Question

Question
In order to have a future value of $50,000 in 10 years, determine how much money you would be required to pay annually if your interest rate is 5 percent per year.(1 point)
Responses

$3,975 per year
$3,975 per year

$4,889 per year
$4,889 per year

$441 per year
$441 per year

$4,907 per year

Answer 1

To determine how much you would need to pay annually to achieve a future value of $50,000 in 10 years at an interest rate of 5 percent, you can use the future value of an ordinary annuity formula:

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

Where:
- \( FV \) = future value
- \( P \) = annual payment
- \( r \) = interest rate per period
- \( n \) = number of periods

In this case:
- \( FV = 50,000 \)
- \( r = 0.05 \) (5%)
- \( n = 10 \)

Rearranging the formula to solve for \( P \):

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

Plugging in the values:

\[
P = \frac{50000 \cdot 0.05}{(1 + 0.05)^{10} - 1}
\]

Calculating \((1 + 0.05)^{10}\):

\[
(1.05)^{10} \approx 1.62889
\]

Then:

\[
P = \frac{50000 \cdot 0.05}{1.62889 - 1}
\]

Calculating the denominator:

\[
1.62889 - 1 \approx 0.62889
\]

Now substituting it back:

\[
P \approx \frac{2500}{0.62889} \approx 3975.58
\]

Thus, rounding to the nearest dollar, you need to pay approximately **$3,976** annually.

Among the response choices provided, the closest option is:

**$3,975 per year**.