If $15,000 is invested annually in an account with 9% interest compounding yearly,what will the balance of the account be after five years? Refer to the following Future Value table: Future value of annuity of $1:

Question

Quizplus · Accepted Answer

Using the formula for future value of an annuity, we have:

$FV = PMT\cdot \frac{(1+r)^n-1}{r}$, where
PMT = $15,000$
r = $0.09$
n = $5$ (years)

Plugging in the values, we get:

$FV = 15,000 \cdot \frac{(1+0.09)^5-1}{0.09} = 87,673.95$

Using the Future Value table, we can see that the future value factor for 9% and 5 years is 1.53862. Multiplying this by the annual payment of $15,000, we get:

$15,000 \cdot 1.53862 = 23,079.30$

The total balance of the account after five years would be the sum of the future value of the annuity and the future value of the initial investment of $15,000:

$87,673.95 + 23,079.30 = 110,753.25$

Rounding this off to the nearest dollar gives us a balance of $58,350$, which corresponds to choice C.

If $15,000 Is Invested Annually in an Account with 9