Question

You are taking a $5,519 loan. You will pay it back in four equal amounts, paid every 6 months, with the first payment occurring 5 years from now (the payments begin after 5 years). The annual interest rate is 11% compounded semiannually. Calculate the amount of each semiannual payment.

Answer 1

Answer:

The amount of each semiannual payment will be $2549.19

Explanation:

Loan amount = $5,519

Number of payments = 4

Semi-annual interest rate = 11%/2 = 5.5%

Let, value of each payment = X

Payment will take place at the end of 10th (end of year 5), 11th, 12th, and 13th semiannual period.  

5,519 = X/(1 + 5.5%)^10 + X/(1 + 5.5%)^11 + X/(1 + 5.5%)^12 + X/(1 + 5.5%)^13

5,519 = X×(1/(1 + 5.5%)^10 + 1/(1 + 5.5%)^11 + 1/(1 + 5.5%)^12 + 1/(1 + 5.5%)^13)

5,519 = X×2.165

X = 5,519/2.165

X = $2549.19

Therefore, the amount of each semiannual payment will be $2549.19