No.1 for CAICWA & MECICEC MASTER MINDS 1. TIME VALUE OF MONEY MODEL - WISE ANALYSIS OF PREVIOUS EXAMINATIONS moo] 5 | MO] | | mas No. Model Name to | £ | 10 | $] 10 | was | mse | ne | w-17 = 2 Nog m2 mets ‘SIMPLE INTEREST sal) an a extn ar fe ‘COMPOUND INTEREST sal) 2 sada ex ns are |r FUTURE VALUE OF SINGLE AMOUNT a) oe | PRESENT VALUE OF SINGLE AMOUNT : : FUTURE VALUE OF ANUITY IMMEDIATE = Eales PRESENT VALUE OF ANNUITYINMEDIATE : : PRESENT VALUE OF PERPETUITY : . '8.__ [PRESENT VALUE OF GROWING PERPETUTY : 7 INTRODUCTION: When individuals or business institutions borrow money from others for certain time period, they pay some extra money other than the borrowed amount which is known as interest. Thus money can also be rented in the same way as objects. It means money has some time value. a) The money being borrowed by an individual is called ‘Principat’. b) The additional sum of money paid for using money is called ‘Interest’, Such interest is usually calculated as a percentage and the interest paid for use of Rs. 100 is called "Rate Percent’. If this rate percent is calculated for a year, itis called Rate percent per annum. c) The sum of Principal and Interest is called “Amount, d) The basic concept in Finance is that “One rupe SS Not equal to one rupee tomorrow, other things being equal’ SO TESST DSSS SS MODEL1 OF SIMPLE INTEREST It is a method of calculation of interest in which interest is computed on the Principal for the entire period of borrowing i.e. principal is same for any number of years. It is calculated using the formula: ST= PNR] [A=P (+n Principal sum of money, n= Number of years 1 = Rate of interest (expressed in decimal from) A. = Amount = Principal + Interest = P + PNR = P (1+NR). MODEL 2 - CONCEPT OF COMPOUND INTEREST It is another method of calculation of interest. Practically everybody will be familiar with this method of calculation of interest. In this method the interest earned by an investment is reinvested so that it also earns interest i.e. interest is again converted into principal and hence ‘one can earn interest on interest. E.g.: Suppose that Rs.100 is invested at the rate of 6% compounded annually. At the end of first year the value of investment is the original principal (Rs.100) plus interest on such principal i.e. Rs.108. Now, Rs.106 becomes principal for the second year. 2 IPCC_38e_F.M. (Problems)_ Time Value of Money 14 Pld+n- 1]8851 25025/26 Where —C..= Compound Interest. A = Amount (principal + Interest) 1 = Rate of interest (expressed in decimal form) n= Number of years P= Principal sum of money This formula assumes that interest is compounded annually. MODEL 3 - CALCULATION OF FUTURE VALUE OF A SINGLE AMOUNT FUTURE VALUE: This is also known as terminal value. The accrued amount (FV,) on a principal (P) after n payment periods at i (in decimal) rate of interest per payment period is given by Annualrateofinterest r F 4 (1+i)" Where, j= “US eee et Number of paymentperiodsper year k (1+) is known as future value factor or compound value factor. So FV, =Po(FVIF,,),when computing is done k times a year at an annual interest rate r. (or) Where, FVIF,, is the future value interest factor ati% for n periods equal( +i)" Computation of FV, shall be quite simple if we make use ofzeither the calculator or the future value table showing values of (1 +i)". PROBLEM 1: If you deposit Rs.1,000 today in a aS pays 10% interest compounded annual, how much wil the depost grow aftr 8 eid 12 years (12 - sient ‘Deposit after By = Rs.2,144 and 12y = Rs.3,138) Note: PROBLEM 2: 2,000 is invested at annual rate of interest of 10%. What is the amount after 2 years if the compounding is done? a) Annually? b) Semi annually? (SM, MTP17\(Ans.: Amount after 2 years annually Rs,2,420, semi annually Rs.2,431) Note: PROBLEM 3: What annual rate of interest compounded annually doubles an of interest 10.41%) Note: PROBLEM 4: A company offers a Fixed deposit scheme whereby Rs.10,000 matures to Rs.12,626 after 2 years, on a half-yearly compounding basis. If the company wishes to amend the scheme by compounding interest every quarter, what will be the revised maturity value? (PM(Ans.: Revised maturity value Rs.12,670) Note: DEL 4 - CALCULATION OF PRESENT WALUE OF A SINGLE AMOUNT PRESENT VALUE: It is the current value of a "Future Amount’. It can also be defined as the ‘amount to be invested today (Present Value) at a given rate over specified period to equal the “Future Amount’ IPCC_38e_F.M. (Problems)_ Time Value of Money 1.2No.1 for CAICWA & MECICEC MASTER MINDS Since finding present value is simply the reverse of finding Future Value (FV), the formula forFuture Value (FV) can be readily transformed into a Present Value formula. Therefore the Present Value (Po), becomes:~ FV, 7 iy» | Where, Pam aap OF PE PM(tD FVn= Future value n years hence Rate of interest per annum n= Number of years for which discounting is done, Computation of PVn shall be quite simple if we make use of either the calculator or the Present value table showing values of (1-+i)” Note: a) The process of computing the present value of future cash flows is called “Discounting” b) The interest rate used to