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28 October, 02:31

A friend wants to borrow money from you. He states that he will pay you $4,100 every 6 months for 9 years with the first payment six months from today. The interest rate is an APR of 6.4 percent with semiannual compounding. What is the value of the payments today

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  1. 28 October, 02:58
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    The value of the payment today is $ 55,447.61

    Explanation:

    A series of equal periodic payments or receipts made for certain number of period is known as annuity.

    To determine the worth of such cash flows, we discount the cash flows at a the given interest rate using the formula below:

    PV = (1 - (1+r) ^ (-n)) / r * Cash flows

    r - rate per period, n - number of periods, PV - present value

    Value of the payments today:

    r = 6.4%/2 = 3.2%

    n = 9 * 2 = 18, (there are 2 six months in a year)

    PV = (1 - (1.032) ^ (-18)) / 0.032) * 4,100

    PV = 13.5238 * 4,100

    PV = $ 55,447.61

    The value of the payment today is $ 55,447.61
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