A loan of $12,000 with interest at 14% compounded annually is to be amortized by equal payments at the end of each year for six years.
-What is the outstanding principal just after the fifth payment?

Question

Quizplus · Accepted Answer

To find the outstanding principal just after the fifth payment, we first need to calculate the annual payment amount using the formula for the present value of an annuity: $P = \frac{PMT}{r} \left(1 - \frac{1}{(1+r)^n}\right)$, where $P$ is the loan amount, $PMT$ is the annual payment, $r$ is the annual interest rate, and $n$ is the number of payments. Rearranging to solve for $PMT$, we get $PMT = P \frac{r}{1 - (1+r)^{-n}}$. Plugging in the given values ($P = $12,000$, $r = 0.14$, $n = 6$), we find the annual payment amount.Next, to find the outstanding principal after the fifth payment, we treat the situation as if a new loan is taken out for the remaining balance with one year left. Using the annuity formula again but with $n = 1$ (since we're looking at the period after the fifth payment, with one payment remaining), we can solve for the new principal, which represents the outstanding balance after the fifth payment. This process involves calculating the annual payment first and then using that payment to find the remaining balance after five payments, which requires understanding of amortization schedules and the present value of annuities. The correct answer reflects the outstanding balance after applying these calculations.

A Loan of $12,000 with Interest at 14% Compounded Annually