You have 40 years left until retirement and want to retire with $4.5 million. Yo

Question

You have 40 years left until retirement and want to retire with $4.5 million. Your salary is paid annually, and you will receive $70,000 at the end of the current year. Your salary will increase at 2.5 percent per year, and you can earn a 14.2 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

Step:1 (find lump sum payment into the retirement account)

PV = FV/(1 + r)t

PV = $4,500,000/(1 + 0.142)40

PV = $22,211.01

Step:2 (solve payment)

Growing annuity equation:

PV = C {[1 – ((1 + g)/(1 + r))t ] / (r – g)}

$22,211.01 = C{[1 – ((1 + 0.025)/(1 + 0.142))40 ] / (0.142 – 0.025)}

C = $2,633.82

Step:3(percentage of your salary is)

Percentage of salary = $2,633.82/$70,000

Percentage of salary = 0.0376, or 3.76%

PV = FV/(1 + r)t

PV = $4,500,000/(1 + 0.142)40

PV = $22,211.01

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