Question

Find the future value of an ordinary annuity if payments are made in the amount R and interest is compounded as given. Then determine how much of this value is from contributions and how much is from interest

R=9200, 6% interest compounded semiannually for 7 years.

The future value of the ordinary annuity is $____?

Round to the nearest cent as needed

The amount from contributions is $___? and the amount from interest is $___?

Round to the nearest cent as needed

Answer 1

Here we will use the future value of annuity formula as per below:

FVA = R * ((1 + r)ⁿ - 1 / r)

where, FVA is future value of annuity, R is the periodical amount = 9200, r is the rate of interest = 6% compounded semi annually, so semi annual rate = 6% / 2 = 3% and n is the time period = 7 * 2 = 14 semi annual periods

Now, putting these values in the above formula, we get,

FVA = 9200 * ((1 + 3%)¹⁴ - 1 / 3%)

FVA = 9200 * ((1 + 0.03)¹⁴ - 1 / 0.03)

FVA = 9200 * ((1.03)¹⁴ - 1 / 0.03)

FVA = 9200 * ((1.51258972486- 1 / 0.03)

FVA = 9200 * (0.51258972486/ 0.03)

FVA = 9200 * 17.0863241618

FVA = 157194.18

So, future value of ordinary annuity is 157194.18

Amount from contributions = Annual payment * number of payments

Amount from contributions = $9200 * 14 = $128800

Amount from interest = Future value of annuity - Amount from contributions

Amount from interest = $157194.18 - $128800 = $28394.18