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30 August, 01:26

What is the value today of $3,200 per year, at a discount rate of 10 percent, if the first payment is received 6 years from today and the last payment is received 20 years from today?

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  1. 30 August, 03:16
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    First, we calculate the present value in year 5 of the annuity and then once again calculate the present value of this result to get the value today

    Present value an annuity = P * (1 - (1+r) ^-n) / r

    where P = 3200, r = 0.10 and n = 15 payments (from year 6 to year 20)

    Present value of the annuity in year 5 = 3200 * (1 - (1+0.10) ^-15/) 0.10

    Present value of the annuity in year 5 = 3200 * (1-1.10^-15) / 0.10

    Present value of the annuity in year 5 = 24,339.45

    Now with 24,339.45 as the FV, we calculate the present value today as

    PV today = FV / (1+r) ^n = 24339.45/1.10^5

    PV today = 15,112.89

    Value today = $15,112.89
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