discount the future cash flow is known as “Discount rate” ¢) The expression 1/(1+i)" is called “Discounting factor’. PROBLEM 5: Calculate the amount which Mr. Shyam should deposit now to receive Rs.50,000 after 15 years. The interest rate is 9 per cent. (PM, EXERCISE) (Ans :Deposit Rs. 13,750) Note: PROBLEM 6: The cost of a new mobile phone is Rs.10,000. If the interest rate is 5 percent, how much would you have to set aside now to provide this-sum in five years? =) (Ans.: Amount set a side Rs. 7,840) Note: PROBLEM 7: An investor has two optio, Rs.9,000 after 4 years. Assuming a di should he opt for? ws [Ans.: if discount rate 10% RQ) option (b) if discount rate 20% then option (a) is advisable} jo0se from: (a) Rs.6,000 after 1 year; (b) ate of (i) 10% and (ii) 20%, which alternative Note: PROBLEM 8: A person opened an account on April, 2012 with a deposit of Rs. 800. The account paid 6% interest compounded quarterly. On October 1, 2012, he closed the account and added enough additional money to invest in a 6-month Time Deposit for Rs. 1,000 earning 6% compounded monthly. i) How much additional amount did the person invest on October 1? ii) What was the maturity value of his Time Deposit on April 1, 2013? iii) How much total interest was earned? (SM)[Ans..:() R8.176.82 ,(i) Rs.1030.38, (ii) Rs.54.56) Note: MODEL 5 - CALCULATION OF AMOUNT OF ANNUITY / FV OF ANNUITY IMMEDIATE ANNUITY: An annuity is a stream of regular periodic payments made or received for a ‘specified period of time. In an ordinary annuity, payments or receipts occur at the end of each period. The interval is generally year, but it may be half year, quarter or month In fact, annuity means an installment. LLC Premium, Deposits into a recurring account, loan installments of homes or automobiles are examples of Annuities. IPCC_38e_F.M. (Problems)_ Time Value of Money 1.38851 25025/26 Please note that: a) The size of each payment of an annuity is called “Periodic payment”. b) Time interval between 2 successive payment dates of an Annuity is called” Payment Period” or “Payment Interval”. ¢) Total time period is called “Term of Annuity”. d) An annuity which is payable forever is called “Perpetuity”. e) Present value of an annuity is equal to sum of present values of all installments, f) The total worth of all payments at the conclusion of annuity is called Amount of Annuity. g) The accumulated sum of series of periodic deposits invested for replacement of an asset or for liquidation of a loan is called "Sinking Fund”. EV OF AN ANNUITY: Future value or Amount of Annuity is the sum of future values of each individual payment at the end of each Year. FVA, =R(FVIFA,,) Where, = ou FVAn Future value annuity, R = Constant Periodic flow FVIFA\n = Future value interest factor of an annuity at i % for n period (or) Computation of future val simple if we make use annuity table FVIFA & Note: a) Itis assumed that each periodic pay jade at the end of each year! period b) Future value/ Amount of Annuity is th3$8m of future values of each individual payment. ¢) Please note that the last payment is made at the end of n year. So, it will not yield any interest. fn annuity (FVAn) shall be quite BF the calculator or the future value PROBLEM 9: A person is required to pay four equal annual payments of Rs.5,000 each in his deposit account that pays 8% interest per year. Find out the future value of annuity at the end of 4 years. (8M, PM) (Ans.: Future value of annuity Rs. 22,535) Note: PROBLEM 10: Rs. 200 is invested at the end of each month in an account paying interest 6% per year compounded monthly. What is the amount of this annuity after 10th payment? Given that (1.005) = 1.0511 (SM) (Ans.: Amount of annuity after 10” payment Rs. 2,044) Note: PROBLEM 11: ABCL Company has issued debentures of Rs. 50 lakhs to be repaid after 7 years. How much should the company invest in a sinking fund eaming 12 percent in order to be able to repay debentures? (SM) (Ans.: Investment amount Rs. 4.96 lakhs) Note: IPCC_38e_F.M. (Problems)_ Time Value of Money 1.4No.1 for CAICWA & MECICEC MASTER MINDS PROBLEM 12: XYZ Company is creating a sinking fund to redeem its preference capital of Rs. 10 lakhs issued on April 6, 2012 and maturing on April 5, 2023. The first annual payment will be made on April 6, 2012. The company will make equal annual payments and expects that the fund will earn 12 percent per year. How much will be the amount of sinking fund payment? (SM) (Ans.: Sinking fund payment Rs.36,997.35) Note: PROBLEM 13: Mr. X wish to get her daughter admitted into a medical college after 15 years from now. He will be required total Rs. 25,00,000 to get admission into the college. For this he has identified a fund, which pays interest @ 9% p.a. In this regard he wanted to know the amount to be invested in each of the following situations: i) If he decides to make annual payment into the fund at the end of each year, ii) If he decides to invest a lump sum in the fund at the end of the year, If he decides to make annual payment into the fund at the beginning of each year. (NOV16 RTP) (Ans:()Rs. 85,146.96 p.a. (i). Rs. 6,86,436.02 (i). Rs. 78,117.68. p.a.) Note: MODEL 6 - PRESENT VALUE OF ORDINARY ANNUITY /ANNUITY IMMEDIATE PRESENT VALUE OF AN ORDINARY ANNUITY: It is sum of the present values of Cash flows occur at the end of each period. It represents the amount that must be invested now to purchase the payments due in future. Unless otherwise spggified, we assume that each payment is made at the end of each payment period, that is calles Idinary Annuity’. We also assume that interest is computed at the end of each payment Where, PVA, =RIPVIFA,)} bya, = Eins ye anu, rn R istant Periodic flow PVIFin Present value interest factor of an annuity at i % for n period. Computation of PV n shall be quite simple if we make use of either the calculator or the Present value annuity table (PVIFA\,.). PROBLEM 14: Find out the present value of a 4 year annuity of Rs.20,000 discounted at 10 per cent, (SM) (Ans.: Present value of 4y annuity Rs.63,400) Note: PROBLEM 15: The ABC company expects to receive Rs.1,00,000 p.a. for a period of 10 years from @ new project it has just undertaken. Assuming a 10% rate of interest, how much would be the present value of this annuity? (Ans.: Present value of annuity Rs. 6,14,500) Note: PROBLEM 16: A doctor is planning to buy an X-Ray machine for his hospital. He has two options. He can either purchase it by making a cash payment of Rs.5 lakhs or Rs.6,15,000 are to be paid in six equal annual installments. Which option do you suggest to the doctor assuming the rate of return is 12 percent? Present value of annuity of Re.1 at 12 percent rate of discount for six years is 4.111 (PM) [Ans.: Opt (1)-cash payment Rs.6,00,000, Opt(2)- present value of annutiy Rs.4,21,378, Opt 2) is better] Note: IPCC_38e_F.M. (Problems)_ Time Value of Money 158851 25025/26 PROBLEM 17: Z plans to receive an annuity of Rs. 5,000 semi-annually for 10 years after he retires in 18 years. Money is worth 9% compounded semi-annually. a) How much amount is required to finance the annuity? b) What amount of single deposit made now would provide the funds for the annuity? ¢) How much will Mr. Z receive from the annuity? (SM) [Ans.: (a) Amount require to finance Rs.65,040, (b)Single deposit Rs.13,334.87, (<)Receiving Rs.1,00,000] Note: PROBLEM 18: Suppose you have borrowed a 3 year loan of Rs.1,00,000 at 9 per cent from your employer to buy a motorcycle. If your employer requires three equal end-of-year repayments. What is the annual instalment? and prepare loan amortization schedule. (SM) (Ans.: Annual installment Rs.39,510) Note: (MODEL 7 - PRESENT VALUE OF PERPETUITY Fixed coupon payments on permanently invested (irredeemable) sums of money are prime examples of perpetuities. PVA x = Where, R= the payment or receipt each period i= the interest rate per payment or recei Ifa deposit of Rs.1,000 is made in a savin, ‘account at 472% for an indefinite period then the yearly interest of Rs.50 is a perpetuity of iNWBEst income so long as the initial deposit of Rs.1,000 is kept unchanged. In order to find out the PV of perpetuity, the present value of each of the infinite number of cash flows should be added. But itis difficult or rather impossible to find out the PV of perpetuity. However, mathematically it can be easily calculated by using following formula: PV, = Annual Cash flowir Where, PV, is the present value of perpetuity and r is the rate of interest. PROBLEM 19: Find out the present value of an investment which is expected to give a return Of Rs.2,500 p.a. indefinitely and the rate of interest is 12% p.a (Ans.: Present value of an investment Rs.20,833) Note: PROBLEM 20: Ramesh wants to retire and receive Rs. 3,000 a month. He wants to pass this monthly payment to future generations after his death. He can earn an interest of 8% compounded annually. How much will he need to set aside to achieve his perpetuity goal? (SM) (Ans.: Amount need to set a side RS.4,52,775) Note: PROBLEM 21: A finance company makes an offer to deposit a sum of Rs.1,100 and then receive a return of Rs.80 p.a. perpetually. Should this offer be accepted if the rate of interest is 8%? Will the decision change if the rate of interest is 5%? (Ans.:Rate of interest= 7.27%) Note: IPCC_38e_F.M. (Problems)_ Time Value of Money 1.6No.1 for CAICWA & MECICEC MASTER MINDS PROBLEM 22: Find out present value of Perpetuity of Rs.400 starting in year 3 at a discount rate of 18%. (Ans.: Present value of Perpetuity Rs. 1596) Note: MODEL 8 - PRESENT VALUE OF GROWING PERPETUITY A stream of cash flows that grows at a constant rate forever is known as growing perpetuity R_Ro+g) Revo Rig)" _ gR(te9)"! __R Cail C14? HH? cog (1+i" — i-g Where, R= cash flow at the end of first period i= the interest rate per payment or receipt period A growing perpetuity may be defined as an infinite series of periodic cash flows which grow at a constant rate per period. In such a case present value of perpetuity is calculated as follows: Pv Cash flow / (rg) Where cash flow = The cash flow at the end of the first period, r rate of interest, And, 9 growth rate in perpetuity amount However, it may be noted that above formula can be used only if the rate of interest is more than the rate of growth ie. r> g, PROBLEM 