SOLVED PROBLEMS IN ENGINEERING ECONOMY 1. Determine the ordinary simple interest on P10,000 for 9 months and 15 days if the rate of interest is 6%. a. P475 c. P467.21 b. P468 d.NOTA 2. Determine the exact simple interest on P20,000 for the period from January 15 to November 15, 2012 if the rate of simple interest is 5% a. P847.22 c.P833.33 b. P835.16 d.NOTA 3. You loan from a bank the amount of P100,000 with a rate of simple interest of 20% but the interest was deducted from the loan at the time the money was borrowed. If at the end of 1 year, you have to pay the full amount of P100,000, what is the actual rate of interest? a. P80,000 c. i = 20% b. i = 25% d. NOTA 4. Mr. Dee Jay borrowed money from the bank and he received the amount of P18,420 and promised to repay P20,000 at the end of 10 months. Determine the rate of simple interest. a. i = 10.29% c. i = 8.58% b. P = 1,580 d. NOTA 5. If P50,000 is borrowed for 90 days at 8% per annum simple interest. How much will be due at the end of 90 days? a. P50,986 c. P51,000 b. i = 8% d. NOTA 6. On his recent birthday on April 18, 2012, Cai was given by his mother a certain amount of money as birthday present. He decided to invest the said amount on a 12% exact simple interest. If the investment will mature on Christmas day at an amount of P15,000, how much did Cai receive from his mother on his birthday? a. P13,859.37 c. P15,000 b. P13,841.47 d. NOTA 7. Carle borrowed money from Cy with simple interest of 12%. worth of P50,000 which is due at the end of 6 months. a. P74,691.18 c. P47,169.81 b. P50,000 d. NOTA Find the present 8. A loan of P5,000 is made for a period of 15 months at a simple interest rate of 15%. What future amount is due at the end of the loan period? a. P5,750.00 c. P5,600.00 b. P5,937.50 d. NOTA SOLVED PROBLEMS IN ENGINEERING ECONOMY 9. Ciel borrowed P20,000 from the bank and promised to pay the amount after one year. He received the amount of P19,200 after the bank collected an advance interest of P800. What was the rate of discount and the rate of interest that the bank collected in advance? a. d=4%; i=4.17% c. P19,200; P20,000 b. i=4%; d=4.17 d. NOTA 10. You pawned your PSP for P5,000 and agreed to pay the amount at the end of 9 months. The pawnshop gave you P4,000 cash after deducting the interest in advance. What was the rate of discount? a. i = 20% c. d = 20% b. d = 25% d. NOTA 11. What was the rate of interest for the problem in # 10? a. i=20% c. d=25% b. i=25% d. NOTA 12. If the sum of P15,000 is deposited in an account earning interest at the rate of 8% compounded quarterly, what will it become at the end of 5 years? a. P22,039.92 c. P22,289.21 b. P32,866.85 d. NOTA 13. An employee has a promissory note, due 5 years hence, whose maturity value is P70,000. If the rate of interest is 12% compounded semi-annually, what is the value of this note now? a. P39,720.82 c. P96,675.79 b. P39,087.63 d. NOTA 14. IEdeas is planning to expand its operations and plans to purchase a parcel of land on which to construct a building for their review center, which they will need 5 years hence. The current costs are: land: P2M; building: P3.5M. Since these are not needed immediately, the company plans to defer the purchase of the land and the construction of the building until they are needed. If the value of the land and the cost of the building are expected to appreciate at the rates of 10% and 8% per annum, respectively. What will be the total cost of the investment after 5 years? a. P8,580,275.74 c. P8,363,668.27 b. P7,244,668.37 d. NOTA 15. A debt of P150,000 was paid for as follows: P40,000 at the end of 3months, P50,000 at the end of 12 months, P30,000 at the end of 15 months, and a final payment F at the end of 21 months. If the rate of interest is 12% compounded quarterly, find the final payment F. a. P15,774.56 c. P12,359.52 b. P157,745.58 d. NOTA SOLVED PROBLEMS IN ENGINEERING ECONOMY 16. Adriste Philippines, Inc. expects to retire an existing machine at the end of 2013 and will replace it with a new machine for the same task at an estimated cost of P600,000. The old machine can be sold for P50,000 when it is replaced. To provide for replacement, the company intends to deposit the following amounts in an account earning interest at 8% compounded quarterly: P200,000 at the end of 2010 P150,000 at the end of 2011 P100,000 at the end of 2012 What additional amount is needed at the end of 2013 to purchase the new machine? a. P15,774.56 c. P12,359.52 b. P35,952.12 d. NOTA 17. If P500,000 is invested at 8% interest compounded quarterly, how many years will it take for this amount to accumulate to P900,000? a. 29.68 c. 14.84 b. 7.42 d. NOTA 18. Charlie wishes to bequeath his youngest son P200,000 ten years from now. What amount should he