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31 December, 01:17

Graham receives $640,000 at his retirement. he invests x in a twenty-year annuityimmediate with annual payments and the remaining $640, 000 - x is used to purchase a perpetuity-immediate with annual payments. his total annual payments received during the first twenty years are twice as large as those received thereafter. the annual effective interest rate is 5%. find x.

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  1. 31 December, 01:43
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    For the amount invested in the 20 year annuity immediate,

    the return will be;

    r / (1 - (1+r) ^-n) = 0.05 / (1 - 1.05^-20)

    = 0.0802425872

    = 8.02425872%

    Now, return on perpetuity-immediate = 5%

    So, 5% + 8.02425872% = 13.02425872

    for equal returns from both investments,

    X = 5 / (13.02425872) x 640,000

    = $245,695.365

    = $ 245,695.36
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