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30 September, 15:28

Maybepay Life Insurance Co. is selling a perpetual annuity contract that pays $3,000 monthly. The contract currently sells for $326,000. What is the monthly return on this investment vehicle? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.) Monthly return % What is the APR? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.) Annual percentage rate % What is the effective annual return? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e. g., 32.16.) Effective annual return %

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  1. 30 September, 19:11
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    Solution:

    1 : The interest rate that fits the lifetime cash flows to the PV of cash flows is expected here.

    PV of an equation of perpetuity:

    PV = C / r

    $326,000 = $3,000 / r

    With the interest rate, we could now solve the following:

    r = $3,000 / $326,000

    r = 0.0092 or 0.92% per month

    2 : The interest rate per month is 0.92 percent.

    In order to calculate the APR, the number of months in a year is determined by:

    APR = (12) 0.92%

    APR = 11.04%

    3 : And using the equation to find the EAR, we find:

    EAR = [1 + (APR / m) ]m - 1

    EAR = [1 + 0.0092]12 - 1

    EAR = 0.1162 or 11.62%
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