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\% =(5.3)/(100)=0.053`

Rate per month =
`(0.053)/(12) =0.004416`

Time = 30 × 12 = 360 month

To find the monthly payment using formula:

`$\text{Monthly payment}=P*(r(1+r)^n)/((1+r)^n-1)`

`$=195000*(0.004416(1+0.004416)^(360))/((1+0.004416)^(360)-1)`

`$=195000*(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.