EXERCISE NO. 3 Ordinary Annuity Bruan, Kimberly C. 2A Engr. Lilian A. Lerios Name, Year & Section Instructor ECON 11. June 30,2020 Subject Date 1. A steam boiler is purchased on the basis of guaranteed performance. However, initial tests indicate that the operating cost will be P2,000 more per year than guaranteed. If the expected life is 25 years and money is worth 10%, what deduction from the purchase price would compensate the buyer for the additional operating cost? Use the forma: P = A(P/A, i%, n) Given: Solution Ar P 2.000 a 25 PEA (PIA, iE, od Te (hs O48 * 2000 (Pia, totky 259 Req'd: = 2000 [ ae] + 1B Is4-bz004 Pee 1b 154-08 2. one-bagger concrete mixer can be purchased witha down payment of P40,000 and equal installments of P3,000 each paid at the end of every month for the next 12 months. If money is worth 12% compounded monthly, determine the equivalent cash price of the mixer. Gives! Solotion: ‘P40,000 = dou payment P00, Pe down payment +A (PA, i%6,9) a Hee (ope = 40 000+ 000 (Tia. 1%fe, 12) nen Homans sooo S600 ne Redd = TS T6S+ 23242 P= P 75,768. 23 LEP 1B, 708. 233, The buyer of a certain machine may pay either P10,000 cash down payment and P10,000 annually for the next 6 years, or pay P17,500 cash and P10,000 annually for the next 5 years. If money is worth 12% compounded annually, which method of payment is better for the buyer and by how much? Given Soltion: ‘Ay P 10,000 . Aye P 10,000 Pe A, (PIA, itn) + OP, PF, * 10,000 + [0000 (PA, 12%, 0) 4 DP, OF, P7500 of liro-bd* =) n tora + 00 [Ue] + to 000 hes Sys a 0732 we MeO BLit4-07324 P+ Psi .07 Regd? Pt Prt Ay (PIA, i", n) + OF 17 = te 000(T/A, [2% S) + OF, (ito na§e=1 + reco [Satine] 7 750° = 83547: 70202 Ps P 63,547. 26 The buyer shovld choose the Ast method of payment - Their difference is ¥ 2,433-64 4. farmer bought a farm and he paid P50,000 cash and agreed to pay P10,000 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 by the seller the entire debt consisting of his accumulated and future liabilities, otherwise the farm would be foreclosed by the seller. What must he pay if money is worth 12% compounded semi-annually? Solution! oo peu) - tee (FE) - Parq, 099 ne tury” ee Sy 7 = 974),105.How much money would you have to deposit for 5 consecutive years starting one year from now if you want to be able to withdraw P250,000 ten years from now? Assume the interest is 12% compounded annually. Gives Solution + FF 250,000 j nfo isi * oun Pe FCPIF, i%,0) Ae PCALP 1%, 0) zs ov0(P/F, 2%%'0) —« go was -31(AlP, 22.9] rey © 250000 it0.12]" rooms. sf 2 ae Pe P50,493:31 + 22029. 62755 P 22, 627-63 6. The cost of constructing and developing an irrigation system averages P8,000 per hectare. If the money borrowed to build it is to be repaid by end users in 15 years, (a) What is the contribution to a sinking fund the end users would have to pay in annual irrigation fees per hectare if the rate of interest on the fund is 8% compounded annually? (b) If the interest on the loan is 12% per annum, and the operation and maintenance expenses, estimated to be P185 per hectare per year, were also assumed by the end users instead of by the government, what would be the total annual irrigation charge per hectare? Solutton’ (0) _ _80p010.0%) _ Pray Trro.onye=) 2 P 274. waaras () pAb. pose (o-t) ot = Payd 5939172 +P ee GD" (roeyP = F294. 547.A supermarket building was constructed 6 years ago financed by a ten-year bank loan of P5,000,000 with 9% annual interest rate, compounded monthly. The company operating the supermarket has paid all the monthly installments for the past 6 years. However, to reduce the amount of the installment 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 10%, compounded quarterly, and with a service charge of 6% to be added to the loan. Determine : (a) The balance due on the original mortgage (>) The amount of the quarterly payments to the insurance conpany. Given FB, 000,000 ne to isq Re . Set eae 5) Ronsning bal # 6% cen charge Poats se ~bieypess Ar quasyer = P 148,974.57 eeoeaey™ 8.4 corporation will make the following disbursements: 250,000 on December 31, 2020 P500,000 on Decenber 31, 2021 P1,000,000 on Decenber 31, 2022 To accumulate these sums, a sinking fund is established by making equal year-end deposits starting December 31, 2015 up to the end of 2022, If the feng earns 10% interest compounded annually, what is the required amount of the annual deposit? ‘Solution: Pot [PRCT = a0 000 (aro) (a 6.10) A = Yo, 444.3702 B = U4, P03. OIE C= 10s 4s. 4997 TOTAL = A+ OtC P2,15¢.569.A company sets aside P1,000,000 at the end of each year for plant expansion. If the fund draws 8% compounded annually, how long will it take before P12,500,000 can be saved? Guren Solution: =P 1,000,000 Fea (F/A, i%, 0) E+ P'2, 500,000 12 520 co * 100 000 ( F/A, 8%, n) ie Bt F000 10-08)" = uoU 2 12.90 090 = (090 00 [ (L*2=08)=1] Reg £4 0064CS3u2 ne? a 4 ges: 10. A certain annuity pay P400 at the end of every 3 months. If the present value of the annuity is P6,000 and the accumulated amount is P10,000, determine the nominal rate. ‘Solvtion* C11)? 2Cl/ e000) +1 = 00! /bo00 wi = 3feer ~ 12002 Gooo 1S00, L=leoovsssg2 -) i = 6-c000 ssss2