23: A company is expected to declare id of Rs.2 at the end of first year from now and this dividend is expected to grow ‘every year. What is the PV of this -v of this stream of dividend Rs.40) stream of dividend if the rate of interest is 15%?, (Ans.: Note: LS PROBLEM 24: Assuming that the disS&QM rate is 7% per annum, how much would you pay to receive Rs. 50, growing at 5%, annually, forever? (SM) (Ans.:Amount pay Rs.2,500) Note: EL 9 - EFFECTIVE RATE OF INTREST It is the actual equivalent annual rate of interest at which an investment grows in value when interest is credited more often than once a year. If interest is paid m times in a year it can be found by calculating Effective Rate of Interest. PROBLEM 25: If the interest is 10% payable quarterly, find the effective rate of interest. (SM) (Ans.: Effective rate of interest 10.38%) Note: PROBLEM 26: Mr. Pinto borrowed Rs. 1,00,000 from a bank on a one-year 8% term loan, with interest compounded quarterly. Determine the effective annual interest on the loan? (PM-EXERCISE) (Ans..: Effective rate of interest 8.24%) Note: IPCC_38e_F.M. (Problems)_ Time Value of Money 178851 25025/26 www.mastermindsindia.com PROBLEM 27: Ms. A has purchased a smart phone from a shop for Rs.25,000. She has paid Rs.5,000 as down payment and the rest will be paid in equated monthly instalments (EMI) for 2 years. The interest rate charged by the bank is 14% p.a. Required: i) Calculate the amount of EMI ii) Calculate the total amount of interest payable to the bank. (RTP 17) Note: How to identify the nature of problem? v ¥ Is ita single payment? Is it a series of payments? Want to know value at Want to know value Want to know value at Want to know value a future point of time? as on today? a future point of time? as on today? v ¥ v v Future Value Present Value Future Value Present Value of Anealy of Annuity ASSIGNMENT PROBLEMS MODEL 3 - CALCULATION OF Ft IE OF A SINGLE AMOUNT PROBLEM 4: A nationalized bank issu estment certificates” for a period of 3 years. IF Rs.5,000 are invested in these tes, their maturity value becomes Rs.6,725 Assuming that the interest is compounded every year, what is the rate of interest? (Ans.:Rate of interest 10%) PROBLEM 2: X is invested Rs.2,40,000 at annual rate of interest of 10 percent. What is the amount after 3 years if the compounding is done? 1) Annually 2) Semi-annually (PM[Ans.: 1) amount after 3 years annually Rs.3,19,440 and 2) semi annually Rs.3,21,624) (MODEL 4 -PRESENT WALUE OF A SINGLE AMOUNT PROBLEM 3: What is the present value of Rs.50,000 to be received after 10 years at 10 per cent compounded annually? (SM) (Ans.: present value Rs.19,277.15) PROBLEM 4: John Smith's great uncle has promised to give him Rs.25,000 at the age 21 John will not reach this ripe old age for four more years. Assuming that he can earn 6%, calculate the amount of money that John Smith will receive as of now? (Ans.: Amount receive now Rs. 19,800) MODEL 5- FUTURE VALUE OF ANNUITY PROBLEM 5: Find the amount of an annuity if payment of Rs. 500 is made annually for 7 Years at interest rate of 14% compounded annually. (Ans.: Amount of annuity Rs.5365.25) PROBLEM 6: How much amount is required to be invested every year so as to accumulate Rs.3,00,000 at the end of 10 years if the interest is compounded annually at 10%? (SM) (Ans.: Amount required to be invested Rs.18,823.62) IPCC_38e_F.M. (Problems)_ Time Value of Money 18No.1 for CAICWA & MECICEC MASTER MINDS PROBLEM 7: A finance company advertises that it will pay a lumpsum of Rs. 10,000 at the end of 6 years to investors who deposit annually Rs.1,000. What interest rate is implicit in this offer? (Ans.: Interest rate is 20% (App)) PROBLEM 8: ABC Ltd. has Rs.10 crores bonds outstanding. Bank deposits eam 10% per annum. The bonds will be redeemed after 15 years for which purpose ABC Ltd. wishes to create a sinking fund, How much amount should be deposited to the sinking fund each year so that ABC Ltd. would have in sinking fund Rs. 10 crores to retire the entire issue of bonds? (Ans.: Amount should be doposited Rs.31,47,426) MODEL G-PRESENT VALUE OF ANNUITY PROBLEM 9: Ramanuj has taken a 20 month car loan of Rs. 6,00,000. The rate of interest is 2 per cent per annum. What will be the amount of monthly loan amortization? (SM) (Ans.; Rs.33,249.1) PROBLEM 10: Y bought a TV costing Rs. 13,000 by making a down payment of Rs. 3,000 and Agreeing to make equal annual payment for 4 years. How much would be each payment if the interest on unpaid amount be 14% compounded annually? (SM\(Ans.: Rs.3,431.71) PROBLEM 11: Suppose Adit has borrowed a 3-year loan of 10,000 at 9 per cent from his employer to buy a motorcycle. If his employer requires three equal end-of-year repayments, then calculate the annual installment. (PM-EXERCISE)(Ans.: Rs.3,951) PROBLEM 12: Z plans to receive an annuity of Rs. 5,000 semi-annually for 10 years after he retires in 18 years. Money is worth 9% compounded semi- a) How much amount is required to finance the annui PROBLEM 13: A finance company Maes an offer to deposit a sum of Rs.1,100 and then receive a return of Rs.80 p.a. perpetually. Should this offer be accepted