Question

A person who filed bankruptcy in the past is able to get a 30-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 $150,000 loan is 11%, compounded monthly.

Assume the person could have received the lower interest rate on the loan and saved all of the difference in the payments for the first 10 years of the loan. If this person invested this total amount in an account paying simple interest at the rate of 2.5%, how much money would have accumulated in interest by the time the mortgage is paid off?
a.
$37,395.18
b.
$74,790.37
c.
$623.25
d.
$3,739.52

Answer 1

Monthly payment at 11% (monthly rate 0.11/12) for 30 years:
PMT11 = 150000 * (0.11/12) / (1 - (1+0.11/12)^-360) ≈ $1,428.48

Monthly payment at 5% (0.05/12):
PMT5 = 150000 * (0.05/12) / (1 - (1+0.05/12)^-360) ≈ $805.23

Monthly difference saved for the first 10 years (120 months):
Δ = PMT11 − PMT5 ≈ $623.25
Amount saved after 10 years (no growth) = 120·Δ

That amount is then invested at simple interest 2.5% for the remaining 20 years, so interest earned = principal · 0.025 · 20 = 0.5 · (120·Δ) = 60·Δ.

Interest accumulated = 60 · 623.25 ≈ $37,395.18

Answer: a. $37,395.18