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17 January, 07:24

Sarah Wiggum would like to make a single investment and have $2.4 million at the time of her retirement in 40 years. She has found a mutual fund that will earn 5 percent annually. How much will Sarah have to invest today? If Sarah invests that amount and could earn a 15 percent annual return, how soon could she retire, assuming she is still going to retire when she has $2.4 million?

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  1. 17 January, 08:02
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    The correct answer for present value is 340,909.64 and for time is 13.96 years.

    Explanation:

    According to the scenario, the given data are as follows:

    Future value (A) = $2,400,000

    Rate of interest (r) = 5% or 0.05

    Time period = 40 years

    So, we can calculate present value by using following formula:

    P = A / ((1 + r) ^t)

    = 2,400,000 / ((1 + 0.05) ^40)

    = 2,400,000 / 7.03998871212

    = 340,909.64

    Now, we calculate time at 15% rate then,

    A = P (1 + r) ^t

    where, P = 340,909.64

    r = 15% or. 15

    A = $2,400,000

    So, by putting the value we get,

    $2,400,000 = 340,909.64 (1 + 0.15) ^t

    t = log (2400000/340,909.64) / log (1.15)

    t = 13.96 years
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