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31 January, 11:04

Jim Hunter has decided to retire to Florida in 10 years. What amount should Jim invest today so that he'll be able to withdraw $25,000 at the end of each year for 30 years after he retires? Assume he can invest money at 9% interest compounded annually.

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  1. 31 January, 14:01
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    The following formula is applicable;

    A=P (1+r) ^n

    Where,

    A = Total amount accrued after 10 years (this is the amount from which the yearly withdrawals will be made from for the 30 years after retirement)

    P=Amount invested today

    r = Annual compound interest for the 10 years before retirement

    n = Number of years the investments will be made.

    Therefore,

    A = Yearly withdrawals*30 years = $25,000*30 = $750,000

    r = 9% = 0.09

    n = 10 years

    P = A/{ (1+r) ^n} = 750,000/{ (1+0.09) ^10} = $316,808.11

    Therefore, he should invest $316,808.11 today.
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