EXERCISE vet NUS S.N.: _ 20170106180 7 -RANJO, VALE RIE Jor —__- _ENGR.F.GTADIQUE Date: _ Name Professor : Board Exam November 2000 ; as Ee oministod rate, how much should you invest today to be able to withdraw P10 000.00 annually for 10 years? AP PIO CCD (Ans. P61 445.67) EES MAG peal Get | { | | ff iti)? TENTS TP e' io. = _U+0.L)' P Proce SAS (=l0% . P= 6144567 02. ECE Board Exam April 2001 How much do ten P2000.00 quarterly payments amount at present, if the interest rate is 10% compounded quarterly? _ : [een O9-= 0025 (Ans. P17 504.13) i = 2.54 ec AL Mitiect = oz5yem) Jin ses a i realty Peo sasehoay | a|a|5(@| FEE ttt P= PITSOV.NS Ae Pzcod 03. ME Board Exam March 2014 Maintenance costs for a new machine are P500.00 each year. What is the present worth of these maintenance costs over a 12 years period if the interest rate is 8%? (Ans. P3768.00) AP \ We) (ae F500 ate | P= P3768 04, EE Board Exam September 2017 Find the present worth of a 5 years annuity paying P3000.00 at the end of each year, with interest at 6% compounded annually. (Ans. P12 637.09) PeA BCE eels TOtiye p= raxo| See | P= F12637-09April 2001 7 . 05. ECE Botte Exar Aitted amount of five years annuity paying P6000.00 at the end of i ied annually? each year, with interest at 45% compound: ly’ (ans. P40 454.28) eA A A A&A i — = a 1.15) [ff re rexo[ gas] 1 2 3s 4 5 Fs 4045429 06. ME Board Exam October 2000 a A sinking fund consists of 15 annual deposits of P1000.00 each with interest eamed at the rate of 4% compounded annually. What is the principal in the fund at its terminal date? (Ans. P20 023.59) aay. tigeae ovd apart] 4 Fee 1000 [0.04 ‘ 0.04 F =F 20003, 59 07. ME Board Exam April 1997 ‘ Mr. Robles plans to deposit P500.00 at the end of each month for 10 years at 42% annual interest, compounded monthly. The amount that will be available in two years is: j=3}#= 0.01 ep issn] (Ans. P13 487.00) real oe Fe Popp (uennee = = 0-01 {=ool Lit 4 a6 4 “ | Fe 8134387 1 08. ECE Board Exam November 1998 A debt of P10 000.00 with 10% interest compounded semi-annually is to be amortized by semi-annual payments over the next five years, the first due after 6 months. Determine the semi-annual payment, Q2-=0.05 (Ans. P1295.00) n=(S)(Z) 210 Las)? a-PLUR Ry At a= Plocsol 0.05 (1+0.05)'°_] CHOOSY™ 1 | A= P1295CE Board Exam November evo 8 if money is worth 8% annually, what annual payment is required to raise P350 ‘mot 000.00 after 12 years? e (ans. P18 443.26) orf — (23 10 thi) ASF lagi A= 350000 Teeeay | AAA Mee, An P18443.26 ). ME Board Exam March 2014 ° ‘A Mechanical Engineer obtained a loan of P50 000.00 at the Hegel annually in order to repair his Grandmother's house. How much must the Me : ae 5 os Engineer pay monthly to amortize the Lv on of ten ane 550.90) ie= - 0.06 =(i+i)*=1 1 *0- 486762 ie eal io® NB 19 125 A=P ee As P0000 [-aesenetesaetene rate of 6% compounded janical (44-BO7Gx OF AP =] A= P5512 KAA PAA 11. A 65-year old retiree invested P400 000.00 in a pension plan that eams 15% interest compounded monthly. If pension payments are given every three months, determine the amount that the retiree (or his heirs) will receive quarterly for the next 15 years. Np 400000 (1+ SE) 1614) (Ans P17 005.63) i= 737 ] : (5-4) | iy = 03797 ( [+ 0.03797 ; LI FLL a péoocnoL sepreztisoscgre A= 17005. 