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

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

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

$441 per year

Answer 1

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

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

Where:
- \(FV\) is the future value ($50,000),
- \(PMT\) is the annual payment (which we are solving for),
- \(r\) is the interest rate (5% or 0.05),
- \(n\) is the number of years (10).

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

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

Plugging in the values:

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

Calculating the denominator:

\[
(1 + 0.05)^{10} = 1.628894626777442
\]

Now, subtracting 1:

\[
1.628894626777442 - 1 = 0.628894626777442
\]

Now, divide by the interest rate (0.05):

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

Now, substituting back to find \(PMT\):

\[
PMT = \frac{50000}{12.57789253554884} \approx 3,976.22
\]

Therefore, the closest answer to the calculated \(PMT\) is approximately **$3,975 per year**.