How Much Did Fozzie Pay for the Loan?
What is the total yield rate of Kermit on both the original loan and the sale to Fozzie? How much did Fozzie pay for the loan?
Gonzo borrows 22200 dollars from Kermit at an effective rate of 9.1 percent, and agrees to make 20 equal annual payments (the first a year from now) to repay the loan. Immediately after Gonzo makes the 4th payment, Kermit sells the loan to Fozzie. If Kermit's total yield rate (on both the original loan and the sale to Fozzie) is 3.4 percent effective, how much did Fozzie pay for the loan?
Answer:
Fozzie paid approximately $19,579.84 for the loan.
To find out how much Fozzie paid for the loan, we need to calculate the present value of the remaining payments Gonzo has to make. The present value is the current value of future cash flows, taking into account the interest rate.
First, we calculate the present value of the remaining 16 payments using the effective rate of 3.4 percent. Each payment is equal, so we can use the formula for the present value of an annuity. Plugging in the values, we find that the present value of the remaining payments is approximately $15,933.72.
Next, we calculate the present value of the 4th payment that Gonzo already made. Using the same formula with the effective rate of 3.4 percent, we find that the present value of the 4th payment is approximately $3,646.12.
Finally, we add the present values of the remaining payments and the 4th payment to get the total present value, which is approximately $19,579.84. This is the amount that Fozzie paid for the loan.