63 we 12. CE Board Exam May 1999 ‘Aman paid 10% down payment of P200 000.00 for a house and lot and agreed to Pay the balance on monthly installments for 60 months at an interest rate of 15% compounded monthly. Determine the required monthly payment. P (Ans. P42 822.00) a . we anP| aR } iy I} 236. (1 4 238) 60 P2000) AA AF F100 00D tease A= #42 B2\.87 Folerce = B1g00 07 347ECE Board Exam November 2000 13. A Company established an annual fund for the purchase of an equipment after 12 ich is ir P20 000.00. If i = 10%, find the annual deposits. years which is a at pats ae ne elraber] i23 0 fie Tri) 5 Ty, = Al Tt JV] Ar P20000[7 25'S ail DAR AKA A= 935.27 44. ME Board Exam April 1998 ‘A manufacturing firm wishes to give each 80 employees a holiday bonus. How much is needed to invest for a year at 12% nominal interest rate, cornpounded monthly, so that each employee will receive a P2000.00 bonus? (Ans. P12 616.00) fF cule A= fanper) | 1 Ar (P2000)(0)/ 3S oye | A=F12G615.81 15. EE Board Exam April 2002 A gasoline engine is available on installment basis with a down payment of 8000.00, and P1000.00 at the end of each month for one year. What is the cash Price of the engine if interest is set at 6% compounded monthly? i p= Aaay (Ans. 19 618.93) \ >? i i } 1 = Pl 1#0.05)"=1 on RA oe TOO SSscaasesy | +P 8000 Detar P= Pi9G18. 93 16. CE Board Exam May 2005 An ordinary annuity has a nominal interest rate of 6% compounded semi-quarterly for eight years. a) What is the present-worth factor? b) What is the sinking-fund factor? c) What is the capital-recovery factor? eee ee Eee: ” Palit *| Se P(e] =f orgy Ou\e4 Lake] [GET | a = 001973 eA" Flame] 20% = 0.01223 (Ans. 50.68; 0.01223; 0.01973)rj Exam May 2004 : 17, CE Boesent value of an annuity of R pesos payable annually for 10 years, with the first payment at the end of 10 years is P100 701.30. If money is worth 8%, what is { ? Ml the value of R’ . Ce (Ans. P30 000.00) — ss un noec ECT C14iy* po are la OM RARRRRRRRR An P1100 70-30 ff poe tiseoe)” (140.08)? A= R= P299399.99 R® P80000.00 18. Determine the present worth of a series of P4500.00 quarterly payments that extend over a period of eight years if the first payment is due three months from now and interest is 9% compounded a) monthly; b) continuously. ies (14 929)" —| B) (Ans. P101 623.58; P101 499.07) ig. 0-095807 ine eg 0. O93807= Cit) 4-1 eo = (Iti)t-] 02267 7 =0.022755 19-2267 (1.02267) P= B45c0] (o22en32- J PP 10\c72 37 2022755)44)_ Fira arse] 49. Determine the amount to be deposited semi-annually in a sinking fund for five years if it is desired to accumulate P1.5M after eight years. The first deposit is due six months from now and interest is 7% compounded continuously. ef B Se ity A*PB50B809-74 (saat Ske B9.846-50) i= 0.03502 (08562) 1 | Be FC4t) ie AF 1OSAGSAS P= F1 500000 (1-03562, Pe 856809. 74 20. CE Board Exam May 2006 Fifty thousand pesos is deposited annually at an interest rate of 6% per annum compounded continuously. How many years will it accumulate to P1000 000.00? ie em (Ans. 13.42) lee =f _ ie = 0.06184- b r Peal cert) fl n ——} nw Pesci = eehoon[wontatal| || n= 13.42 ;° 3-1921. ME Board Exam April 1997 Mr. Ramirez borrowed P15 000.00 two years ago. The terms of the loan are 10% interest for 10 years with uniform payments. He just made his second annual payment. How much principal does he still owe? P pea AP RPT | (Ans, P13 024.00) rt ¢ Pz Welyinydt xe Pesaiie [recur] | by X= P13023.52 leat Elms 22. Ahouse and lot costing P2M is purchased with a down payment of PO.5M and the remaining balance payable by equal monthly payments for 10 years. If interest is 12% compounded monthly, determine a) the monthly payment; b) the lump sum payment at the end of the seventh year to discharge the buyer's remaining liability. peal GH%= (Ans. P21 520.64; P669 453.42) A) { aN] ouacn’ 4 8) 2000000-500 goo(ran) - Z ory?