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17 June, 20:47

Jenny wants a monthly retirement income of $12,000. She will retire on her birthday at age 70 with a $3,000 per month social security monthly benefit and a $4000 per month defined benefit pension.

She expects to die on her birthday at age 95 and would like to leave $75,000 to each of her 6 children.

She expects a 7.9% annual return on her Roth 401k. She expects a 2.6% annual rate of inflation.

How much will she need to have saved to invest when she retires?

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  1. 17 June, 21:25
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    Since she wants to receive the income per month, change the interest rate and duration on investment variables to monthly basis;

    Out of the $12,000, find Jenny's own savings after deducting social security income & Pension benefit;

    = 12,000 - 3,000 - 4,000 = $5,000

    Since the 5,000 is recurring, it will be the PMT in annuity calculation.

    If marginal tax rate = 28%, find the aftertax nominal rate;

    Pretax nominal rate = 7.9% or 0.079

    After tax nominal rate = (1-0.28) * 0.079

    After tax nominal rate = 0.05688 or 5.688%

    Next, find the real interest rate using Fisher equation that applies the nominal rate and inflation rate

    Real rate = [ (1+Nominal) / (1+inflation) ] - 1

    =[ (1+0.05688) / (1+0.026) ] - 1

    = 1.0301 - 1

    = 0.0301

    Real rate = 3.01%

    Next, using financial calculator, enter the following inputs;

    N = 95 - 70 = 25 years, but convert to months = 25*12 = 300

    I/Y = 3.01% / 12 = 0.2508%

    PMT = 5,000

    FV = 75,000*6 = 450,000

    then CPT PV = $1,265,460.78

    Therefore, she need to have saved $1,265,460.78
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