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29 April, 03:57

Your father loans you $12,000 to make it through your senior year. his repayment schedule requires payments of $1,401.95 at the end of year for the next 15 years. what interest rate is he charging you?

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  1. 29 April, 04:10
    0
    Calculating how much the son will pay, multiply the $1401.95 x 12 = $21 029.25. Then, taking $21029.25-12000 = 9029.25 interest. So 9029.25/12000 = 75% interest which is rather high and surprising the father would charge this much to his son unless he wanted him to see the value of money and getting the loan.
  2. 29 April, 04:21
    0
    P = $12,000, the principal

    t = 15 years, the duration of the loan

    n = 12, assume monthly compounding

    n*t = 12*150 = 180

    Because there are 15 yearly payments of $1,401.95, the value of the loan is

    A = 1401.95*15 = $21,029.25

    If the interest rate is r, then

    12000 * (1 + r/12) ¹⁸⁰ = 21029.25

    (1 + r/12) ¹⁸⁰ = 1.7524

    Because 1/180 = 0.00556, therefore

    1 + r/12 = 1.7524⁰°⁰⁰⁵⁵⁶ = 1.003121

    r/12 = 0.003124

    r = 0.0375 = 3.75%

    Answer: The interest rate is 3.75%
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