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9 June, 19:19

A company must repay the bank a single payment of $20,000 cash in 3 years for a loan it entered into. The loan is at 8% interest compounded annually. The present value of 1 (single sum) at 8% for 3 years is 0.7938. The present value of an annuity (series of payments) at 8% for 3 years is 2.5771. The present value of the loan (rounded) is:

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  1. 9 June, 20:45
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    The present value of the loan is $15,877

    Explanation:

    Solution

    Given that:

    A company must pay back the bank a single payment of = $20,000

    The loan of interest = 8%

    Present value of 1 = 8% for 3 years (0.7938)

    Present value of annuity = 8% for 3 years (2.5771

    Now,

    We solve for the loan present value

    which is,

    $20,000 * 0.7938 = $15, 877

    For the annuity (series of payment) = $20,000 * 2.5771

    = $51,542
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