Question

Use the formula or a calculator application to find the monthly payment on a home mortgage of ​$286 comma 922 at 5.100​% interest for 20 years.

Answer 1

To calculate the monthly payment on a mortgage, you can use the formula for a fixed-rate mortgage:

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

Where:
- \(M\) is the total monthly mortgage payment.
- \(P\) is the loan principal (the amount borrowed).
- \(r\) is the monthly interest rate (annual interest rate divided by 12).
- \(n\) is the number of payments (loan term in months).

For this example:
- \(P = 286,922\)
- Annual interest rate = 5.100%, so the monthly interest rate \(r = \frac{5.100\%}{100} \div 12 = \frac{0.051}{12} \approx 0.00425\)
- Loan term = 20 years, so \(n = 20 \times 12 = 240\)

Now, plug these values into the formula:

1. Calculate \(r(1 + r)^n\):
\[
(1 + r)^n = (1 + 0.00425)^{240} \approx (1.00425)^{240} \approx 2.86844
\]
\[
r(1 + r)^n = 0.00425 \times 2.86844 \approx 0.01217114
\]

2. Calculate \((1 + r)^n - 1\):
\[
(1 + r)^n - 1 \approx 2.86844 - 1 = 1.86844
\]

3. Calculate the monthly payment \(M\):
\[
M = 286,922 \times \frac{0.01217114}{1.86844} \approx 286,922 \times 0.006514715 \approx 1,868.94
\]

Thus, the monthly payment on the mortgage is approximately **$1,868.94**.