Question

Ian has the choice of taking out a 25-year loan for $205,000 at 3.2% interest, compounded monthly, or the same loan at 20 years for a higher monthly payment. If he would pay a total of $93,077 in interest on the 25-year loan, how much in total would he pay in interest on the 20-year loan?

A. $93,077



B. Less than $93,077



C. More than $93,077 but less than $205,000



D. $205,000

Answer 1

B. Less than $93,077

Answer 2

Option B is correct.

Explanation:

we are given that:

Principal Amount for loan, P = $ 205,000

Rate for 25-year loan , R = 3.2 % compounded monthly

Time, T = 25 years.

Total Amount of interest paid for 25-year loan = $ 93,077

Rate for 20-year loan, R = 3.2% compounded monthly

Time, T = 20 years.

Monthly installments in 20-year loan is more than 25-year loan.

There is 5-year gap in time period of both loan.

Interest is compounded monthly means in 25-year loan Ian will pay for 60 monthly installment more than 20-year loan.

So, this implies that Total interest amount for 20-year loan will be less than total interest amount for 25-year loan instead of higher monthly installments.

Therefore, Option B is correct.