Economics Sample Problem

ENGINEERING ECONOMY – ANNUITY 1. Mr. Richardson borrowed ₱16,000 two years ago. The repayment terms of the loan are 12% interest for 10 years and uniform annual payments. He just made his second payment. How much principal, most nearly, does he still owe? Ans. ₱14,069 2. A company issued 54 bonds of ₱1,500 face value each, redeemable at par at the end of 15 years. To accumulate the funds required for redemption, the firm established a sinking fund consisting of annual deposits, the interest rate of the fund being 5%. What was the principal in the fund at the end of the 10 th year? Ans. ₱47,213.95 3. An engineer deposits ₱10,000 in a savings account on the day her child is born. She deposits an additional $1000 on every birthday after that. The account has a 5% nominal interest rate, compounded continuously. How much money will be in the account the day after the child’s 21st birthday? Ans. ₱64,808.45 4. A machine costs ₱20,000 today and has an estimated scrap cash value of ₱2,000 after eight years. Inflation is 8%. How much money needs to be set aside each year to replace the machine with an identical model eight years from now? Ans. R=₱3292.27 5. Calculate the rate of return for an investment with the following characteristics. Initial Cost ₱20,000 Project life 10 years Salvage value ₱5,000 Annual receipts ₱7,500 Annual disbursements ₱3,000 Ans. 19.56% 6. A man borrowed ₱100,000 at 11% compounded annually for 12 years. And promised to pay the amount starting 5 years from now. Find the annual payment. Ans. ₱23,382.93 7. A student needs $4000/yr for 4 years to attend college. Her father invested $6000 in an 8% account for her education when she was born. If the student withdraws $4,000 at the end of her 17th, 18th, 19th and 20th years, how much money will be left in the account at the end of her 21st year? Ans. $10,736.69

8. What annuity over a 10 year period at 8% interest is most nearly equivalent to a present worth of $7000? a. ₱104.32* b. ₱114.32 c. ₱124.32 d. ₱134.32 9. ₱10,000 is invested at the beginning of a year in a 15% security and held for 5 yr. During that time, the average annual inflation is 8%. Approximately how much, in terms of year zero dollars will be in the account at maturity? a. ₱13,689* b. ₱13,789 c. ₱13,889 d. ₱13,989

10. An engineering graduate plans to buy a home. She has been advised that her monthly house and property tax payment should not exceed 35% of her disposable monthly income. After researching the market, she determines she can obtain a 30 year home load for 6.95% annual interest per year, compounded monthly. Her monthly property tax payment will be approximately $150. What is the maximum amount she can pay for a house if her disposable monthly income is $2500? a. $109,521* b. $119,521 c. $129,521 d. $139,521

