Find the future values of the following ordinary annuities:

a. FV of $400 each six months for five years at a simple rate of 12 percent, compounded semiannually.

b. FV of $200 each three months for five years at a simple rate of 12 percent, compounded quarterly.

c. The annuities described in parts a and b have the same amount of money paid into them during the 5-year period and both earn interest at the same simple rate, yet the annuity in part b earns $101.76 more than the one in part a over the five years.

Why does this occur?

Instructions are listed below

Explanation:

Giving the following information:

To find the final value, we need to use the following formula:

FV = {A*[ (1+i) ^n-1]}/i

A = annual deposit

A) FV of $400 every six months for five years at a simple rate of 12 percent, compounded semiannually.

Effective rate = 0.12/2 = 0.06

FV = {400[ (1.06^10) - 1]}/0.06 = $5,272.32

B) FV of $200 every three months for five years at a simple rate of 12 percent, compounded quarterly.

A = $200

i = 0.12/4 = 0.03

n = 20

FV = {200*[ (1.03^20) - 1]}/0.03 = $5,374.08

C) The difference is that it compounds the interest gain rapidly.