invest now if it will earn interest of 6% compounded annually during the first 5 years and 8% compounded quarterly during the next 5 years? a. P200,000 c. P100,576.67 b. P134,594.27 d. NOTA 19. Find the nominal rate compounded monthly which is equivalent to 16% compounded quarterly. What is the corresponding effective rate? a. r=15.79% ; Eri = 16.98% c. r=16.98% ; Eri=15.97% b. i=15.97% ; r=16.98% d. NOTA 20. What payment X 10 years from now is equivalent to a payment of P500,000 7 years from now, if interest rate is 12% compounded semi-annually? a. P221,150.05 c. P709,259.56 b. P155,902.36 d. NOTA 21. At a certain interest rate compounded annually, P100,000 will become P450,000 in 15 years. What is the amount at the end of 10 years? a. P272,638.68 c. P100,000.00 b. P450,000.00 d. NOTA 22. Compare the accumulated values at the end of 5 years if P100,000 is invested at the rate of 12% per year compounded annually, semi-annually, quarterly, monthly, daily, and continuously. Which gives the highest return interest. a. ANNUALLY c. CONTINUOUSLY b. DAILY d. NOTA SOLVED PROBLEMS IN ENGINEERING ECONOMY 23. In preparation for the college education of his son, DJ plans to deposit equal amounts money for five consecutive years starting one year from now. If he wants his son to be able to withdraw P1,000,000 ten years from now at 8% interest compounded annually, what is the amount of each deposit? a. P190,651.28 c. P116,010.09 b. P161,010.09 d. NOTA 24. A farmer bought a farm and he paid P100,000 cash and agreed to pay P20,000 at the end of each 6 months for 5 years. He failed to pay the first 5 payments. At the end of 3 years, he is required to pay the seller the entire debt consisting of his accumulated and future liabilities, otherwise the farm will be foreclosed. What must he pay if money is worth 14% compounded semi-annually? a. P200,863.70 c. P68,661.62 b. P197,018.73 d. NOTA 25. IEDeas constructed its building 6 years ago financed by a 10-year bank loan of P10M with 12% annual interest rate compounded monthly. The company has paid all the monthly instalments for the past 6 years. However, to reduce the amount of instalment payments, it was decided to refinance the balance of the loan through an insurance company. The new loan is for 10 years with interest at 8% compounded quarterly. A service charge of 5% will be added to the loan amount. Determine the balance on the original mortgage and the amount of the quarterly payments to the insurance company. a. P209,119.55; P5,448,161.75 c. P5,448,161,75 b. P5,448,161.75; P209,119.55 d.NOTA 26. Bright Futures Inc. will make the following disbursements for their retiring employees: P500,000 on Dec. 31, 2011 P1,000,000 on Dec. 31, 2012 P2,000,000 on Dec. 31, 2013 To accumulate these sums, a sinking fund was established by making equal yearend deposits starting Dec. 31, 2006 up to the end of 2013. If the fund earns 8% compounded annually, what is the required amount of the annual deposits? a. P344,395.77 c. P106,366 b. P3,633,200 d. NOTA 27. Ceila invests P100,000 for the college education of her 3-year old son, Ciel. If the fund earns 12% effective interest rate, how much will Ciel get each year starting from his 18th to his 22nd birthday? a. P324,486.82 c. P324,483.37 b. P135,574.26 d. NOTA 28. Carle buys a piece of property for P100,000 down payment and 10 deferred semiannual payments of P10,000 each starting three years from now. What is the present value of the investment if the rate of interest is 8% compounded semiannually? a. P166,665.65 c. P60,165.45 b. P691,665.56 d. NOTA SOLVED PROBLEMS IN ENGINEERING ECONOMY 29. Sir DJ spent the following amounts for the maintenance of the machine he bought: P4,000 each year for the 1st five years, P6,000 each year for the next five years. In addition, he spent P15,000 for overhauling at the end of the 4 th year and another P20,000 for overhauling at the end of the 8th year. If money is worth 6% compounded annually, what was the equivalent uniform annual cost for the 10year period? a. P8,174.54 c. P60,165.45 b. P16,849.46 d. NOTA 30. UST Hospital purchased a CT Scan machine on the basis of guaranteed performance. However, initial tests indicate that the operating cost will be P5,000 more per year than guaranteed. If the expected life of the machine is 20 years and money is worth 15%, what deduction from the purchase price would compensate UST for the additional operating cost? a. P13,269.99 b. P84,590.92 c. P31,296.66 d. NOTA 31. A brand new car can be purchased with a down payment of P150,000 and equal instalments of P18,000 each paid at the end of every month for the next 36 months. If money is worth 12% compounded monthly, determine the equivalent cash price of the car. a. P150,000 c. 168,000 b. P691,935.09 