Calculating Fozzie's Payment for the Loan

Question:

How much did Fozzie pay for the loan after Kermit sells it to him following Gonzo's 4th payment?

Answer:

To find out how much Fozzie paid for the loan, we need to determine the remaining balance on the loan after Gonzo's 4th payment is made. This involves calculating the present value of the loan and subtracting the total of the 4 payments made. Let's break down the process step by step.

Calculating Remaining Balance:

Step 1: Calculate the present value of the loan using the formula:

PV = PMT * ((1 - (1 + r)^(-n)) / r)

Where PV is the present value, PMT is the equal annual payment, r is the interest rate as a decimal, and n is the number of payments.

In this case, Gonzo borrowed $18,800 with an effective interest rate of 8.9% for 13 annual payments. Plugging these values into the formula gives us the present value of the loan.

Step 2: Calculate the remaining balance after the 4th payment:

Subtract the sum of the 4 payments made from the present value of the loan. This remaining balance is the amount that Fozzie paid for the loan when Kermit sells it to him.

Conclusion:

By following these steps and calculations, we can determine the exact amount that Fozzie paid for the loan after Kermit sells it to him following the 4th payment made by Gonzo. It involves understanding the present value of an annuity and applying it to the specific loan scenario in this case.