You have $50,000 in savings for retirement in an investment earning a stated ann

Question

You have $50,000 in savings for retirement in an investment earning a stated annual rate of 5% compounded monthly. You aspire to have $1,000,000 in savings when you retire. Assuming you add no more to your savings, how many years will it take to reach your goal?

Please round your answer to the nearest hundredth.

Note that the HP 12c financial calculator rounds up the periods result to the next integer and will not give the correct answer to the nearest hundredth. Therefore, you should use Excel or a financial calculator that does provide decimal precision to the number of periods.

Explanation / Answer

Initial Investment Value = $ 50000 and Return Rate = 5 % compounded monthly

Monthly Rate of Return = (5/12) = 0.4167 %

Target Final Wealth Value = $ 1000000

Let the number of years required to reach target wealth value be T

Therefore, 50000 x (1.004167)^(T) = 1000000

(1.004167)^(T) = 20

T = 720.4151 years ~ 720 + (0.4151 x 12) = 720 years and 4.98 months ~ 720 years and 5 months

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