Question

Calculate the monthly payment and the portions of the payments that go to the principaland to interest during the first 3 months for a home mortgage of $100,848 with a fixed APRof 7.0% for 15 years.

Answer 1

We have to find the monthly payments for a principal of $100,848 and a fixed APR of 7.0% for 15 years.

The APR is the annual percent rate, will be used as representing the interest rate.

We can then calculate the monthly payment as:

`PMT=(P\cdot r\/m)/(1-(1+r\/m)^(-n\cdot m))`

where P is the principal, r is the APR, m is the number of subperiods per year and n is the total number of years.

Replacing with the values, we can get:

`\begin{gathered} PMT=(100848\cdot0.07\/12)/(1-(1+0.07\/12)^(-15\cdot12)) \\ \\ PMT\approx(588.28)/(1-(1.00583)^(-180))\approx(588.28)/(1-0.351)\approx(588.28)/(0.649)\approx906.44 \end{gathered}`

We can now calculate which part of the payment corresponds to interest and which one to principal payment using the simple interest to calculate the first.

For example, the first payment will have a interest payment equal to the simple interest in a period of one month and an APR of 7%:

`I=(r)/(m)\cdot P=(0.07)/(12)\cdot100848\approx588.28`

Then, the principal payment will be:

`PMT-I=906.44-588.28=318.16`

Now, for the second payment, the principal will be the previous principal minus the principal payment. Then, given that the principal is smaller, the interest portion of the payment will be smaller too and bigger the principal part of the payment.

We can then calculate it in a table as:

Answer: the monthly payment is approximately $906.44.