You have 36 years left until retirement and want to retire with $4.9 million. Yo

Question

You have 36 years left until retirement and want to retire with $4.9 million. Your salary is paid annually, and you will receive $78,000 at the end of the current year. Your salary will increase at 4.6 percent per year, and you can earn a 12.6 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))

Please help and show steps if possible

Explanation / Answer

Let you save x% of your salary

Thesavings will also increase with time

Present value of retirement savings = 4.9/(1+12.6%)^36 =

Present value of all savings = 68,361.884

68,361.884= x%*78000/1.126 + x%*78000*(1+4.6%)/1.126^2 + x%*78000*(1+4.6%)^2/1.126^3........ x%*78000*(1+4.6%)^35/1.126^36

x= 7.54%

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