Question

A person who filed bankruptcy in the past is able to get a 25-year mortgage loan at a rate that is 6% higher than what they could have received if they had not filed. The interest rate this person pays on a $130,000 loan is 13%, compounded monthly.

Assume this person could have received the lower interest rate on the loan and saved all of the difference on the payments for the first five years of the loan. If this person then invested this total amount in an account paying simple interest at the rate of 2%, how much money would have accumulated in interest by the time the mortgage is paid off?
a.
$547.37
b.
$32,842.38
c.
$13,196.95
d.
$17,179.23


Please select the best answer from the choices provided.

A
B
C
D

Answer 1

C

Work (brief):
- Monthly rate at 13%: r1 = 0.13/12; at 7%: r2 = 0.07/12. Number of months n = 25*12 = 300.
- Monthly payments: P1 = 130000 * r1 / (1 - (1+r1)^-300) ≈ $1,466.37; P2 = 130000 * r2 / (1 - (1+r2)^-300) ≈ $919.00.
- Monthly savings for first 5 years = P1 − P2 ≈ $547.37. Total saved S = 60*(P1−P2) ≈ $32,842.38.
- Invested at simple interest 2% for remaining 20 years: interest = S * 0.02 * 20 = 0.4*S ≈ $13,136.95.

The closest choice is C ($13,196.95).