Question

Liam had an extension built onto his home. He financed it for 48 months with a loan at 3.8% APR. His monthly payments were $740. How much was the loan amount for this extension?

A. $32,904
B. $46,066
C. $52,646
D. $39,485

Answer 1

To calculate the loan amount, use the present value formula for an annuity. Substituting the given values and performing the calculations, the loan amount for the extension is approximately A. $32,904.

Step-by-step explanation:

To calculate the loan amount, we can use the formula for the present value of an annuity:

Loan Amount = Monthly Payment x (1 - (1 + Monthly Interest Rate)-Number of Payments)) / Monthly Interest Rate

Using the given information:

• Monthly Payment = $740
• Number of Payments = 48 months
• APR = 3.8%

First, we need to convert the annual interest rate to a monthly interest rate. The formula for the monthly interest rate is Monthly Interest Rate = (1 + Annual Interest Rate)(1/number of months) - 1. Substituting the values, we have Monthly Interest Rate = (1 + 0.038)(1/12) - 1. Using a calculator or spreadsheet, we can calculate that the monthly interest rate is approximately 0.003135.

Now we can substitute the known values into the present value formula:

Loan Amount = $740 x (1 - (1 + 0.003135)-48)) / 0.003135

Calculating this equation yields a loan amount of approximately $32,904. Therefore, the correct answer is A. $32,904.