if the rate of interest is 8%? Will the decision change if the rate of interest is 5%? (Ans.: Rate of interest 7.27%) MODEL-8 PRESENT VALUE OF GROWING PERPETUITY PROBLEM 14: A person is going to retire shortly and he wants to maintain his present standard of ving he should get a regular income of Rs.50,000 p.a, How much he has to invest now so as to earn interest perpetually. Please note that inflation is growing at the rate of 8%. Investors expected rate of return is 10%. (Ans.: Amount invest now Rs. 25,00,000) MODEL-9 EFFECTIVE RATE OF INTEREST PROBLEM 15: Bank of Delhi pays 8 per cent interest, compounded quarterly, on its money market account. The managers of Bank of Gurgaon want its money market account to equal Bank of Delhi's effective annual rate, but interest is to be compounded on monthly basis. What Nominal, or quoted, or APR rate must Bank of Gurgaon set? (SMI(Ans.: Nominal or APR rate 7.94%) ABC ANALYSIS A Category B Category G Category Classroom | 2.4,7,8,10,11,12,14,15,19,21,24.26 | 36,9,19,16,18,20.22,23 | 1,5,13,17,25 Assignment 48.13.14 379,112, 1256.10.15 IPCC_38e_F.M. (Problems)_ Time Value of Money 1.9Ph: 98851 25025/26 ‘APPENDIX-1 (TIME WALUE OF MONEY. ‘Table A.1 : Compounded Value of a given Amount ie, CVF») Period 7 7 T ] a | om | se | om | 5% om | m™ | a | 10% Tord | Tod | 1080-|LO | .080 | L060 | L070 | L080 | Toso | Li00 2 | 1020 | 2040 | 1061 | 108 | ito2 | iia | 1ia5 | 1z66 | 1ss | 1210 3 | 1030 | 1061 | 1098 ) 1425 | 1158 | 1am | 1225 | 1260 | 1295 | 1391 4 | 109 | no | 1126 | 1170 | 1216 | 1262 | 1811 | 1360} 1412 | 1464 5 | 1051 | 110s | iso | iai7 | i276 | 1338 | 140s | 1469 | 1599 | 160 6 7 8 9 oer Tia | Lies | 1265 | 1840 | 149, 1601 | 1587 | L677 | 1772 rome | 1149 | 1230 | 116 | 1407 | 104 | 1606 | a7 | 128 | 1949 zoe | 172 | 1267 | 1969 | 1477 | 1504 | uma | 1a51 | 1989 | 214 109 | 1195 | 1305 | 1423 | 1551 | 1689 | 1833 | 1999 | 2172 | 2258 11os_| m9 | isa | 1480 | 1629 | 1701 | 1967 | 2159 | 2367 | 2504 ui | 1aie | 1243) 198¢ | 1539 | 1710 | 1898 | 2105 | 2992 | 2590 | 2853 12 | aa27 | 1968 | 1426 | 160 | 1796 | 2012 | 2252 | 2518 | 2a | sis8 13 | 1438 | 1904 | 1469 | 1665 | 1896 | 2133 | 2410 | 2720 | 3.056 3452 a4 | iaas | 119 | 1s | 1732 | 1990 | 296 | 2579 | 2937 | sai) 3797 as_| ier | 1946 | 1558 | 1801 | 2079 | 2397 | 2759 | sam | so | 4177 16 | 1173 | 1373 | 1605 | 1873 2540 | 2952 | 3426 | 3.970 | 4595 1400 | 1653 | 1948 2693 | 3.159 | 3.700 | 4528 | 5.054 1428 | 1702 | 2028 2ass | 3380 | 3996 | 477 | 5560 1st | 1754 | 2107 soe | seit | aste | 5102 | 616 1496 | 1.806 | 2.191 s207_| 870 | 4661 | 550s | 6725 | eat | 2094 | 2.666 4202 | 5427 | 6.848 | 8.629 | 10885 an_| 2427 | 3.249 s.43_| 7012 | 10063 | 19.268 | 17449 ‘Compounded Value of a given Amount ie,, CVF, we | oe | um | se | se | am | son | ame | oon Taso [nae | ies [hae | aes uate | hae ] oe | nate ras | tsrr| too | saee| ssa] tomo| aon) ase] nam vaos| ve | see] tam | aser | moe | 10s | sos | ame 1574 1.630 1.689 1749 18 18%} 1939 2.005 | 2.074 asez| 1842 | 1925 | 2011 | 2300 | 2192 | 2268 | 2.986 | 2.488 1974 | 2062] 2195) 2313| 2496] 2565 | 2700| 2840 | 2.986 zai} 2353) 2602} 2660} 2825 3001 3185) 3379 3.588 ate | 2055) 2950 | soso) azre | aaun| azo | com | aa00 2.773} 3004} 3252] 3518] 3803) 4108 | 4495} 4.785 5.160 | 3.106 3.395 | 8.707 4.046 4401 4.307 5.234 | 5.695 6.192 | ‘3479 ‘3.896 4.226 4.652 6117 5.624 6176 6.777 7.430 | ae | ason| ane} sovo| soos | camo | cam | aoc | eos] 436s | 4308 | sez | 613 | sess | 7200 | 500 | 9596 | 10609 am | seas] 2st | tore| see | sorr | snaet | saz | s2a20 6.130 7.067 8.137, 9.358 | 10.748 | 12930 | 14.129 | 16.172 18.488 | ote | roo | mre | sozen | s2asa | 1aa2s | aser | moase | saans vaso | ane | 0sr6 | ansts| cass | teste | insta | 225m | 26000 ais | roasr | soe | sease | sre | anzie | sna | ase | siod sete | 11523 | 13.743 | 16.367 | 19.461 | 25.106 | 27.993 | 32.429 | 38.338 vz000 | 21281 | 26462 | s20i9 | aoeva | 50658 | 2.600 | 77368 | 95006 | 2e960 | 39.116 | 50.950 | 66.212 | 85.950 11.065 | 143.71 | 184675 | 237.376 IPCC_38e_F.M. (Problems)_ Time Value of Money 1.10for CAICWA & MECICEC MASTER MINDS ‘Table A. : Compounded Value of a given Amount ie, CVF, | Period ] n | 2m | oom | 25e | a4e | 25% | oe | orm | 6m | 20K i azo) 1920; 120[ 120] 1250/ 1260/1270 2 | ast} sass) 1513] 1588] 1.502] 1586} 1613) 1638) 1.664 3 | aya} 1sis) set] 1907) 1953] 2000, 2018) 2007) a7 4 | 244} 2215! 2280] 2564) 24st) 2520/2001) 26a) 2768 5 | 2so] 2703) 2015) 2902] 052) 3176) sg04} 9496/9572 6 7 8 9 suse] age7| 9.sa| soos] sis] om) 4s6|¢a08| 400 aot] —soay] 4250] «soe] 4768) —soa2]caa9| same) sous 4595) 4g05| 23/5380) 5960/6350, ero7) 7208/7080 sso] sev] as goon z4s1| soo.) sos) 2m) oean 10 | err] ra05| ro] asi os) sa006 | woos unan6 | 12761 11 | 80] 912) 8749] to6sr) in6ia| 12708) 9860) 18210) _164se 12 | 9850) 0872) 119] ina) sss) aso) rze05] 2s9| 21.295 13 | mo18} wae] 474) 16986, 1890/2075] apas0| aa7e9| 2996 ue | saat] 6se2| rea] amaie) 2707) asaan| 2ases| aise) ssa 15_| 11aso| sw74e| 2s] 25196 o54m0 | s0.000|_s6.002| 40ses | _asse7 16 | aunis] 24084) 27a] aia) assur] aoast| azo] sion) saans 1 | asser| 9284| sn7se) serax | sado0) soso] sasos| on4ei| 15862 vs | soz] asses) sz) deom) sssi1| osorn| taaso | ason1| onan 10 | sraos| 9725/ suors) 58560 cose) sor00 90812 | 108800| 126242 20 45.258 | 53.357 | 62.820| 73.864 86.796} 101.720 119.143! 