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

Answer 1

Compute the monthly payments at 13% and at 7% (nominal annual rates, compounded monthly).

Monthly rates:
r_high = 0.13/12 = 0.0108333333
r_low = 0.07/12 = 0.0058333333
n = 25*12 = 300 months
P = 130000

Monthly payment formula: PMT = P * r / (1 - (1+r)^(-n))

PMT_high ≈ 130000*(0.0108333333)/(1-(1.0108333333)^(-300)) ≈ $1,466.56
PMT_low ≈ 130000*(0.0058333333)/(1-(1.0058333333)^(-300)) ≈ $919.18

Monthly difference ≈ 1,466.56 - 919.18 = $547.38 (≈ choice a).

Saved for 5 years (60 months): saved total S ≈ 547.38*60 ≈ $32,842.80 (≈ choice b).

Invested as a lump sum at simple interest 2% for the remaining 20 years: interest = S * 0.02 * 20 = 0.4*S ≈ 0.4 * 32,842.80 ≈ $13,196.95.

Answer: c. $13,196.95.