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# Investing and Retirement

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Suppose you want to retire in 30 years. You want to have a retirement fund from which you can draw an income of \$75,000 per year forever. How much do you need in your savings account when you retire in order to draw \$75,000 in interest every year. Assume a constant APR of 5% with monthly compounding.

Oct 12, 2018

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1- When you retire and wish to withdraw \$75,000 per year forever, then that means you must have a "Perpetual Annuity".
2 - The amount of your perpetual annuity would depend on the interest rate you are going to get on that annuity. If we assume that it will be 5% compounded monthly, then the amount of your annuity will come out as follows:

3 - You have to convert your interest rate of 5% compounded monthly to an annual effective rate. And that you do as follows: [1 + 0.05/12]^12 =5.11618978817%.

4-Then you would divide your annual payment of \$75,000 by the above annual effective rate and you would get: \$75,000 / 0.0511618978817 =\$1,465,934.67 - which would be the amount of your perpetual annuity.

5 - In order to save that amount of money over a period of 30 years, or 360 months, you would use this financial formula to accomplish that: FV=P{[1 + R]^N - 1/ R}, Where R=Interest rate per period, N=number of periods, P=periodic payment, FV=Future value.

6 - FV=P x [[1 + R]^N - 1 / R]
\$1,465,934.67 = P x [[1 + 0.05/12]^(30*12) - 1 / (0.05/12]]
= P x [[1.004166667]^360 - 1 / (0.004166667)]]
= P x [3.467744314 / 0.004166667]
= P x               832.2586354............
PMT =\$1,465,934.67 / 832.2586354
PMT =\$1,761.39 - This is the monthly payment that you must save for 360 months to meet your future objective.

Oct 12, 2018