Question

A family is purchasing a house and needs to finance a $195,000 mortgage from the bank with an annual percentage rate (APR) of 5.3%. The family is financing it over 30 years and making monthly payments. What is the monthly payment?
Group of answer choices

$541.67

$860.25

$1082.84

$1242.25

Answer 1

Monthly payment is $1082.84.

Solution:

Given data:

Principal = $195000

Rate per year = $5.3\% =\frac{5.3}{100}=0.053$

Rate per month = $\frac{0.053}{12} =0.004416$

Time = 30 × 12 = 360 month

To find the monthly payment using formula:

$\text{Monthly payment}=P\times\frac{r(1+r)^n}{(1+r)^n-1}$

                           $=195000\times\frac{0.004416(1+0.004416)^{360}}{(1+0.004416)^{360}-1}$

                           $=195000\times\frac{0.004416(1.004416)^{360}}{(1.004416)^{360}-1}$

If you simplify this using calculator, we get

                           $=1082.84$

Monthly payment = $1082.84

Option C is the correct answer.

Hence monthly payment is $1082.84.