Find the present value of a loan with an annual interest rate of 6.3% and periodic payments of $749.94 for a term of 8 years, with payments made and interest charged 12 times per year.
A) $101,587.38
B) $56,437.43
C) $112,874.87
D) $45,149.95

Question

Quizplus · Accepted Answer

The present value of a loan can be calculated using the formula for the present value of an annuity: $PV = P \times \left[\frac{1 - (1 + r)^{-n}}{r}\right]$, where $PV$ is the present value, $P$ is the periodic payment, $r$ is the periodic interest rate, and $n$ is the total number of payments. Given an annual interest rate of 6.3% and monthly payments, the periodic interest rate is $0.063 / 12 = 0.00525$. With payments made 12 times a year for 8 years, the total number of payments is $12 \times 8 = 96$. Substituting these values into the formula gives: $PV = 749.94 \times \left[\frac{1 - (1 + 0.00525)^{-96}}{0.00525}\right]$, which calculates to approximately $56,437.43.

Find the Present Value of a Loan with an Annual