Question

Marian Kirk wishes to select the better of two 9​-year annuities. Annuity 1 is an ordinary annuity of ​$1,900 per year for 9 years. Annuity 2 is an annuity due of ​$1,730 per year for 9 years.

a.  Find the future value of both annuities at the end of year 9​,assuming that Marian can earn​ (1) 7% annual interest and​ (2) 14​% annual interest.

b.  Use your findings in part a to indicate which annuity has the greater future value at the end of year 9 for both the​ (1) 7 % and​ (2) 14​% interest rates..

c.  Find the present value of both​ annuities, assuming that Marian can earn ​(1) 7​% annual interest and​ (2) 14​% annual interest.

d.  Use your findings in part c to indicate which annuity has the greater present value for both the​ (1) 7​% and​ (2) 14​% interest rates.

e. Briefly​ compare, contrast, and explain any differences between your findings using the 7​% and  14​% interest rates in parts b and d.

Answer 1

for formulas used, refer to the next image -

B9 1 at 7% at 14% annuity 1_annuity 2 annuity 1 annuity 2 annuity amount 1,900 1,730 rate period annuity amount 1,900 rate 1,730 14% 14% period annuity 1 annuity 2 $ 30,562 $ 31,724 annuity 2 has higher greater future value annuity 1 annuity 2 future value future value 10 b)annuity 1 has higher greater future value. 12 13 14 15 16 17 18 resent value $ 12,379 $ 12,060 resent value 9,398 $ 9,755 d)annuity 1 has higher greater present value. annuity 2 has higher greater present value here is no difference in findings At 7%, annuity 1 is better, both in terms of FV and PV At 1496, annuity 2 is better, both in terms of FV and PV 20 21

B9 1 at 796 annuity1 at 14% annuity1 annuity 2 annuity2 annuity amount 1900 rate period 1730 0.07 annuity amount 1900 1730 0.14 0.07 rate 0.14 annuity1 annuity 2 annuity1 annuity 2 a) future value FV(D5,D6,D4,0,0) FV(E5,E6,E4,0,1) future value FV(H5,H6,H4,0,0) FV(15,16,14,0,1) annuity 2 has higher greater future value annuity 1 10 annuitv 1 has higher greater future value 13 14 15 16 17 18 19 20 21 annuity1 annuity 2 annuity2 c) present value PV(D5,D6,D4,0,0PV(E5,E6,E4,0,1 present value PV(H5,H6,H4,0,0)PV(15,16,14,0,1) annuity 1 has higher greater present value annuity 2 has higher greater present value there is no difference in findings At 7%, annuity 1 is better, both in terms of FV and PV At 14%, annuity 2 is better, both in terms of FV and PV