139.380/ 162.852 a5 | Tae8| 144207) ireas7| fies 264608) soso o93625| 78006) 581.765 a0 | ossrs| se0.s) 457.904} 624620 607.799 005.004 1900477 | 645604 | 078.28 of an Annuity ic, CVA,» me | om | oe | ae | oe | om | mm | se | oe | 20% 1 | 1000 | 1.000 | 1.000 | 10007 1.000 | 1.000 | 1.000 | 1.000 | 1.000 | 1.000 2 | 2010 2020] 20%) 20% 2050 2060 | 207} 2080 | 2000 | 2.00 3 | 3030} 3060 | soo} s2z2/ aasz) sau | 225] 326 | sze| sat0 4 | 4050} save | ase | 4266 | 4210 | 437 | aso | 4506 | 4579 | son 5_| sior| 520 | 5309 | sai | 5226 | sos | 5751 | 5067 | 5005 | 6:05 | 6 | 1s | 6308 | 64s | sem | eanz | som | 750 | ta06 | 7508 | 176 7 | rma] race) co52 | a9 | s1sa | aos | ease | so20 | 9200 | 9487 a | s2a| sos) seer) oz | esi) 9se7 | 10260 | 1067 | 11028 | 11496 9 10 a 2 seo | 9.755 | 10.159 | inses | t1027 | 11401 11.978 | 12448 | 19021 | 19579 so4s2 | 10950 | 11484 | 12.006 | 1257e | 131s iasie | 144s7 | 15.199 | 15.997 nise7 | 12369 | 12808 | 13496 | 14207 | 1497 16784 | i645 | 17560 | 12.683 | 13.412 | 14.192 | 15.026 | 15.917 | 16870 17.888 | 18.977 | 20.141 | 1s | 13809 | 14680 | 15.618 | 16627 | 17713 | tassz 20.141 | 21495 | 22.959 | 24525 x4 | s49e7 | i597 | 17086 | 18202 | 19590 | 2.015 22550 | 24215 | 25010 | 15_| 16007 | 17205 | 18500 | 200m | axsz | as276 | av | orase | oosei | a1772 16 | 17258 | 1s6s9 | 2nast | a1sas | 23657 | 25673 | 27eee | a0324 | 39.009 | 95.950 at | 18490 | 20012 | 21762 | 2s6oe | ase40 | 2523 | aoeco | anzn0 | aso 18 is61s | 21412 | 23414 | 25645 | 28.2 | s0906 | a.999 | 37.450 | 41.901 | a | 20s | zee | asir7 | azar | ans | 93760 | 7979 | sass | s6018 | st.1s9 (20 22.019 | 24.297 | 26.870 | 29.778 | 33.066 | 36.786 | 40.995 | 45.762 | 51.160 | 57.275 25 | 28243 | 92.050.| seas | anus | 7.727 | suaes | 3.249 | 73105 | 047017 osaa7 | | 30 | ss7as | 4055s | 47575 | s805 | e439 | 79.058 | 94.461 | 113283 | 196.08 | 164.494 | IPCC_38e_F.M. (Problems)_ Time Value of Money AtPh: 98851 25025/26 ‘Table A.2: Compound Value of an Annuity Le, CVAF sw) um | me | me | ie | 1% | toe | re | we | tom | 20% . 7 1000 | 1.000) 1.000] 1.000] 10001 t.000) 1.000) 1.000) 2.000] i.000 2 | 2a10} 2120] 2330) 2140] 2150] 2160/ 2170) 2180} 21901 2200 3 ssa2| 3374) 407; 9.440] 3473! a.506/ s599/ 3572| 3.606 3640 4 ano} 479} 4850] 4921} 4993] 5.065) 5141] 5215) 5201] 5.368 5 | 6228] 653} e490] 6610] 62] 6877 70} 7154] 7207] 7442 6 | 7s] 81I5| asm] 8585 | 87688577 | 9207 | 94a2 | 9.483 | 9.990 7 | 9783) 10089 | 10.405) 10.790 L087 | nad 1772) 12142 | 12523 2916 8 9 189 | 12300 | 12767 | 19293) 13.727| 14240 | 14:73] asa27 | 5900 | 16490 wares | 14776) 15416 | 16085 | 16.786 | 7518 | 18255 | 19086 | 19900 | 20700 io | 16722 | 17549 | 18420 | 19597 | 20306) 21am | 22396 | 23m | 24709 | 25980 1] 18s61 20a | Brae | BBO] BAH] —BsTEG |B 200 | 28755 | —G0.408 | 9a160 w | 227s) 2413) 25650 | amram | 29002} 20850) 22s2e| sgas1| s7aa0 | 90500 12 | 26212 | 28029 20985 | 2.080 | s4asz | s07s6 | se4oe| azo | asoue | ssas7 ua | s000s | 92990 | s4ses | 97581} 40505} ago72 | 47103 | sosia | s4an 50196 La | 3440s | 97260 | 4047 | aai2 | 47580 | sx660| soto | s0s6s | os2si | 72035 [a6] aoas0 | a2758-| aera | s09a0 | S577 |—eose5 |eaaza | 72.80 | T9850 | a7 44a 17 | aso | see | sa7g9 | sone | 6507} mie7 73979 87.058 | 90022 | 105901 1 | 50306 | 55750} e172 | oasss | 15836 | e141 | ss406 | 103740 | 115.256 | 128117 1s | s6939| s4so | ro79 | 7a969 | 98.212 | 98609 | 110.285 | rasa | 198.166 | 154.740 ao | 6420 | rz0s2| scour | o1c25 | 19244 | 115280 190009 | 145.608 | 165418 | 186.688 cy 1144s | 199.394 | 155.620 [181.871 | 212-795 | 249.214 | 292.105 | 342.603 | 402.042 | 471.981 a0_| 902: | zurase | anno | aseza7 | 4047s | sooant | savas | roo.ss | ewan | usiese | ‘Table A2: Compound Value of an Annuity ie, CAF) Period | T aim | ae | 29% | 2am | oom | aoe | ome | aoe | oon | som | 1.000, 1.000 1.000|i.000[ 1.000 1.000] .000[ 1.000/ 1.000) 1.000) 1 2 2210] 2220/2930] 2.240) 2.950 © 2.260] 2.270, 2.280, 2290 2.300) 3 seu] 3.708) -3.743| 3.778381) 8.843] 3.888, 3.918, ©3954) 3.990) 4 5446] 5.524] 5.604, 5684 5.766) 5.848, 5:931| G16) ©6101] 6.187) 5 7.589] 7.740] 7.893) go4s|__8.207| 8.368, __8.533| 8.700] __8870|__ 9.043) 6 7 a 9 ioe3]~ 10.44a/v0.708| 1osso| 11.259[ 11.544) m.897| 12.196 12442) 12.756) 13321} 13740) 14371] 14615] 15.073| 15.546) 16.032} 16.534) 17.051] 17.589 vrais] 17.762] 18.490] 19123) 19.842] 20588) 21.861) 22.169] 22.996] 23.858 aims} 22670] 23.669] 24.712] 25.802] 26.040] 28.129) | 20.260) avesa| 2.015 10_| 2774] 28657] 30.113] 31.643, ss.zsa| 4945] 96.723, 38599| 40.556] 42.9 11 84003] 85.062) 38.039) 40.238) 42.566] 45.000] 47.39] 50399| s3.s18| _56.06| 12 | 42.241) 44873) 47.787| 50.985 54.208] 57.738] 61.501} 65.510, 69.780) 74.326) 13 | s1g991} 55.745] 69.778) 64.110) 68,760] 73.750] 79.106] 84853| 91.016 97.624) 14 | 62909] 69.009) 74528) 80.496) s6949| 93.925] 101.465) 109612, sigan) 127.912, 78.390] 85.191| 92.669] 100815) _109.687| 19:46] 120.860,_141,909,_159:750__167.285 