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 $4,907 per year $4,907 per year $3,975 per year $3,975 per year $4,889 per year $4,889 per year $441 per year

Answer 1

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

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

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

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

We need to solve for \( P \):

\[
50,000 = P \times \frac{(1 + 0.05)^{10} - 1}{0.05}
\]

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

\[
(1.05)^{10} \approx 1.628894626777442
\]

So:

\[
(1.05)^{10} - 1 \approx 1.628894626777442 - 1 \approx 0.628894626777442
\]

Now plug that back into the formula:

\[
50,000 = P \times \frac{0.628894626777442}{0.05}
\]

Calculating \( \frac{0.628894626777442}{0.05} \):

\[
\frac{0.628894626777442}{0.05} \approx 12.57789253554884
\]

Then the equation becomes:

\[
50,000 = P \times 12.57789253554884
\]

Now solve for \( P \):

\[
P = \frac{50,000}{12.57789253554884} \approx 3,976.56
\]

Based on the options provided, the closest amount is **$3,975 per year**.