Solve the problem.
-Find the present value of a loan with an annual interest rate of 5.9% and periodic payments of $778.63 for a term of 7 years, with payments made and interest charged 12 times per year.
A) $96,254.83
B) $53,474.90
C) $42,779.92
D) $106,949.81

Question

Quizplus · Accepted Answer

The present value $PV$ of an annuity (in this case, a loan payment) can be calculated using the formula: $$PV = P \times \left(\frac{1 - (1 + r)^{-n}}{r}\right)$$ where $P$ is the periodic payment amount, $r$ is the periodic interest rate (annual rate divided by the number of periods per year), and $n$ is the total number of payments (years times the number of periods per year).Given:- Annual interest rate = 5.9% or 0.059 when expressed as a decimal.- Periodic payments = $778.63.- Term = 7 years.- Payments made and interest charged 12 times per year.First, calculate the periodic interest rate:$$r = \frac{0.059}{12}$$Then, calculate the total number of payments:$$n = 7 \times 12$$Substitute these values into the formula:$$PV = 778.63 \times \left(\frac{1 - (1 + \frac{0.059}{12})^{-7 \times 12}}{\frac{0.059}{12}}\right)$$This calculation will give you the present value of the loan, which is approximately $53,474.90, matching choice B.

Solve the Problem. -Find the Present Value of a Loan with an Annual