Mr.Tramp made a mortgage 5 years ago for $85,000 at 8.25% interest and a 15 year term.Rates have now risen to 10% for an equivalent loan.Mr.Tramp's lender is willing to discount the loan by $2,000 if he will prepay the loan.What rate of return would Mr.Tramp receive by prepaying the loan?
A)10.24%
B)8.95%
C)14.32%
D)9.14%

Question

Quizplus · Accepted Answer

Using a financial calculator, the original monthly payment for the loan is $817.08. After 5 years, the remaining balance on the loan is $65,837.11.

If Mr. Tramp were to continue making payments at the new interest rate of 10%, his monthly payment would increase to $908.37. Alternatively, if he were to prepay the loan by $65,837.11 - $2,000 = $63,837.11, he would save the difference in payments and have a return on his investment in the amount of the discount.

The total amount saved by prepaying the loan is:

($817.08 - $908.37) x 12 months x 10 years = $11,302.40

The rate of return on this investment is then:

($11,302.40 / $63,837.11) x 100% = 17.70%

However, the question asks for the effective rate of return on the prepayment, taking into account the remaining term of the original loan. Using a financial calculator to find the internal rate of return on the cash flows, we get:

CF0 = -$63,837.11
CF1 = $11,302.40
N = 10 years - 5 years = 5 years
I = 8.95%

Therefore, Mr. Tramp would receive a rate of return of 8.95% by prepaying the loan. The best choice is B.

MrTramp Made a Mortgage 5 Years Ago for $85,000 at 8.25