11. A machine has a maintenance of ₱40,000 in 2 nd year, ₱60,000 in the 6th year and ₱80,000 in the 8th year. If interest is 10% compounded annually, find the equivalent equal annual maintenance of the machine for a period of 10 years. a. ₱14,973.45 b. ₱12,084.02 c. ₱16,965.70* d. ₱18,028.89 12. A piece of machinery has a first cost of $35,000 with monthly operating cost of $12,000. If the company wants to recover its investment in five years at an interest rate of 1% per month, the monthly income must be closed to: a. $5,498 b. $6,386 c. $8,295 d. $12,779* 13. A man applied for a loan with 12% compounded semi-annually. He promised to pay an amount ₱20,000 semi-annually starting 4 years from now for 10 years. Find the amount stated in the loan. a. ₱122,563 b. ₱132,563 c. ₱142, 563 d. 152, 563* 14. A series of bank deposits of ₱2000 quarterly from 5th year to 11th year. If interest rate is 16% compounded quarterly, find the total amount at the 15 th year. a. ₱177,177 b. ₱146,401.97* c. ₱197,177 d. ₱207,177 15. A series of deposits of ₱1000 bi-monthly starting today up to the 10th year. Find the amount at the 12th year if interest rate is 8% compounded bi-monthly. a. ₱98,106 b. ₱107,976.16* c. ₱138,106 d. ₱178,106 ENGINEERING ECONOMY – SIMPLE & COMPOUND INTEREST 16. Kathy buys a television set from a merchant who asks ₱1,250.00 at the end of 60 days (cash in 60 days). Kathy wishes to pay immediately and the merchant offers to compute the cash price on the assumption that money is worth 8% simple interest. What is the cash price today? a. ₱1233.55* b. ₱1324.45 c. ₱2195.60 d. ₱2135.50 17. How many years will ₱100,000 earned a compound interest of ₱50,000 if the interest rate is 9% compounded quarterly? a. 3.25 b. 4.55* c. 5.86 d. 2.11 18. Fifteen years ago ₱1,000.00 was deposited in a bank account, and today it is worth ₱2,370.00. The bank pays interest semi-annually. What was the interest rate paid? a. 4.9% b. 5.8%* c. 5.0% d. 3.8% 19. ₱200,000 was deposited on Jan. 1, 1988 at an interest rate of 24% compounded semiannually. How much would the sum be on Jan. 1, 1993? a. ₱421,170 b. ₱521,170 c. ₱401,170 d. ₱621,170* 20. Mr. W borrowed ₱2,000.00 from Mr. Y on June 1, 1928 and ₱500 on June 1, 1930, agreeing that money is worth 5% compounded annually. Mr. W paid ₱500 on June 1, 1931, ₱400 on June 1, 1932 and ₱700 on June 1, 1933. What additional sum should Mr. W pay on June 1, 1936 to discharge all remaining liability? a. ₱1780.29 b. ₱1690.28* c. ₱1754.53 d. ₱1896.77 21. Consider a deposit of ₱600, to be paid back in 1 yr by ₱700. What are the conditions on the rate of interest, I, in %/yr compounded annually, such that the net present worth of the investment is positive? Assume i ≥ 0%. a. 12.5% ≤ i ≤ 14.3% c. 0% ≤ i < 16.7%* b. 0% ≤ i < 14.3% d. 16.7% ≤ i < 100%

ENGINEERING ECONOMY – DEPRECIATION 22. A member of congress wants to know the capitalized cost of maintaining a proposed national park. The annual maintenance cost is expected to be ₱20,000. At an interest rate of 6% per year, the capitalized cost of the maintenance would be closest to: a. ₱1,500 b. ₱25,000 c. ₱333,333* d. ₱416,667 23. A machine has a first cost of ₱100,000 and salvage value of ₱10,000 after 10 years. The annual maintenance of the machine is ₱4,000. If interest rate is 10%. Find the annual cost of the machine. a. ₱17,009.34 b. ₱19,647.08* c. ₱21,083.56 d. ₱32,074.56 24. A certain product has the following corresponding cost: 250 units for ₱4,000 and 400 units for ₱5,000. Find the increment cost. a. 3.46 b. 4.05 c.5.31 d. 6.67 25. A machine has an initial cost of ₱50,000 and a salvage value of ₱10,000 after 10 years. What is the book value after seven years using straight-line depreciation? a. ₱22,000* b. ₱23,000 c. ₱24,000 d. ₱25,000 26. A machine that costs ₱20,000 has a 10 year life and a ₱2,000 salvage value. If straight line depreciation is used, what is the book value of the machine at the end of the fourth year? a. ₱12,200 b. ₱12,400 c. ₱12,600 d. ₱12,800* 27. An item purchased for ₱150,000. Annual cost is ₱10,000. Using 10%, what is the capitalized cost of perpetual service? a. ₱352,000 b. ₱250,000* c. ₱532,000 d. ₱325,000 28. An asset is purchased for P10,000. Its estimated life is 10 years after which it will be sold for P1,000. Find the book value during the first year if sum-of-the-years digit (SOYD) depreciation is used. a. ₱8,363.64* b. ₱6,500.00 c. ₱7,545.00 d. ₱6,000.00 29. A machine has a first cost of ₱60,000 and has an expected salvage value after 10 years of ₱6,000. Find the book value after 5 years using declining balance method. a. ₱10,028.34 b. ₱15,071.32* c. ₱20,083.45 d. ₱25,083.45 30. A machine has a first cost of ₱50,000 with interest rate of 10% annually. Expected salvage value after 10 years is ₱5,000. Find the book value after 5 years using sinking fund method. a. ₱12,039 b. ₱22,084 c. ₱42,084 d. ₱32,762* 31. What is the book value of equipment purchased 3 yr ago for ₱15,000 if it is depreciated using the sum of the year’s digits (SOYD) method? The expected life is 5 years. a. ₱3,000* b. ₱4000 c. ₱6,000 c. ₱9000 32. Approximately how many years will it take to double an investment at a 6% effective annual rate? a. 10 yrs. b. 12 yrs.* c. 15 yrs. d. 17 yrs. 33. An individual contributes $200 per month to a 401(k) retirement account. The account earns interest at a nominal annual interest rate of 8%, with interest being credited monthly. What is the value of the account after 35 years? a. $368,000 b. $414,000 c. $447,000 d. $459,000*

