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# annuity

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Suppose a woman has decided to retire as soon as she has saved \$900,000. Her plan is to put \$1,000 each month into an ordinary annuity that pays an annual interest rate of 2.3%. In how many years will she be able to retire?

Guest Mar 8, 2017
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#1
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I don't know, but all I know is if your waiting for that long than you should probably get a better job, HA.

ClownPrinceofChaos  Mar 8, 2017
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FV = P x [1 + R]^N - 1 / R

900,000 = 1,000 x {[1 + 0.023/12]^N - 1 / [0.023/12]}

900 ={[1.001916667]^N - 1} / 0.001916667

Solve for N over the real numbers:
900 = 521.739 (1.00192^N - 1)

900 = 521.739 (1.00192^N - 1) is equivalent to 521.739 (1.00192^N - 1) = 900:
521.739 (1.00192^N - 1) = 900

Divide both sides by 521.739:
1.00192^N - 1 = 1.725

Add 1 to both sides:
1.00192^N = 2.725

Take the logarithm base 1.00192 of both sides:
Answer: |N = 523.528 - months =or about 43 years and 7.5 months.

Guest Mar 8, 2017

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