- 4 ; Peceocon Pome (uay* CE Board Exam November 1995 ind the present value in pesos, of a perpetuity of P15 000.00 i if money is worth 8%, compounded quarterly. eae iez™ leg (Ans. P371 287.00) (iti)? = (14 8 y i = 0.0404 - P15000 Pe Sotoe P= P37) 287 ME Board Exam March 2014 What amount of mone) it y deposited 50 years ago at 8% interest would i Perpetual payment of P10 000.00 per year? The first payment is ‘due a are : 50 _ 1OCD0_ (Ans. P2665. 15) P(it0.08)° = Fe (Ans 5.15) P= P2065.15: ; ey i 4a savings account to provide P500 000.00 in year 6. _ Kind Heart Foundation opened 2 TTT io verast annually forthe first 15 years it its. The account I f sa rest thereat Determine the single deposit required for the grants to eee (Ans. P5855, 947.87) eo. GaOC=L Le Agy® eal tal Hy ve 7500 COO yo 1.21 p= psxnooo) Seeeals]* Pro (0%) P5955 947.81 \t I i ° 17 37. P2.5M worth of heavy equipment is purchased by a civil engineer. He pays P1M Cash and will pay PO.4M at the end of two years, and another PO.5M a year later. To pay off the remaining lability, he has to make eight equal yearly payments starting at the end of the fourth year. Find the amount of the annual payments if interest is 6% effective ref@O0 2(25M-IM)= Todna(non) “+ POsN(-CE) “+ A A= 2166 630.3 Bu {2 | 28. ME Board Exam April 1996 A series of year-end payments extending over eight years are as follows: P10 : P10 000. for the first year, P20 000.00 for the second year, P50 000.00 for the third year, ond P40 000.00 for éach year from the fourth through the eighth year. Find the equivalent annual worth of these payments if the annual interest is 8%. ae refQd (Ans, P33 563.85) P= PFloo 9 2 7 .08¥_) 1 a ‘oct 108 sy -¥20c05( +08) 7.4 R50000( LOBY%} 4odoa[-2SF="] (98) FP ce OOR(LORY | seat os] B08 | At Paz 272 Ax P35 503.25 3-2439. 40. 41. On the day his son was born, an engineer opened a trust fund by investing P60 000.00 at 7% effective interest. If the son is to withdraw P40 000.00 a year from his 17® to his 20" birthday, determine the remaining amount in the fund on his 21% birthday. refOO: fo (ans. P58 404.18) P60 = ae td adhd te, “21 000+ F40.000 [L107 Sel (L07Y"*+ Fa (107) F -Psp404.1g a “Wie 2021 ME Board Exam March 2014 Maintenance on an old machine is P1000.00 this year but is expected to increase by 250.00 each year thereafter. What is the present worth of five years of maintenance? Use an interest rate of 10%. ref@ 5 5 ares], 250 (P=) 5} C14 px eicoo SE |e { 0.4 cH) o (Ans.P5506.25) P=PFS5S0G-A To provide for the replacement of equipment, a sinking fund is established. The fund requires 10 consecutive yearly deposits that increase by P5000.00 each year. If the initial deposit is P15 000.00, determine the value of the fund at the end of the 10° year. Interest is 10% effective. 