Find the monthly payment needed to amortize principal and
interest for the following fixed-rate mortgage.
Mortgage amount:
Term of mortgage: 25 years
Interest rate:

Ask by Sullivan Munoz. in the United States

Dec 06,2024

Question

Find the monthly payment needed to amortize principal and interest for the following fixed-rate mortgage. Mortgage amount: $$ \$ 110,300 $$ Term of mortgage: 25 years Interest rate: $$ 10.0 \% $$

UpStudy AI · Accepted Answer

To calculate the monthly payment for a fixed-rate mortgage, we can use the formula for the monthly payment $$ M $$:

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

where:
- $$ M $$ = monthly payment
- $$ P $$ = principal loan amount (mortgage amount)
- $$ r $$ = monthly interest rate (annual interest rate divided by 12)
- $$ n $$ = number of payments (loan term in months)

Given:
- $$ P = 110,300 $$
- Annual interest rate = $$ 10.0\% $$ or $$ 0.10 $$
- Term of mortgage = 25 years

First, we need to convert the annual interest rate to a monthly interest rate and calculate the total number of payments:

1. Calculate the monthly interest rate $$ r $$:
$$
r = \frac{0.10}{12} = \frac{0.10}{12} \approx 0.0083333
$$

2. Calculate the total number of payments $$ n $$:
$$
n = 25 \times 12 = 300
$$

Now we can substitute these values into the monthly payment formula:

$$
M = 110,300 \frac{0.0083333(1 + 0.0083333)^{300}}{(1 + 0.0083333)^{300} - 1}
$$

Calculating $$ (1 + r)^n $$:

$$
(1 + 0.0083333)^{300} \approx 8.646
$$

Now substituting this back into the formula:

$$
M = 110,300 \frac{0.0083333 \times 8.646}{8.646 - 1}
$$

Calculating the numerator and denominator:

$$
\text{Numerator} = 0.0083333 \times 8.646 \approx 0.072
$$
$$
\text{Denominator} = 8.646 - 1 \approx 7.646
$$

Now substituting these values into the formula:

$$
M = 110,300 \frac{0.072}{7.646} \approx 110,300 \times 0.009426 \approx 1,039.36
$$

Thus, the monthly payment needed to amortize the principal and interest for the mortgage is approximately:

$$
\boxed{1,039.36}
$$
The monthly payment for the mortgage is approximately \$1,039.36.

Find the monthly payment needed to amortize principal and
interest for the following fixed-rate mortgage.
Mortgage amount:
Term of mortgage: 25 years
Interest rate:

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