Question

Abbey purchased a house using a fixed rate mortgage. The annual interest rate is 4.2% compounded monthly for 20 years. The mortgage amount is $235,000. What is the monthly payment on the mortgage? This isn't a multiple choice question sadly...I have to show my work

Answer 1

Monthly payment is $1448.82

Explanation:

Given : Abbey purchased a house using a fixed rate mortgage. The annual interest rate is 4.2% compounded monthly for 20 years. The mortgage amount is $235,000.

To find : What is the monthly payment on the mortgage?

Solution : First we find the monthly payment

Formula of monthly payment

Monthly payment,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

Discount factor
`D=(1-(1+i)^(-n))/(i)`

Where, Amount = $235,000

Rate r= 4.2%=0.042

`i=(0.042)/(12)=0.0035`

Time = 20 years

`n=20*12=240`

Now, put all the values we get,

`D=(1-(1+i)^(-n))/(i)`

`D=(1-(1+0.0035)^(-240))/(0.0035)`

`D=(1-(1.0035)^(-240))/(0.0035)`

`D=(1-0.4323)/(0.0035)`

`D=(0.5677)/(0.0035)`

`D=162.2`

Monthly payment,
`M=\frac{\text{Amount}}{\text{Discount factor}}`

`M=(235000)/(162.2)`

`M=1448.82`

Approximately,monthly payment is $1448.82