95.779] 104993] 114.983) 126.011) 198.100) 151.75] 165.922) 161.868) 199.997 218.470 146.602) 129019) 142428) 167253] 173.636) 191.799) 211721) 260701) 258.145 285.011 142.439] 158.403) 176.187) 195.994) 218.045] 242.589] 269.885) 300.252, 334006 971.514 y73.381| 194251] 217-710) 244.033] 273.556) 306654) 349.754] 385.923, 491.868) 469.968, 210.755| 287.986] 268.783] 303.601] 342.945] 387384] 437.568) 494213, 558.110, 630.157, 564.220] 650944) 764596] 896.092) 1054.791| 1298617| 1454.180] 1706.800| 2002608) 2948.705| 1.111] 1767044] 2160450] ae4016| 9207.72) 994.963] 4812.01) se7a.2a2| 7162785 (S88 SES se IPCC_38e_F.M. (Problems)_ Time Value of Money 4.12No.1 for CAICWA & MECICEC MASTER MINDS Table AS : Prosent Value of a given Amount ie. PYF») Period | a | m | oe | om | oe | oe | om | mm | ow | om | tom 1 | 0990 | 0980 | 0971 | 0962 | 0952 | 094s | 0995 | 0926 | o917 | 0909 2 | aga | og | oo | 0925 | o9o7 | ogg | os7a | oss7 | os | 82s 3 0971 0.942 0.915 | 0.889 0.864 0.840 osis | 0794 | 0772 0.781 4 0961 0924 i 0.889 | 0.855 0.823 | 0.792 0.763 0.735 0.708 | 0.683 5_| 0951 | 906 | 0863 | ose | ova | o7a7 | oma | oss 0650 | osat @ | oss | ome | oma | 0700] 0746 | o705 | 0.665 | 0.690 | os05 | ones 7 | oss | oan | osis | 0760 | o7m | 066s 062 | ose | oss | oss 8 | os23 | oass | ozs | ova | ost | 0627 | ose | 0540 | oso2 | 0467 9 | oss | osa7 | 0765 | 0702 | os4s | osv osss | 0500 | 460 | o42s | 10 0.905. 0,820 O744 0676 | 0614 0558 0.508 0.463. 0.422 386 | a ‘oss | 0804 | 0722 | 0650 | 0585 | 0527 | 0475 | 0429 | 0388 | 0.3950 1 | oss | 0738 | o7or | 0625 | o5s7 | o4s7 | oase | oso7 | o2s6 | oto 13 | oar | o77 | oss. | osm | 0530 | 469 | o41s | 0368 | 0326 | 0200 x | ato | 0758 | 0681 | o57r | 050s | oaiz | 038s | ost | 02a | o2ss 1s_| oaer | oss | oes | oss5 | osm | om7 | osm | oats | 027s | 0200 16 | 0853 | 0728 | 0628 | 05% | 0458 | 0384 | 0399 | 0202 | 0282 | o2ts 17 | oa | ome | os0s | osis | o4s6 | ost: | ost | o270 | o2m1 | 198 18 | 0836 | 0700 | 0587 | 04s | o416 | 0350 | 0296 | 0250 | o212 | 280 19 | 08% | 0936 | os7 | o47s | 0996 | oa: | o27e | o2a2 | o14 | 154 20_| 082 | os7s | ssa | o4se | os77 | osiz | ozs | ows | 0178 | 019 25] azo | oso | oa7e | 037s | ozs | ozaa | ois | 014s | 0116 | 0.0m so | om | osse | ost | oans | oom | orm | ors | cov | ao7s | o0sr ‘Table AS : Present Value ofa given Amount ic. PVF x) Period a | ue | we | sme | me | ise | som | sre soe | 9e | 208 1 | oso | oa | oss | oa77 | ovo | oa | oass | ose | naa | as 2 | ome | ong | ores | ore | o7ss | ore | o7ar | ome | 0706 | osos a | om | omz | oss | osrs | o6se | oss: | ose ose | osea | os70 4 | oss | o6s6 | oats | ose | osrz | ossz | oss | ome | 0499 | o4s2 s_| ose | oser | osss | osio | o4s7 | ours | o4ss | oas7 | osi9 | 0.402 6 | 0535 | 0507 | 0480 | 0458 | o4s2 | 0410 | 0390 oa70 | oas2 | 033s 7 | o4se | o4s2 | 0425 | o4o0 | 376 | 0354 | 0333 asi | 0296 | o279 8 | oss | o4os | ots | 0951 | oae7 | 0305 | ogas 0256 | 0249 | o2aa 9 | oss | og6: | ass | 0908 | 0284 | 025s | ozs | oza6 | 0209 | oxo 10 | oss | oa | o2e5 | oxo | ozs7 | aze7 | ozo | oan | 0176 | 0162 uu] arr | oae7 [0261 | oas7 | ozs | oss | 017 | 01s | 0148 | 0185 12 | 0286 | 0257 | 021 | o2ns | o1s7 | oss | oas2 | oss? | 01m | oz 13 | 0258 | 0229 | 0204 | o1s2 | o1es | ots | ots0 | 0.116 | 0.108 | 0098 x4 | o2s2 | 0205 | o1s: | orso | ors | o125 | cam | 9.009 | 0088 | 0.078 15_| oa09 | oases | o1so | o1so | o12s | otos | 00s | aos | 007 | 0.065 16 0.188 0.163 0.141 0.123 0.107 0.093 | 0.081 0071 0.062 0.054 at | oavo | 0145 | 0125 | 010s | 00s | aoa | oon a.060 | 0.052 | 0.045 x | o1ss | 0230 | 011 | 0995 | 0.981 | 0.069 | 0059 aos | o0s4 | o038 19 0.138 O16 0.098 | 0.083 0.070 0.060 0.051 0.043 0.037 0.031 20 | o1z | o1os | oosr | oors | aosi | ans | oow | 00s | 00s | 0.025 25 | ova | 0059 | 00a | 0038 | 0090 | oom | oom | 0018 | 0013 | 0.010 wo | cos | oo | cos | oom | cos | oo | 000 0007 | 000s | 000s IPCC_38e_F.M. (Problems)_ Time Value of Money 1.43Ph: 98851 25025/26 Table A : Present Value of a given Amount ie. PVF...) Period ] ais | 22% | 23% | ee | 25% | 26m | 27% | Dee 20% | 90% 1 | oaas [osm | oais | oa0e | oaw | ozo | orer | over | ave | o7eo 2 | 06s | osm | cee | 0650 | oss | ces | 0620 | osio | oso | oss2 | 3 | ose | oss: | oss | oz | osiz | ost | o4ss | oar | oes | o4ss 4 | cage | o4st | o4s7 | 0423 | oso | 0997 | 03st | oara | ager | 0360 5_| ose | os | oss | osm | 0928 | ons | aes | oan | oe | 0260 6 1 8 9 ‘osig | 0.303 | 0289 | 027 | 0.262 | 0.250 | 0.238 | 0227 | 0.217 | 0.207 0263 | ozs | 0235 | 0222 | oz | 0198 | 0.188 | 0.178 | 0.168 | 0.159 021s | 0204 | 0191 | 0.179 | 0168 | 0.187 | 0148 | 0159 | 130 | 0.123 0180 | 0.167 | 0.185 | 0.144 | 0.134 | 0.125 | o116 | 0108 | oor | 0.004 3o_| 019 | 0197 | 01% | ore | o107 | cov | cos | 00s | ome | 0073 n | 0123 | 012 [0103 | ooo | 0.086 | 0079 | o072 | 0.066 | 0.061 | 0.056 12 | 0102 | 0092 | 0088 | o076 | 0069 | 062 | 0057 | 0.052 | oa | 0.048 13 | 0982 | 0075 | 0068 | 0081 | 0.055 | o.050 | 004 | 040 | 0037 | 0.39 14 | 0.069 | 0.082 | 0055 | oo19 | aot | 039 | 0.035 | 0.082 | 0.028 | 0.025 15__| 0057 | 051 | 0045 | o.o4 | 0.035 | oo | 0.028 | 0.025 | 