Question

Corey buys 10 Tufflift 4-post, 4.5-ton car hoists for his parking garage at a total cost of $414,000. He finances this with a five-year loan at 7% APR with monthly payments. After he has made the first 20 payments, how much is the outstanding principal balance on his loan?

A. $291,707
B. $233,366
C. $408,390
D. $583,414

Answer 1

The outstanding principal balance on Corey's loan after 20 payments is $291,707.

Step-by-step explanation:

To calculate the outstanding principal balance on Corey's loan, we need to use the amortization formula:

Outstanding balance = P * (1 + r)^n - (PMT * ((1 + r)^n - 1) / r)

Where:
P = starting principal amount = $414,000
r = monthly interest rate = 7% / 12
n = number of payments made before the balance is calculated = 20
PMT = monthly payment

Plugging in the values, we get:

Outstanding balance = $414,000 * (1 + (7% / 12))^20 - ($414,000 * ((1 + (7% / 12))^20 - 1) / (7% / 12))

Simplifying the equation gives us:

Outstanding balance = $291,707