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5 November, 07:38

You have just retired with savings of $1.5 million. If you expect to live for 30 years and to earn 8% a year on your savings, how much can you afford to spend each year? Assume that you spend the money at the start of each year.

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  1. 5 November, 08:35
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    The amount I can afford to spend each year is $133,241.15

    Explanation:

    The amount I can afford to spend each year can be determined using the formula for present value of annuity due which is given below:

    PV (Annuity due) = A * (1 - (1+r) ^-N) / r

    PV is the present value of the investment which is $1.5 million

    A is the annual spending which is unknown

    r is the rate of return on the investment at 8% per year

    N is the duration of investment which is 30 years

    The formula can be rewritten as

    A=PV / (1 - (1+r) ^-N) / r

    (1 - (1+r) ^-N) / r=1 - (1+8%) ^-30/8%

    =1 - (1+0.08) ^-30/0.08

    = (1-0.099377333) / 0.08

    =11.25778334

    11.25778334 is known as annuity factor

    A=$1500000/11.25778334

    A=$133,241.15
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