Question

Time value- Annuities Personal Finance Problem 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 the (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

Answer 1

Marian Kirk wishes to select the better of two 10-years annuity, C and D. Annuity C is an ordinary annuity of $2,500 per year for 10-years and Annuity D is an annuity due of $2,200 per year for 10-years. Let us solve the given cases one by one

a) To calculate the future value of Annuity C you are required to use the general equation for future value of an ordinary annuity as given below:

.

1. Assuming 10% annual interest

2. Assuming 20% annual interest

To calculate the future value of Annuity D you are required to use the general equation for future value of an annuity due as given below:

3. Assuming 10% annual interest

4. Assuming 20% annual interest

a. The findings of Part a clearly indicate that

1. At 10% annual interest, annuity C has the greater future value than annuity D

2. At 20% annual interest, annuity D has the greater future value than annuity C

b. To calculate the present value of Annuity C you are required to use the general equation for present value of an ordinary annuity as given below:

1. Assuming 10% annual interest

2. Assuming 20% annual interest

To calculate the present value of Annuity D you are required to use the general equation for future value of an annuity due as given below:

1. Assuming 10% annual interest

2. Assuming 20% annual interest

d. The findings of Part c clearly indicate that

1. At 10% annual interest, annuity C has the greater present value than annuity D

2. At 20% annual interest, annuity D has the greater present value than annuity C

e. The findings of part b and part dare same. It can be seen that at the annual interest of 10% the present value and future value of Annuity C is greater than Annuity D. It can be observed that the amount of annuity C is greater than annuity D. In Annuity D one year extra interest will be earned when compared to ordinary annuity but this extra interest earned is less than the extra amount of annuity deposited in case of Annuity C.

Similarly it can be seen that at the annual interest of 20% the present value and future value of Annuity D is greater than Annuity C this is because in annuity D one year extra interest will be earned when compared to ordinary annuity. This extra interest earned is more than the extra amount of annuity deposited in case of Annuity C.