You have 30 years left until retirement and want to retire with $3.0 million. Yo

Question

You have 30 years left until retirement and want to retire with $3.0 million. Your salary is paid annually, and you will receive $40,000 at the end of the current year. Your salary will increase at 2.0 percent per year, and you can earn a 15.0 percent return on the money you invest. If you save a constant percentage of your salary, what percentage of your salary must you save each year? (Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16)) Percent of salary to save %

Explanation / Answer

We need to find the lump sum payment into the retirement account.

The present value of the desiredamount at retirement is = FV/(1 +r)^t = $3,000,000/(1 + 0.15)^30 = $45,309.16

This is the value today. Since the savings are in the form of a growing annuity, we can use the growing annuity equation and solve for the payment.

Doing so, we get: PV =C{[1–((1 +g)/(1 +r))t] / (r–g)}

$45309.16 =C{[1–((1.02)/(1.15))^30] / (0.13)}

C = $ 6,057.37

This is the amount you need to save next year.

So, the percentage of your salary is = $6057.37/$40,000 = 15.14%

Note that this is the percentage of your salary you must save each year. Since your salary is increasing at3 percent, and the savings are increasing at 3 percent, the percentage of salary will remain constant

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