10 (Ans. P535 932.60) _, Fe Proconl wre | + mpi : . o- 1 Ol Fe #535 922-60 |42. To pay off a P100 000.00 loan, it is i q . it is required that 20 semiannual payments that increase by P500.00 be made. Determine the amount of the first payment if it is due six months after the loan is made and interest is 7% compounded semiannually. (Ans. P2853.56) waghy tp A= 2953-56 AAKS 43. _ Same as problem number 42 except that payments decrease by P400.00. | 100 CoO) (Ans, P10 382.15) F100 Os Pi- Fe 10 auee . 035 )29— FIO 0 = To, a eo A] tes (008s) * , 400. (gee 20] (038)? 0.085 | 0.085 A> Flo 33215 44, Aplant manager establishes a sinking fund of eight equal yearly deposits to provide for the replacement of a heat exchanger. The estimated cost of replacement due to depreciation is P50 000.00 for the first year, and this is expected to increase by 8000.00 per year until the heat exchanger is replaced. If money is worth 9% effective, determine the amount of each deposit. evi, Feat |+¢ coe " P74 409.33) \ 1 | 9-1, 3000 | P50 On| oe eS (oro ~ 8] = F820621.36 ) a yA ar rresmanh | Sor A=P74 402.33 3-2645. Find the present worth of the cash flow series shown if interest is 9% compounded semi-annually. The first payment is P4000.00 with succeeding payments increasing uniformly by P500.00 until the end of the fourth year, where payments become uniform. (Ans, P78 896.61) rR teths Prob. 45&46 P7500 ret©O: 7 (1045)'9=1 e500 _{(1045)%-1 8 1 Srzcny[ (1045)°—1 acy? 7 Proen esr as S| -a(-org 1 20 a (1048) P= P78 29061 48. For an interest rate of 8% compounded semi-annually, determine the future worth at the end of nine years of the cash flow series shown. The first payment is P7000.00 with payments increasing by P800.00 every six months until the end of the fourth year, where payments become identical (Ans. P282 699.11) [Hosea s[eopnanzan este et] 0.04 al 0.04 ~47. Determine the present value of a mine to an investor if an initia profit of P250 000.00 is expected after four years, net operating profit is projected to increase by P75 000 every six months until the mine is depleted at the ond of 12 years. Money is worth 8% compounded semi-annually. ref@O rl (Ans, P7210 308.51) Pres | LDP ty Se (oe i) (04) p=F7 210208. 51 725000 } |i | al 667869 Ibn 12 48. EE Board Exam September 2004 and May 2008 ‘Suppose a man receives an initial annual salaty of P 60 000.00 increasing at the rate of P 5000.00 a year. If money is worth 10%, determine his equivalent uniform salary \ for a period of eight years. P| (Ans. P75 022.39) Se RRRSE SE! g_} Ty TT TT p5o00 [LUI 3} 6 ye ag prreoonl ivan |* ot [‘s a 1|] | P= P400 233.93 . 8 n-ptooconos| the | Ae 7 75 022.29Solved Problems 3.01 ME Board Exam March 2014 . What present sum would need to be put in a savings account now to provide a 1000.00 annual withdrawal for 50 years, if interest is 6%? Solution: A= P1000 yn _ af G@epr-1 | | ie = 10% pal a+)" pee 48 a8 aD) years = P1990 | 1+ 0.06 -2 i 0.06 (1 + 0.06 )* tp P = P15 762,00 3.02 ECE Board Exam April 1998 and April 2014 Money borrowed today is to be paid in 6 equal payments at the end of 18 months. If the interest is 12% compounded quarterly, how much was initially borrowed if quarterly payment is P2000.00? Solution: Ph i i i=3% thas [a ]s | é [quarters P= 10 834.38 A=P2000 3.03 ECE Board Exam November 2000 A man secured a P10 000.00 loan at 12% effective interest. Find the annual amortization to extinguish it in six years. Solution: 4P=P10 