Given the following information on a 30-year fixed-payment fully-amortizing loan, determine the remaining balance that the borrower has at the end of seven years. Interest Rate: 7%, Monthly Payment: $1,200.
A) $17,143
B) $79,509
C) $164,402
D) $180,369

Question

Quizplus · Accepted Answer

To determine the remaining balance, we need to calculate how much of the loan principal is paid off over the first seven years. The formula for the remaining balance on a fully-amortizing loan is:

Remaining Balance = Present Value * (1 + r)^n - Payment * [(1 + r)^n - 1]/r

where:
Present Value = loan amount
r = monthly interest rate (7% / 12 = 0.0058333)
n = total number of payments (30 years * 12 months/year = 360 payments)

Plugging in the numbers, we get:

Remaining Balance = $100,000 * (1 + 0.0058333)^84 - $1,200 * [(1 + 0.0058333)^84 - 1]/0.0058333
Remaining Balance = $164,402

Therefore, the best choice is C.

Given the Following Information on a 30-Year Fixed-Payment Fully-Amortizing Loan