A $22,500 loan is being repaid with annual payments of $4000 at the end of each year for 5 years,followed by annual payments of $2000 thereafter for as long as is needed.The interest rate is j₁= 7%.What is the outstanding balance of the loan just after the 6^th payment?

Question

Quizplus · Accepted Answer

To find the outstanding balance just after the 6th payment, we first calculate the balance after the 5th payment and then apply one more year of interest and subtract the 6th payment. The loan is initially $22,500. Each payment of $4,000 is made for 5 years at an annual interest rate of 7%. The formula for the balance after n payments is given by the formula for the remaining balance of an annuity: $B = P \left(1 + i\right)^n - PMT \left(\frac{\left(1 + i\right)^n - 1}{i}\right)$, where $B$ is the balance, $P$ is the principal, $i$ is the interest rate per period, $n$ is the number of periods, and $PMT$ is the payment amount.After 5 payments of $4,000, the balance can be calculated, and then we apply a 7% interest for one year and subtract the 6th payment of $2,000. The correct calculation shows that the balance just after the 6th payment is $7,153.27.

A $22,500 Loan Is Being Repaid with Annual Payments of $4000