Question

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?

Answer 1

Instructions are listed below

Step-by-step 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.