d. NOTA 32. A brand new house and lot costs P5M if paid in cash. On the instalment plan, the buyer should pay 30% down and 20 quarterly instalments. The first payment due at the end of the 1st year. If money is worth 12% compounded quarterly, determine the amount of quarterly instalments. a. P257,069.41 c. P3.5M b. P4.85M d. NOTA 33. You have a building for rent and you were offered two options by a prospective client: A) P1.2M a year for 6 years, the rent being paid at the beginning of each year. B) P300,000 for the 1st year, P400,000 for the 2nd year, P500,000 for the 3rd year, and P600,000 a year for the next three years. All rentals are paid at the beginning of each year. If money is worth 12%, which is the better offer? a. OFFER A c. SAME OFFER b. OFFER B d. NOTA 34. It costs P500,000 at the end of each year to maintain a section of Kennon Road in Baguio City. If money is worth 10%, how much would it pay to spend immediately to reduce the annual cost to P100,000? a. P4M c. P1M b. P5M d. NOTA SOLVED PROBLEMS IN ENGINEERING ECONOMY 35. For its maintenance, a bridge in NLEX requires P250,000 at the end of 3 years and annually thereafter. If money is worth 8%, determine the capitalized cost of all future maintenance. a. P214,334.71 c. P3,125,000 b. P2,679,183,81 d. NOTA 36. API installed a new steam boiler at a total cost of P1.5M and is estimated to have a useful life of 10 years. It is estimated to have a scrap value of P50,000 at the end of its life. If interest is 8% compounded annually, determine its capitalized cost. a.P1.5M c. P1.45M b. P2,751,159.48 d. NOTA 37. The capitalized cost of a certain piece of equipment was found to be P1.42M. The rate of interest is 12% with a salvage value of P100,000 at the end of its useful life of 10 years. Assuming that the cost of perpetual replacement remains constant, determine the original cost of the equipment. a. P994,973.76 c. 1.42M b. P47,487.89 d. NOTA 38. DJ & Charlie Foundation wishes to set-up a trust fund to provide the following expenditures: P15M for the lot and the building and P5M for the initial equipment of a Methods and Ergonomics Laboratory; P1M for the annual operating costs every year; and P3M for the purchase of new equipment and replacement of some equipment every 5 years beginning 5 years from now. If money is worth 10% compounded annually, how much money should be put into the fund? a. P34,913,924.42 c. P24M b. P30M d. NOTA 39. A fund is to be donated by APIEMS Foundation to provide annual scholarships to deserving Industrial Engineering students. The fund will grant P500,000 each for the first 5 years, P800,000 for each of the next 5 years, and P1M each year thereafter. The scholarship will start one year after the fund is established. If the fund earns 8% interest, what is the amount of the donation? a. P1,996,355.02 c. P2,173,897.09 b. P9.96M d. NOTA 40. IEdeas signed a contract to lease a building at P60,000 a year with an annual increase of P1,000 a year for 5 years. Payments are to be made at the end of each year, starting one year from now. If money is worth 8%, what lump sum paid today is equivalent to the 5-year lease-payment plan? a. P246,935.03 c. P7,372.43 b. P239,562.60 d. NOTA SOLVED PROBLEMS IN ENGINEERING ECONOMY 41. Find the equivalent annual payment of the following obligations at 12% interest: End of Year 1 2 3 4 5 a. EUAC = 127,940.32 b. EUAC = 360,477.62 Payment (Pesos) 100,000 80,000 60,000 40,000 20,000 c. P64,507.68 d. NOTA 42. Two brothers, Cy and Ciel decided to save money in a fund that earns 8% interest compounded annually but on different ways. Cy decided to save money by making an end of year deposit of P10,000 on the 1st year, P11,000 on the 2nd year, 12,000 on the 3rd year, and so on increasing the next year’s deposit by P1,000 until the end of 10 years. Ciel decided to save by just making annual deposits of P14,000 annually for 10 years. Who has more savings at the end of 10 years? a. CY c. SAME b. CIEL d. NOTA 43. As an IE consultant for the World Bank you are earning an average annual salary of $5M for 10 years. A private company would like to acquire your services and offers you an initial salary of $3M but is increasing at the rate of $400,000 annually. If money is worth 10%, are your going to accept the offer? a. YES, ACCEPT THE OFFER c. P93,941.14 b. NO, Don’t accept the offer d. NOTA 44. An Industrial Engineer wrote a best selling book in IE and was offered two alternatives by a publishing company for the rights to publish and sell his book. The 1st offer was a single lump sum payment of P3.5M. The 2nd offer was an initial payment of P2.5M plus 4% of the gross receipts for the next 5 years estimated to be as follows: End Of Year Gross Receipts (Pesos) 1 2 3 4 10M 8M 6M 4M 4% of Gross