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Kelly Malone plans to have $50 withheld from her monthly paycheck and deposited in a savingr account freorelee 8 -16 that earns 12% annually, compounded monthly. If Malone continues with her plan for twe and one-balf Future visue of an years. how much will be accumulated in the account on the date of the last deposit? annutey P4 Graph of FV of an Annulty The future value of an ondinary nimwiny is the nccume: lated value of each annaity payrnent with interest as of the date of the final payment. To ithat: point in time for the future value (f). The first payrnent is mado two periods priot io the poitit when future value is thetermined, and the final payment occurs on the future value date. Formula and Itlustration of FV of an Annuity One way to compute the futate value of an annuity ts to tive the formula to find the future value of each payment and add them. If we assume an intered rate of 15%, our calculatiod is f=5100(1+0.15)2+5100(1+0.15)1+5100(1+0.15)2=53.47.25 This is identical to using Table 82 and squmming the future values of each gayment, ot adding the future valucs of the throe payments of 1 and nsultiplying the sum by 5100. Using Future Value Table to Compute FV of an Annulty A mote ditce way is to use a table showith future values of annaitics. Such a table is called a future talu I annuity of I table. Table B,4 af ate end of this appendix is one sach table Note that in Table B a when n=1, the future values equal 1(f=1) for all rates of interer2. This ts because yach = antas: ify consicts of only one payment, and the furure valuc is determined on the date of that pay entitino time passes between the paymen and its fature value. The future value of att annuity furatila is used to coastruct Table B.4. We alwo can construct it by adding the amoents from a funure vilue of I table. To illustrite, we use Tables B,2 and B, 4 to confirm this relation for the price ex mintho Note that the furure value in Table B.2 is 1.0000 when a=0, but the future value at Table B a is 10000 when n=1. Is this a contradiction? No. When n=0 in Table B 2, the future value bs determined on the date when a single payment occurs. This means that no inlereit is earect because no time has passed, and the fumare value equals the payment. Table 8,4 describes antis. ities with equal payments oceurring at the end of esch period. When n=1. the \#nuify has one payment. and its future value equals 1 os the daie of its final and only paryment. Again, go time? passes between the payment and its future value date. ity iavestment it the end of ifive years. Solution Future valoe =$45,0006,3928=$285 \$ 76 (diing F V of antraity factor from Table B=,1=128,=5 ) (PV): f= future value (FV): i= rate of interest jer period: and n= number of periods. butel follows: (FV):i = rate of inieret per poriolly and n= number of penode. Excel fotioms: FV OF A SINGLE AMOUNT FV OF AN ANNUITY r=7+11+it Where p= present value (FV): 1= rate of interest per period: f= fulure value (FV), f= rate of intereil and 11= number of periods. Excel follows: per period; and n= number of peritids. Exed follows

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