Question

# Find the future value of an ordinary annuity if payments are made in the amount R...

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

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

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