0.022 | 0.020 36 | 0097 | 0042 | 0086 | 0082 | 0025 | 0025 | oom | 0019 | om? | 0.015 a | 0.099 | 0984 | 0.030 | 0.026 | 0023 | 0020 | oo17 | oo5 | os | om 18 | 0082 | 0028 | oo2t | oon | oo1s | oor | oom | m2 | 0.010 | 0.009 19 | oozr | ooas | coz | oot | oo1 | 012 | 0.12 | 0.009 | 0.008 | 0.007 20 | 0022 | 0019 | oo16 | aor | oo12 | a0. | 0.008 | 0.007 | 0.008 | 0.005 25 | 0.009 | 0007 | 0008 | 0005 | 0004 | coo | 000s | 002 | 0.002 | 0.008 30 | 0.003 | 0.003 | 0.002 | 0.002 | 9.001 | coo | 0.001 0.001 | 0.000 | 0.000 {ie Ads Prema Vilas Fore Arlyn, PYAR T a we | a | ow | a | se | om | mm | om | 9% | 10m | 1 0990 | 0980 | 0971 | ose2 | 0952) 0983 | 0995 | 05268 | 0917 | 009 2 | asm | 192} 19s} 1986} 189 1595 | 1783 | 1788) 1.89 | 1.786 3 zou | 2ase| 2629) 2775 | 2723) 2673 | 2624) 2577) 2581 | 2487 | 4 | a0} sso} 77) sea) ssi | 455] sai) ssiz| 20] 9170, 5_| ass | aria | seo | case | asym | ani | 4100 | a995 | sso | aa | 6 7 8 ° 3795 | se | saiT| 6242] 076] 4917) 4767 | 4029 | aaas | 4355 sims | carz| e200 | om | seo) sea) ase | sane | soso | 4568 7.662 7.326 7020 | 6733) 6.463 6210 5.971 5.47 5.586 5.335 8.566 8.162 1.786 7435 7.108 | 6802} 6.515 6.247 5.995 5.759, wo | san) see | sao | aim) tma| raw | tom) eno) sae 61s ni | 10s6a | s7e7 | S253 | e760 | aa06 | 7887 | 7499) 7109] 6805 | 6495 2 11.255 | 10575 | 9.954) 9.385 | 8.963 | 8.54) 7943 | 7.536) 7.161 6814 [as | azase | sree | 1062s | 0986 | osm | ease | sae | rao | rast | tae at 13.004 | 12.106 | 11.296 | 10.563 9.899) 9.295 | 8.746 8244) 7.786 7.367 15__| 13865 | 12840 | inga8 | 1118 | 10380 | 9712 | 9108 560 | 8061 | 7608 te] ene | teste Pass | vies tems] toa | paar aan] sae] ran | W 15.562 | 14.292 | 13.166 | 12166 | 11274) 10477 | 9.768) 9.122 | 8.546 | S00 7 we | wea | om | save | insse | rom | isos wooo | oar | ass | sam » 17.26 | 15679 | 14.324 | 13.134 | 12.085 | 11.158 10.336 9.604 8.950 8.365, mo_| sso | sesso | sears | i3so0 | szaco | nara tose | esis | ome | sou os | mom | reser vasis | ase) ooo | i278 | tiem | aoets | 9mm 907 20 | soe | aasov | asso | vzaxe | sara | ia765 tae | mass | oa 9427 IPCC_38e_F.M. (Problems)_ Time Value of Money 1.44No.1 for CAICWA & MECICEC MASTER MINDS ‘Table AA : Present Value of a Future Annuity ie, PVAF,«) [Period a 11% 12% 1% | 15% 16% 17% 18% 19% 20% 1 | aor | 60s asm? | eavo | oas2 | oass | oad” | caso | oans 2 | ins | 1600 ue | o26 | 160s | 1585 | 1566 | set | 1608 3 | ane | 2400 asa | 2980 | aos | 220 | 214 | 2140 | 2108 4 | aioe | 3007 ao | 2855 | 278 | 27 | 2000 | 2000 | 2509 5 | 3606 | 0s ease | saz | szra | 3309 | s1o7 | sss | 201 oat [aa jase | a7ez | 308s | as | ase | eat) aa25 7 | ana | see | aan | aso | 4009 | as22 | ase | are | 360s 8 | sis | 4968 | asso | aasr | saee | ca07 | aoe | sone | esr 9 5.537 5.328 4.946 4.772, 4.607 4.451 4303 | 4163 | 4.091 Lxo | sso | 5080 sais | soi | 4820 | 4609 | 44oe | 409 | ase ae 6.207 5.938 5.453 5.234 6.029 4.836 tase | 4487 4.327, | a2 | ease | ease sooo | san | sasz | 49s | 472 | aon | 449 | aa | e7so | eae | ss | 5583 | sas | sus | aio | ams | 4ss3 [ou | ea | soos | cow | sro | saee | saze | sone | ace | aon 15 7191 6811 6.142 5.847 5.575, 5.324 5.092, 4876 | 4.675 16 | tate | este | eso | e265 | 5901 | 5050 | saos | sam | ae08 | 4130 x | tea | 7320 | om | eave | coer | sus | sare | som | ase | aris 18 7.702 7.250 6.840 | 6.467 6.128 5818 5.594 5.273 5.033 | 4812 1 | 193 | 7366 | sos | 650 | 610s | sar | ses | sai | som | ans zo_| ro6a_| vaso | 7005 | 62s | oaso | som | sexs | sas | sam | 4svo 25 | sana | ais | a0 | esa | 64s | c0o7 | 6706 | 6467 | 6.105 | 4008 30 | scot | aoe | ras | ros | 6566 | cars | saxo | ssi7 | sae | com Table ad Period jan eae eee sme | ose | moe | ae i 0.826 | 0.820 0.813 0.806 | 0.800 0.794 0787 0.781 077% | 0.769 rsoo | a2 | aura | rast | ato | rane | aor | aso | ime | am pare | zou | aon | ras | rose | 1909 | 1806 | 180s ae | ete zeio | 2404 | 2445 | 2404 | 2962 | 2500 | 2250 | 2am | 2203 | 2168 ‘3245 | 3.67 | s.o92 | so20 | 2951 | 2685 ) 2921 | 2759 | 2700 | 2649 asos | aio | asar | sae | ase: | soma | sooo | ager | agen | asoa ara | asie | 2518 | aaa 905 | a7 | sera | 3566 saz | azn | aase | 3076 | 2999 2925 sass | sass | az7a aise | 3100 | an19 10_| 4054 | za | ago | sooo | aszo | sass | asc | a260 | 3.178 | 3.002 nr] 4377 | 4035 | a0) 776 | ses6 | ssa) 2.457 | aaa | 999) 9147 12 | 427 | 4uz7 | ages | 851 | 275 | see | 24sa | ass? | 328s | 3300 | 13 | 4362 | 4203 | 4053 | soi | 3780 | 3656 | sas | s427 asz2 azz | 14 | 442 | 4355 | 410s | 962 | sea | sons | sors | sas | 3951 9240 | 15_| dss | 415 | a1sa_| 4001 | aaso | args | se | aaa | ara 268 aae7 | avs1 | aezs | aso3 | 3990 ages | 4576 | 4301 | 4219 | 4059 | a0 | a7 | aeso | asus | saos | 3205 : 8 | 2026 | 286s | 2603 | 2715 | 2689 | 2635 | 2569 | 2saz | 24s | 2436 | : : | | | | | 16 | 4586 4357 | 4389 | 40a | | | | | T T i i | 460s | cao | 4210 | 400 | seu | see | sess | sa | gas ssn 1 | seas | daz | aaee | coor | aoa | sro | ses | as | san aan zo_|_aesr_| sso | 427 | aso | aos | save | sora | sous | aazr | sae | [as azar [asia] 4az3 | aaa7 | aos | asas | ess | asea | asia | a.sc9 THE END IPCC_38e_F.M. (Problems)_ Time Value of Money 1.45