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30 July, 15:57

You want to have $1.5 million in real dollars in a retirement account when you retire in 40 years. The inflation rate is 2.7% and the nominal rate of return on your investment is 10%. What real amount must you deposit each year in the account to achieve your goal?

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  1. 30 July, 16:32
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    Annual deposit = $6,952.82

    Explanation:

    Giving the following information:

    You want to have $1.5 million in real dollars in a retirement account when you retire in 40 years.

    Inflation rate = 2.7%

    Interest rate = 10%

    First, we need to deduct from the interest rate the inflation rate.

    Real interest rate = 0.10 - 0.027 = 0.073

    Now, using the following formula, we can determine the annual deposit:

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

    A = annual deposit

    Isolating A:

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

    A = (1,500,000*0.073) / [ (1.073^40) - 1]

    A = $6,952.82
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