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29 May, 04:55

Donald Martin is 30 years and wants to retire when he is 65. So far he has saved (1) $6,450 in an IRA account in which his money is earning 8.3 percent annually and (2) $4,300 in a money market account in which he is earning 5.25 percent annually. Donald wants to have $1 million when he retires. Starting next year, he plans to invest the same amount of money every year until he retires in a mutual fund in which he expects to earn 8.54 percent annually. How much will Donald have to invest every year to achieve his savings goal

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  1. 29 May, 05:21
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    Annual deposit = $4,169.59754

    Explanation:

    Giving the following information:

    Donald Martin is 30 years and wants to retire when he is 65.

    PV = 6,450 + 4,300 = $10,750

    i = 0.0854

    Number of years = 35

    First, we need to calculate the final value of the initial investment:

    FV = PV * (1+i) ^n

    FV = 10,750 * (1.0854^35)

    FV = 189,257.05

    Now, we can calculate the annual deposit required. We need to use the following formula:

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

    A = annual deposit

    Isolating A:

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

    FV = 1,000,000 - 189,257.05 = 810,742.95

    A = (810,742.95*0.0854) / [ (1.0854^35) - 1]

    A = $4,169.59754
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