A home buyer signed a 20-year,8% mortgage for $72,500.How much should the annual loan payments be? (Assume annual compounding.)

Question

Quizplus · Accepted Answer

To calculate the annual loan payments, we can use the formula for the present value of an annuity:
PMT = PV * (r(1+r)^n) / ((1+r)^n - 1)
where PMT is the annual loan payment, PV is the present value of the mortgage ($72,500), r is the annual interest rate (8% or 0.08), and n is the total number of payments (20 years or 20 periods).

Plugging in the values, we get:
PMT = 72,500 * (0.08(1+0.08)^20) / ((1+0.08)^20 - 1)
PMT = $7,384.07

Therefore, the annual loan payments should be $7,384, which is answer choice B.

A Home Buyer Signed a 20-Year,8% Mortgage for $72,500