Question

Find the future values of the following ordinary annuities:

a. FV of $200 paid each 6 months for 5 years at a notminal rate of 8% compounded semiannual.

b. FV of $100 paid each 3 months for 5 years at a nominal rate of 8%, 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 nominal rate, yet the annuity in part b earns more than the one in part a over the 5 years. Why does this occur?

Answer 1

Formula to calculate future value of annuity
Future value of annuity	Annuity amount*(((1+r)^n)-1)/r
where r is interest rate and n is number of payments
a.
Calculation of future value of annuity is shown below
r	4.00%	8%/2
No of payments	10	5*2
Future value of annuity	200*(((1.04)^10)-1)/0.04
Future value of annuity	200*12.00611
Future value of annuity	$2,401.22
b.
Calculation of future value of annuity is shown below
r	2.00%	8%/4
No of payments	20	5*4
Future value of annuity	200*(((1.02)^20)-1)/0.02
Future value of annuity	200*24.29737
Future value of annuity	$4,859.47
c.
In case of (b) the compounding of interest is happening more often than in part (a)
This mean every quarter interest earned is again being invested and earnings interest
Whereas in (a) every six months interest earned is again being invested and earning interest.
The value of (b) is higher than in (a) due to increase in compounding period