Question

#9 The available interest rate on a $200,000 house is 7% per year. What are themonthly payments for a 30 year loan and 15 year loan?

Answer 1

For the 30 year loan, the monthly payments will be of $1330.6.

For the 15 year loan, the monthly payments will be of $1797.66

Explanation:

The formula for the monthly payment is given by:

`M=P((i(1+i)^n)/((1+i)^n-1))`

In which:

P is the principal(the price of the house).

i is the monthly interest rate.

n is the number of payments.

30 year loan:

$200,000 house, so P = 200,000.

Interest rate of 7%, YEARLY. So monthly, we have that i = 0.07/12.

Monthly payments for 30 years. Then n = 30*12 = 360. So the monthly payment is:

`M=200000\ast(((0.07)/(12)(1+(0.07)/(12))^(360))/((1+(0.07)/(12))^(360)-1))=1330.6`

For the 30 year loan, the monthly payments will be of $1330.6.

15 year loan:

Now, the only thing that changes is the number of monthly payments.

15 years, each with 12 months. 15*12 = 180, so n = 180.

`M=200000\ast(((0.07)/(12)(1+(0.07)/(12))^(180))/((1+(0.07)/(12))^(180)-1))=1797.66`

For the 15 year loan, the monthly payments will be of $1797.66