end of 75days?

2. It is the practice of almost all banks in the Philippines that when they grant a loan, the interest for one year is automatically deducted from the principal amount upon the release of the money to a borrower. Let us assume that you applied for a loan with the bank and the P100,000 was approved at an interest rate of 12% of which P12,000 was deducted and you were given a check of P88,000. Since you have to pay the amount of P100,000 one year after, what then will be the effective interest rate?

COMPOUND INTEREST 1. A man invests $10,000 in an account that pays 8.5% interest per year, compounded quarterly. What is the amount of money that he will have after 3 years?

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

2. A sum of $5000 is invested at an interest rate of 9% per year. Find the time required for the money to double if the interest is compounded semi-annually.

3. A man invests $10,000 in an account that pays 8.5% interest per year. What is the amount of money that he will have after 3 years if it is compounded continuously?

4. Find the effective rate of interest for an investment that earns 5 ½ % per year (a) compounded quarterly, (b) compounded continuously.

5. If money is invested at 8% compounded semi-annually, find equivalent nominal rate compounded quarterly.

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

ORDINARY ANNUITY

1. A man deposits P500 every month in an investment which earns 7% compounded monthly. a. What is the accumulated amount in 5 years? b. If in two years, instead of depositing P500 per month, you deposit P1000 per month, what is the sum of your money in 5years?

2. A man paid 10% down payment of P2, 000,000 for a house and lot. If the rate of interest is 15% compounded monthly a. What is the monthly installment if he agrees to pay the balance on monthly installment for 5 years? b. He fails to pay the monthly installment for the first three years and decides to pay his present and future obligations at the end of the 3rd year. What single amount must he pay to cancel his entire obligation at the end of the 3rd year?

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

DEFFERED ANNUITY 1. A man paid 10% down payment of P2, 000,000 for a house and lot. If the rate of interest is 15% compounded monthly. What would be his monthly installment if he agrees o pay his balance on a monthly installment starting at the end of the 2nd year until the end of the 5th year?

2. A person buys a piece of lot for P100,000 down payment and 10 deferred semiannual payments of P8,000 each, starting three years from now. What is the present value of the investment if the rate of interest is 12% compounded semiannually?

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

ANNUITY DUE 1. A contractor wish to buy a machine worth P1, 000,000 after one year. If the bank gives an investment of 1.5% monthly a. What single amount must be deposited in order to have the desired amount after one year? b. What amount must be deposited at the bank at every beginning of the month in order to have P1, 000,000 after one year?

CAPITALIZED COST 1. A machine cost P300,000 new, and must be replaced at the end of each 15 years. If the annual maintenance required is P5, 000, find the capitalized cost, if the money is worth 5% and the final salvage value is P50,000.

2. A certain equipment cost P150,000, last for 6 years, and has a salvage value of P30,000. How much could the investor afford to pay for another machine for the same purpose, whose life is 10 years and salvage value is P40, 000, if the money is worth 5%?

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

STRAIGHT LINE DEPRECIATION 1. The first value of a machine is P1,800,000 with a salvage value of P300,000 a the end of is life of 5 years. Determine the book Value after 3 years using Straight Line method.

SUM OF THE YEARS DIGIT METHOD (SYOD) 1. The first value of a machine is P1,800,000 with a salvage value of P300,000 a the end of is life of 5 years. Determine the book Value after 3 years using sum of the years digit method

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

DECLINING BALANCE METHOD 1. The first value of a machine is P1,800,000 with a salvage value of P300,000 a the end of is life of 5 years. Determine the book Value after 3 years using declining balance method.

DOUBLE DECLINING BALANCE METHOD 1. The first value of a machine is P1,800,000 with a salvage value of P300,000 a the end of is life of 5 years. Determine the book Value after 3 years using double declining balance method

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

SINGKING FUND METHOD 1. The first value of a machine is P1,800,000 with a salvage value of P300,000 a the end of is life of 5 years. Determine the book Value after 3 years using sinking fund method if the money worth 6% per annum.

CAPITAL RECOVERY – DEPLETION 1. A mine cost P21 million, and will last for 20years. Its Plant has a salvage value of P1 million at the end of the time. The mine will yield an equal dividend at the end of each year, what is the annual dividend, if it is sufficient to pay interest annually a the rate of 6% on the original investment and accumulate a replacement fund invested at 4%?

PHILIPPINE INSTITUTE OF CIVIL ENGINEERS, INC. International Charter No. I-07

COST-BENEFIT RATIO 1. A project cost P100,000. The benefits at the end of each year for a period of 5 years is P40,000. Assuming money is worth 8% with no salvage value. a. Find the present worth of benefits b. What is the benefit-cost ratio. c. Is it profitable or not?

BREAK-EVEN ANALYSIS 1. A plywood manufacturer produces a piece of plywood at a labor cost of P0.50 and material at P3.00. The fixed charges on business are P50, 000 a month and a variable cost is P0.50 per piece. If one plywood sells for P6.00 each, how many pieces must be produced each month for the manufacturer to break-even?