Time value Annuities Marian Kirk wishes to select the better of two 10- year ann

Question

Time value Annuities Marian Kirk wishes to select the better of two 10- year annuities, C and D. Annuity C is an ordinary annuity of $ 2,500 per year for 10 years. Annuity D is an annuity due of $ 2,200 per year for 10 years. a. Find the future value of both annuities at the end of year 10, assuming that Marian can earn ( 1) 10% annual interest and ( 2) 20% annual interest. b. Use your findings in part a to indicate which annuity has the greater future value at the end of year 10 for both the ( 1) 10% and ( 2) 20% interest rates. c. Find the present value of both annuities, assuming that Marian can earn ( 1) 10% annual interest and ( 2) 20% annual interest. d. Use your findings in part c to indicate which annuity has the greater present value for both ( 1) 10% and ( 2) 20% interest rates. e. Briefly compare, contrast, and explain any differences between your findings using the 10% and 20% interest rates in parts b and d.

Explanation / Answer

a) future value of annuity = A*FVIFA(k,n) A=annuity k=int rate n=no of years 1)k=10% n=10 for annuity C fV=2500*15.93=39825 for annuity D=2200*15.93=35046 2)k=20% n=10 for C=2500*25.95=64875 for D=2200*25.95=57090 b) for both interest rates C has higher future value c) present value=A*PVIFA(k,n) 1) k=10 n=10 for C=2500*6.14=15350 for D=2200*6.14=13508 2) k=20 n=10 for C=2500*4.19=10475 for D=2200*4.19=9218 D) for both interest rates C has higher present value e) for both the interest rates the one with higher annuity value will have higher present and future value

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