000 i i i= 12% =pj_sa) Tar| 3 6 | years ° ARAAAA ‘A =P2432.26 37id off in eight equal Yeer'y PENNE, ea. is to be paid off in compounded quarter, 3.04 4.735 000.00- ead interest at 10% comPo Maney, jortization I 4% Solution: 1 P= P36 000 : i, = 10.38% oo A=P y]2)3 8 | eas l AA AA 3.05 ECE Board Exam November 1995 and October 2007 | ‘An employee obtained a loan of P10 000.00 at the rate of 6% con, annually in order to repair @ house. How much must he pay monthly to amir: loan within a period of 10 years? Solution: i, = 6% ; mMe12 ; nm © 10x12 =120 dp=P4 . ; 10.000 Le(t+i"-1 | i : | sh = (+i. )e <1 = (1.06) = 0.004868 | {air P10 009 | 2.004868(1.0048 Noy 0 la+if | 866) | 1.004868)" A=P110.20 | 3.06 ECE Board Exam November 199 | ° 8 ve Ee the accumulated amount of a five. : f year, with interest at 15% comayas%ee! 2nnuity paying P6000.00 at mpounded an al Solution: nee (sip P6099 | (1+0.15)'-} 0.153.07 EE Board Exam April 2017 ‘The president of an engineering firm wishes to give each of his 50 employees a holiday bonus of P10 000.00. How much should he invest monthly for a vor at 12% nominal interest rate compounded monthly to be able to give the bonus? Solution: F=P10000x50 =P500000 ; n=1x12= Ir ‘ n=tx12=12 i 12% _ i= 1% i alr soon] 29, | Pape TTT | mons Gif -1 @+0.01)?=1 A =P39.424,39 alata Aa al 3.08 ME Board Exam April 1998 A parent on the day that their child is born wishes to determine what lump sum would have to be paid into an account bearing interest at 5% compounded annually, in order to withdraw P20 000.00 each on the child's 18%, 19%, 20%, and 21% birthdays? Solution: A AAA as-1], 5 paal Gt =1) (4 iy aon a idee (Ot) i oot mH yeas =p20000| +005) : 0.05 (1 +0.05)" P=P30941.73 3.09 CE Board Exam May 1998 The present value of an annuity of R pesos payable annually for eight years, with the first payment at the end of 10 years, is P187 481.25. Find the value of 2 if money is worth 5%. Solution: 4P=P167 481.25 R-P ie | iy i ay] i i= 5% 0.05(1 et] =n aa Oost sh (1.05? Tab tapap aa a yeas Q.osf-1 R = P45 000.06 RR RRR 3.10 An engineer wishes to take out a P150 000.00 educational policy for his son. If Money is worth 14% effective, find the premiums to be paid a) if five yearly Payments are needed; b) if 20 quarterly payments are required, 3-9Solution: 3.11 3.12 3-10 interest peri peginning of each in log, ts made oe yen ums are equal paym m ereridered ‘as annuity due. P= 0.14(1.14 = P150.000 = 10 0.40.4)" ap A=P150 00 [sae] {bee A =P38 326.78 al “ys AAAAA ;\4 i) _1-@si'- ie=(1+4) -1=(+i)'-1 b) 4 P=P150000 1 1 i 4 +i,)4 -1=(1.14)s -1 i i= 3.33% 0333 Pep Pie | utes .0333 (1.0333}°] 1/2 hy ie A=misno0n| 268226 333) adi AKA (1.0333)? -1 A =P10 057.55 To accumulate P150 000.00, uniform di leposits every six months will be requie!” the next 12 years, Determine the amou! int of each deposit if the applied nomi! is 9% compounded continuously, Solution: Femso000 F=P1S0000 + n=1242—24 OE i m9 = 45% asp Feferringto equation 3-14 ' alu Periods e } = 1 0.085 _} A-F/—~ |=Pisoooo| © AAA AAR e -1] encase) 1 A=P3550.29 ME Board Exam October 1997 Maintenance cost ofan equipment is poy , semana amount ee 2 0.0 a 4,82" fr two years, pao" must end PAO Af compounded annually, 7 Set aside for thie equipment years. como, Money isAp pone eo on tans rs P2000 (Sey +P40 000 (1.1) * + P80 000 (1.1) ® = P99 351.87 F2= P80 000 The interest rate per period (semi-annually) must first be adjusted to conform with the equivalent annuity series. =) -1=(4i)"-1 LP = (b+ig)m -1 = (1.1)? 