Time value-Annuities Personal Finance Problem Marian Kirk wishes to select the b

Question

Time value-Annuities Personal Finance Problem Marian Kirk wishes to select the better of two 11-year annuities, C and D. Annuity C is an ordinary annuity of $1,820 per year for 11 years. Annuity D is an annuity due of $1,680 per year for 11 years. a. Find the future value of both annuities at the end of year 11, 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 11 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.

Explanation / Answer

Hello

I'm solving this problem using excel. If you want it through any other means, let me know.

In ordinary Annuity, payment is made/ received at the end of each period where as in Annuity Due, payment is made in the beginning of the period.

(e) The difference between present value/future value of annuity due and ordinary annuity is based on the timings of payment and the difference in amounts(it is variable in respect to the discounting rates, as the number of period increases, with constant amount, the later payments make lesser ans lesser effect on PV and more and more effects on present value) and hence, receiving payment early/1 year late have a huge impact.

All these factors explain the contrast and reason between the results of (b) and (d).

I hope this solves your doubt.

Feel free to comment if you still have any doubt.

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Ordinary Annuity Annuity Due Formulas Used Yearly Payment 1820 1680 No. of Installments 11 11 (a) Future Value at r=7% ($28,726.15) ($28,372.60) =FV(0.07,11,C5,0,0) =FV(0.07,11,D5,0,1) Future Value at r=14% ($41,941.02) ($44,134.86) =FV(0.14,11,C5,0,0) =FV(0.14,11,D5,0,1) (b) At r = 7% Greater Lower At r = 14% Lower Greater c) Present Value at r=7% ($13,647.59) ($13,479.62) =PV(0.07,11,1820,0,0) =PV(0.07,11,1680,0,1) Present Value at r=14% ($9,923.97) ($10,443.07) =PV(0.14,11,1820,0,0) =PV(0.14,11,1680,0,1) (d) At r = 7% Greater Lower At r = 14% Lower Greater

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