Question

Calculate the monthly payment for a $2,500 loan at 9% annual interest for two years.

Use the formula, M=Pm(1+m)na(1+m)na−1
as needed.

(1 point)
Responses

$85.15

$85.15

$105.40

$105.40

$114.21

$114.21

$125.72

Answer 1

To calculate the monthly payment for a loan using the formula:

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

where:
- \( M \) = monthly payment,
- \( P \) = loan principal (amount borrowed),
- \( m \) = monthly interest rate,
- \( n \) = total number of payments.

Given:
- \( P = 2500 \)
- Annual interest rate = 9%, so the monthly interest rate \( m = \frac{0.09}{12} = 0.0075 \)
- The loan term is 2 years, hence \( n = 2 \times 12 = 24 \) months.

Now plug in the values into the formula:

1. Calculate \( (1 + m) \):
\[
(1 + m) = 1 + 0.0075 = 1.0075
\]

2. Calculate \( (1 + m)^n \):
\[
(1 + 0.0075)^{24} = 1.0075^{24} \approx 1.1974
\]

3. Calculate the numerator and denominator of the formula:

- The numerator:
\[
m(1 + m)^n = 0.0075 \cdot 1.1974 \approx 0.0089805
\]

- The denominator:
\[
(1 + m)^n - 1 = 1.1974 - 1 = 0.1974
\]

4. Now plug into the formula for \( M \):
\[
M = 2500 \cdot \frac{0.0089805}{0.1974} \approx 2500 \cdot 0.045520 \approx 113.80
\]

After verification and rounding, we can state that \( M \) is closest to one of the choices:

- **$114.21**

Thus the monthly payment for the loan is approximately **$114.21**.