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14 November, 01:50

A woman is planning to retire in 10 years. She wishes to deposit a regular amount every six months until she retires, so that beginning one year following retirement she will receive annual payments of $20,000 for the next 20 years. How much must be deposited every six months if the annual nominal interestra te is 8%, compounded semiannually?

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  1. 14 November, 02:02
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    The deposit should be of $8,059.62

    Explanation:

    Giving the following information:

    A woman is planning to retire in 10 years.

    She wants to receive 20 annual payments of $20,000.

    Interest rate = 8% compunded semiannually

    To calculate the semiannual deposit, we need to use the following formula:

    FV = {A*[ (1+i) ^n-1]}/i

    A = semiannual deposit

    Isolating A:

    A = (FV*i) / {[ (1+i) ^n]-1}

    FV = 20*20,000 = 240,000

    i = 0.08/2 = 0.04

    n = 10*2 = 20

    A = (240,000*0.04) / [ (1.04^20) - 1]

    A = $8,059.62
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