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17 January, 13:20

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.

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  1. 17 January, 13:34
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    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
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