Receipts(Pesos) 400,000 320,000 240,000 160,000 5 2M 80,000 After the 5th year, the author will not receive further royalties. If money is worth 10%, which alternative should he select? a. Choose Offer 1 c. Get them both b. Choose Offer 2 d. NOTA SOLVED PROBLEMS IN ENGINEERING ECONOMY 45. APIEMS Corporation is establishing a sinking fund for the purpose of accumulating a sufficient capital to retire its outstanding bonds at maturity. The bonds are redeemable in 10 years and their maturity value is P10M. How much should be deposited each year if the fund pays interest at the rate of 4%. a. P10M c. P832,909.44 b. P400,000 d. NOTA 46. PIIE Corporation issued 5,000 bonds of P1,000 face value each, redeemable at par at the end of 10 years. To accumulate the funds required for redemption, the company established a sinking fund consisting of annual deposits, the interest of the fund being 5%. What was the principal in the fund at the end of 7 years? a. P397,522.64 b. P3,236,632.68 c. P5M d. NOTA 47. You were offered a Land Bank certificate with a face value of P1M. The bond is bearing an interest of 6% per year payable semi-annually and due in 5 years. If you want to earn 8% semi-annually, how much are you willing to pay for the certificate? a. P1M c. P30,000 b. P918,891.04 d. NOTA 48. A P100,000, 6% bond pays dividend semi-annually and will be redeemed at 120% on December 31, 2015. If you bought this bond on December 31, 2011 to yield 5% interest compounded semi-annually, find the price of the bond. a. P120,000 c. P21,510.41 b. P98,489.59 d. NOTA 49. You want to make 14% nominal interest compounded quarterly on a bond investment. How much are you willing to pay now for a 12%, P100,000 bond that will mature in 5 years and pays interest quarterly? a. P100,000 c. P92,893.80 b. P50,256.59 d. NOTA 50. You bought a bond having a face value of P10,000 for only P9,000. The bond rate was 14% nominal and interest payments were made to you semi-annually for a total of 7 years. At the end of this period, you sold the bond at a price that yielded 16% nominal on your investment. For how much did you sell the bond? a. P9,484.30 c. 410.453.66 b. P26,434.75 d. NOTA DEPRECIATION AND DEPLETION 51. A machine costsP80,000 and an estimated life of 10 years with a salvage value of P5,000. What is the book value after 5 years using the straight line method? a. P42,500 c. P7,500 b. P75,000 d. NOTA 52. A knitting machine is purchased for P500,000. The salvage value in 10 years is P100,000. What is the total depreciation in the first 6 years using the SLM? a. P40,000 c. P400,000 b. P240,000 d. NOTA SOLVED PROBLEMS IN ENGINEERING ECONOMY 53. The cost of a Tajima embroidery machine is P1.2M and the cost of installation is P50,000. If the salvage value is 10% of the cost of the machine at the end of 10 years, determine the book value at the end of the 3rd year. Use SLM. a. P339,000 c. P1.25M b. P911,000 d. NOTA 54. A linking machine is purchased for P20,000. It is estimated to have a useful life of 10 years and a salvage value of P10,000. Find the depreciation for the 1st year using the SYD method. a. P10,000 c. P1,818.18 b. P18,812 d. NOTA 55. Zach’s Corporation purchased a Jacquard machine for P6M, freight and installation charges amounted to 3% of the purchase price. If the machine will be depreciated over a period of 10 years with a salvage value of 6%, determine the depreciation cost during the 5 th year using the SYD method. a. P633,730.91 b. P6.18M c. 360,000 d. NOTA 56. Kaizen Corporation makes it a policy that for any new equipment purchased, the annual depreciation cost should not exceed 20% of the 1 st cost at any time with no salvage value. Determine the service life necessary if the depreciation method used is the SYD. a. 7 YEARS c. 9 YEARS b. 8 YEARS d. NOTA 57. A stop watch used for TMS has a selling price of P1,500. If its selling price is expected do decline at a rate of 10% per year due to obsolescence, what will be its selling price after 3 years? a. P1,093.5 c. P150.50 b. P1,500 d. NOTA 58. A circular linking machine costing P45,000 has a book value of P4,500 when retired at the end of 10 years. Depreciation cost is computed using a constant percentage of the declining book value. What is the annual rate of depreciation in %. a. P4,500 c. K=20.57% b. P45,000 d. NOTA 59. A generator costing P750,000 depreciates in value each year by 20% of its value. Find its book value when the generator is 5 years old. a. P245,760 c. 750,000 b. P150,000 d. NOTA 60. An electric sewing machine costs P10,000 with a salvage value of P500 at the end of 10 years. Calculate the annual depreciation cost by the sinking fund method at 5% interest. a. P755.29 c. P500 b. P755,293.5 d. NOTA
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