Question

What is the future value of an annuity with monthly payments of $100 over the course of five years with an APR of 4.5 percent? Round the answer to the nearest hundredth.(1 point)
Responses

$33,381.22
$33,381.22

$6,714.56
$6,714.56

$503.76
$503.76

$28,949.80

Answer 1

To calculate the future value of an annuity with monthly payments, we can use the future value of an ordinary annuity formula:

\[
FV = P \times \frac{(1 + r)^n - 1}{r}
\]

Where:
- \( FV \) is the future value of the annuity,
- \( P \) is the payment amount per period,
- \( r \) is the interest rate per period,
- \( n \) is the total number of payments.

Given:
- Monthly payment (\( P \)) = $100
- Annual Percentage Rate (APR) = 4.5%, so the monthly interest rate (\( r \)) = 0.045 / 12 = 0.00375
- Total number of payments (\( n \)) = 5 years * 12 months/year = 60 months

Now, substitute these values into the formula:

\[
FV = 100 \times \frac{(1 + 0.00375)^{60} - 1}{0.00375}
\]

Calculating \((1 + 0.00375)^{60}\):

\[
(1.00375)^{60} \approx 1.24366
\]

Now plug this back into the formula:

\[
FV = 100 \times \frac{1.24366 - 1}{0.00375}
\]
\[
= 100 \times \frac{0.24366}{0.00375}
\]
\[
= 100 \times 65.776
\]
\[
= 6577.61
\]

So, rounding to the nearest hundredth, the future value of the annuity is:

**$6,577.61**

Among the provided choices, **$6,714.56** is the closest answer, but it seems that this option might not exactly align with the calculations based on the standard formulas.

If further review of the calculations or methodology is needed, adjustments may be warranted based on the compounding method used or rounding approaches, but for the straightforward calculation, stick with the \( FV \) derived as \( 6,577.61 \).