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7 October, 09:56

bob and barbara are friends. bob takes out a $10000 loan and agrees to repay it over 12 years making annual level payments at an effective rate of 5.62499%. at the same time barbara takes out a $10000 loan and agrees to repay it by making annual interest payments at an annual effective interest rate of i. she also agrees to make annual level deposits into a sinking fund that earns 4% annual effective interest so as to accumulate $10,000 at the end of the 12 years. bob and barbara discover they have the same total annual expenditures resulting from their loans. find the rate i.

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  1. 7 October, 10:21
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    5.0285%

    Explanation:

    Bob's annual payment is $1,168.37 (using a financial calculator)

    Barbara's annual interest payment = $1,168.37 - annuity that will have a future value of $10,000 in 12 years

    future value of annuity = payment x [ (1 + r) ⁿ - 1] / r

    r = 4% future value = $10,000 n = 12

    $10,000 = payment x [ (1 + 0.04) ¹² - 1] / 0.04

    $10,000 = payment x 15.0258

    payment = $10,000 / 15.0258

    payment = $665.52

    Barbara's annual interest payment = $1,168.37 - $665.52 = $502.85

    Barbara's effective interest rate i = $502.85 / $10,000 = 5.0285%
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