# annuaties

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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?

• annuaties -

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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