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

$4,907 per year
$4,907 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 reach a future value of $50,000 in 10 years at an interest rate of 5 percent, we can use the future value of an annuity formula:

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

Where:
- \(FV\) = future value (\$50,000)
- \(P\) = annual payment
- \(r\) = annual interest rate (0.05)
- \(n\) = number of years (10)

We need to rearrange this formula to solve for \(P\):

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

Now we can plug in the values:

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

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

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

Now plug that into the formula:

\[
\frac{(1.05)^{10} - 1}{0.05} \approx \frac{1.628894626777442 - 1}{0.05} \approx \frac{0.628894626777442}{0.05} \approx 12.57789253554884
\]

Now we can find \(P\):

\[
P = \frac{50,000}{12.57789253554884} \approx 3,976.00
\]

So, rounding it gives us approximately \(3,975\) per year.

Therefore, the answer is:

**$3,975 per year**.