Use the actuarial method to find the payoff amount for the loan paid in full before its due date.
-Regular Monthly Payment: $329.42 APR: 10.2%
Remaining Payments After Payoff: 20

Question

Quizplus · Accepted Answer

The actuarial method for calculating the payoff amount of a loan involves determining the present value of the remaining payments, using the loan's interest rate. Given a regular monthly payment of $329.42, an APR of 10.2% (which translates to a monthly interest rate of 10.2% / 12 = 0.85%), and 20 remaining payments, the formula for the present value of an annuity can be used:$$ PV = P \times \left( \frac{1 - (1 + r)^{-n}}{r} \right) $$Where:- $PV$ is the present value (the payoff amount we're solving for),- $P$ is the payment amount ($329.42),- $r$ is the monthly interest rate (0.85% or 0.0085 in decimal form),- $n$ is the number of payments (20).Plugging in the numbers:$$ PV = 329.42 \times \left( \frac{1 - (1 + 0.0085)^{-20}}{0.0085} \right) $$$$ PV = 329.42 \times \left( \frac{1 - (1 + 0.0085)^{-20}}{0.0085} \right) $$$$ PV = 329.42 \times 19.305 \approx 6364.74 $$Therefore, the payoff amount for the loan, if paid in full before its due date, is approximately $6364.74.

Use the Actuarial Method to Find the Payoff Amount for the Loan