1 = 0.0488 15 [16 [periods A= oat | 0.0488 a @+ifP (10488) -1 ‘A-=P9089.05 3.13. EE Board Exam September 2010 A loan of P10 000.00 is to repaid at the rate of P200.00 per month, with an annual effective rate of 19.56% charged against the unpaid balanced. What principal remains to be paid after the 3" payment? Solution: P=P10000 ; A=P200 ie 9 =f14) -1- ei (1-4) 1=(+i" 1 i =(1+1,)m 1 =(1.1956)2 -1 = 0.015 With reference at 3: PQ+if =P, afte) P10 000(1.015) =P, + rag ay =19.56% ; n=3 P, = P9848.00rly, determine the single Pay nded quarter al series ty + money i wort 12% ra replace @ unorm anne rts 3.14 If monet fourth year end of the years. Solution: ie = 12.55% meme FD | years rfefs|a]s ‘A= P2500 PY vlog) eee) vaaftet=t) P =P25 858.07 4 (1-22) 10.1255 4 3.15 ME Board Exam March 2014 “ ‘A company deposits P1000.00 every year for ten years in a bank. The ein makes no deposits during the subsequent five years. If the bank pays 8% interes: amount in the account at the end of fifteen years is nearest to: F 4 i ie = 89% i tf2}3 22 “Tropa a ate yeas A= P1000 F=A [sr +i = rn oF = aoe F =P21 286.00 Solution: 3.16 The pre-seling price of a plush ini } and semi-annual payment. of 0 00D 00 for Tequires a down paymert e annual payments of P75 000,00 1 eae zi .00 for the next ran te nent etsy nate eer re lis investment. Solution: = 996 fF ne i ‘fafa fF alte j 2B P50 000 “potas PIM P75 o 000Solution: P=PIM ; A, =P50000; A, =P75000; i=18%/2-9% With reference at 24: a (f=) VA (“Ho sip Psy 7 0 =P75 on =I P50 on Fy +P1000 o09(1.09)"* F =P12 401 053.56 3.17 An individual makes five deposits that increase uniformly by P300.00 every month in a savings account that earns 12% interest compounded monthly. If the initial deposit is P4500.00, determine the accumulated amount in the account just after the last deposit. Solution: The diagram on the left shows the cash flow schedule as given by the problem. This diagram is divided into two separate sets of cash flows - an annuity series of A= P4500 and a gradient series of G = P300, as shown by the diagram on the right. ‘Thus, the future worth of the original cash flow equals the total future equivalents of the two separate cash fiows. 3-13deposits decrease un same stem number 3.17 except that the deposit my, ol ue sap. evey month. tr, i Solution: This problem again requires for the Gif -1] 6f@ut—1 original cash flow diagram to be broken =A) *—— 7 Gena into. two as shown. With tis, the , ; difference between the future wor 4.01)'-1] P500/ (1.01) -1 > the annuity sees and the gradient series = P4500 on’ —1)_P500/ (1.01) -1 0.01 | 0.01} 0.01 is teken, such that Fr= Fi - Fe F, =P17 904.27 3.19 A series of seven annual payments starting with P4000.00 on the first year inces: by P800.00 yearly, If interest is 10% effective, determine the equivalent uiir series of payments. Solution: Condition 1 fF This problem is best solved by equating fan i future worth of the desired cash fiow i 21% the future worth the of the original fl alana flow, such that Fr = F,. r= P4000 cpm [sP]na, fe =A].$[set i i A, fer aff =1_, Condition 2 iF Me———__[| I) i asia i 10% i =A,4S___Gn ep he Gyn yeas = P4000 “ar P800(7) Gay hy A, = P6097,29 4 3-14