34. A graduating high school student decides to take a year off and work to save money for college. The student plans to invest all money earned in a savings account earning 6% interest, compounded quarterly. The student hopes to have $5000 by the time school starts in 12 months. How much money will the student have to save each month? a. $396/month b. $405/month c. $405/month* d. $411/month 35. A gold mine is projected to produce $20,000 during its first year of operation, $19,000 the second year, $18,000 the third year, and so on. If the mine is expected to produce for a total of 10 years, and the effective annual interest rate is 6%, what is its present worth? a. $118,000* b. $125,000 c. $150,000 d. $177,000 36. $5,000 is put into an empty savings account with a nominal interest rate of 5%. No other contributions are made to the account. With monthly compounding, how much interest will have been earned after five years? a. $1250 b. $1380 c. $1410 d. $1420* 37. An engineer deposits $10,000 in a savings account on the day her child is born. She deposits an additional $1000 on every birthday after that. The account has a 5% nominal interest rate, compounded continuously. How much money will be in the account the day after the child’s 21st birthday? a. $36,200 b. $41,300 c. $64,800* d. $84,300 38. A machine costs $10,000 and can be depreciated over a period of four years, after which its salvage value will be $2000. What is the straight-line depreciation in year 3? a. $2000* b. $2500 c. $4000 d. $6000 39. A groundwater treatment system is needed to remediate a solvent-contaminated aquifer. The system costs $2,500,000. It is expected to operate a total of 130,000 hours over a period of 10 years and then have a $250,000 salvage value. During its first year in service, it is operated for 6500 hours. What is its depreciation in the first year using the MACRS method? a. $113,000 b. $125,000 c. $225,000 d. $250,000* 40. A machine initially costing $25,000 will have a salvage value of $6000 after five years. Using MACRS depreciation, what will its book value be after the third year? a. $5470 b. $7200* c. $10,000 d. $13,000

41. Given the following cash flow diagram and an *% effective annual interest rate, what is the equivalent annual expense over the five year period?

a. $209 b. $218 c. $251* d. $268 e. 42. The construction of a volleyball court for the employees of a highly successful mid-sized publishing company in California is expected to cost $1200 and have an annual maintenance costs of $300. At an effective annual interest rate of 5%, what is the project’s capitalized cost? a. $1500 b. $2700 c. $7200* d. $18,000

43. A warehouse building was purchased 10 years ago for $250,000. Since then, the effective annual interest rate has been 8%, inflation has been steady at 2.5%, and the building has had no deterioration or decrease in utility. What should the warehouse sell for today? a. $427,000 b. $540,000 c. $678,000 d. $691,000*

44. A delivery company is expanding its fleet by five vans t a total cost of $75,000. Operating and maintenance costs for the new vehicles are projected to be $20,000/year for the next eight years. After eight years, the vans will be sold for a total of $10,000. Annual revenues are expected to increase by $40,000 with the expanded fleet. What is the company’s rate of return on the purchase? a. 19.7% b. 20.8% c. 21.7%* d. 23.2%

45. A company is considering replacing its air conditioner. Management has narrowed the choices to two alternatives that offer comparable performance and considerable savings over their present system. The effective annual interest rate is 8%. What is the benefit-cost ratio of the better alternative?

a. 1.73* b. 1.76 c. 1.84 d. 1.88 46. A gourmet ice cream store has fixed expenses (rent, utilities, etc.) of $50,000/year. Its two full-time employees each earn $25,000 per year. There is also a part-time employee who makes $14,000 plus $6,000 in overtime if sales reach $120,000 in a year. The ice cream costs $4/L to produce and sells for $7/L. What is the minimum number of liters the store must sell to break even? a. 38,000 L b. 39,000 L c. 40,000 L* d. 41,000 L