Find the monthly payment for a mortgage of at for 20 years.
Select one:
a.
b.
c.
d.

Ask by Tran Lowe. in the United States

Mar 21,2025

Question

Find the monthly payment for a mortgage of $$ \$ 85,500 $$ at $$ 6^{\frac{3}{4}} \% $$ for 20 years. Select one: a. $$ \$ 6,500.00 $$ b. $$ \$ 650.66 $$ c. $$ \$ 876.54 $$ d. $$ \$ 393.60 $$

UpStudy AI · Accepted Answer

We start with the formula for the monthly payment on a mortgage:

$$
\text{PMT} = P \cdot \frac{r(1+r)^n}{(1+r)^n - 1}
$$

where:
- $$ P $$ is the principal: $$ \$85,\!500 $$
- $$ r $$ is the monthly interest rate
- $$ n $$ is the total number of payments

The annual interest rate is given as $$ 6^{\frac{3}{4}}\% $$ which is equivalent to $$ 6.75\% $$ per year. Therefore, the monthly interest rate is:

$$
r = \frac{6.75\%}{12} = \frac{0.0675}{12} \approx 0.005625
$$

The loan term is 20 years, so the total number of monthly payments is:

$$
n = 20 \times 12 = 240
$$

Substitute these values into the payment formula:

$$
\text{PMT} = 85500 \cdot \frac{0.005625 \cdot (1+0.005625)^{240}}{(1+0.005625)^{240} - 1}
$$

First, compute $$ (1+0.005625)^{240} $$:

$$
(1.005625)^{240} \approx 3.843
$$

Now, calculate the numerator:

$$
0.005625 \times 3.843 \approx 0.021621
$$

Multiplying by the principal:

$$
85500 \times 0.021621 \approx 1849.39
$$

Calculate the denominator:

$$
3.843 - 1 = 2.843
$$

Thus, the monthly payment is approximately:

$$
\text{PMT} \approx \frac{1849.39}{2.843} \approx 650.66
$$

The correct answer is

b. $$ \$650.66 $$
The monthly payment is approximately \$650.66.

Find the monthly payment for a mortgage of at for 20 years.
Select one:
a.
b.
c.
d.

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Find the monthly payment for a mortgage of at for 20 years. Select one: a. b. c. d.