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22 December, 17:44

What is the present value of a perpetuity that pays you annual, end-of-year payments of $950.00? Use a nominal rate (monthly compounding) of 7.75%. (Hint: use EAR).

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  1. 22 December, 18:06
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    Present value of perpetuity is $12,242.27

    Explanation:

    Nominal rate is compounded monthly so the effected rate will be different due to monthly compounding effect.

    Effective annual rate is calculated as follows

    EAR = [ (1 + r) ^n ] - 1

    EAR = [ (1 + 0.0775/12) ^12 ] - 1

    EAR = [ (1.0775) ^12 ] - 1

    EAR = 7.76%

    Present value of perpetuity = Cash flow / discount rate

    Present value of perpetuity = $950 / 7.76%

    Present value of perpetuity = $950 / 0.0776

    Present value of perpetuity = 12,242.27
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