Your banker suggests that, rather than obtaining a $90,000 mortgage over 25-years, you should simply obtain a 15-year loan for the same amount. The rate on this loan is 7.75% compounded
Monthly. By how much will your monthly payment be (higher/lower) for the 15-year loan than the
Regular payment on the 25-year loan?

Question

Quizplus · Accepted Answer

To compare the two loan options, we need to calculate the monthly payment for each loan. Let's start with the 25-year mortgage:

Using an online mortgage calculator or formula, we can find the monthly payment for a $90,000 mortgage with a 25-year term and a 7.75% annual interest rate compounded monthly:

N = 25 years x 12 months/year = 300 months
r = 7.75%/12 months = 0.64583% per month
P = $90,000

Plugging these values into the formula (or using a mortgage calculator), we find that the monthly payment would be:

M = P(r(1+r)^N)/((1+r)^N - 1)
M = $694.76

Now, let's calculate the monthly payment for the 15-year loan:

N = 15 years x 12 months/year = 180 months
r = 7.75%/12 months = 0.64583% per month
P = $90,000

M = P(r(1+r)^N)/((1+r)^N - 1)
M = $882.11

Comparing the two monthly payments, we can see that the 15-year loan has a monthly payment that is higher than the 25-year loan by $882.11 - $694.76 = $187.35. Therefore, the answer is D: higher; $167.35.

Your Banker Suggests That, Rather Than Obtaining a $90,000 Mortgage