annuaties

Mr. Strupp expects to retire in 12 years. Beginning one month after his retirement, he would like to receive $500 per month for twenty years. How much must he deposit into a fund today to be able to do so if the rate of interest on the deposit is 12% compounded monthly?

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  1. t = 20yrs * 12mo/yr = 240mo.

    Pt = $500/mo * 240mo = $120,000.

    Pt = Po(1+r)^n = $120,000.

    r = 12%/12mo = 1%/mo = 0.01 = Monthly
    % rate expressed as a decimal.

    n = 1 comp/mo. * 240mo = 240 comp. periods.

    Po(1.01)^240 = 120,000,
    Po = 120,000 / (1.01)^240 = $11,016.70.

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