Given the following information on a fixed-rate fully amortizing loan, determine the maximum amount that the lender will be willing to provide to the borrower. Loan Term: 30 years, Monthly Payment: $800, Interest Rate: 6%.
A) $6,707
B) $9,295.15
C) $13,333
D) $133,433

Question

Quizplus · Accepted Answer

To determine the maximum loan amount the lender will provide, we use the formula for the present value of an annuity because a fixed-rate fully amortizing loan's payments can be considered as such. The formula is P = PMT × [(1 - (1 + r)^-n) / r], where P is the loan amount, PMT is the monthly payment, r is the monthly interest rate (annual rate divided by 12), and n is the total number of payments (months). Given a monthly payment of $800, an annual interest rate of 6% (or 0.06/12 = 0.005 monthly), and a loan term of 30 years (or 360 months), plugging these values into the formula gives a loan amount of approximately $133,433, which matches option D.

Given the Following Information on a Fixed-Rate Fully Amortizing Loan