Question

Nick plans to retire at age 67, and estimates that $63,600 a year in retirement for 28 years will be needed. That annual amount will be paid out in monthly income checks. To save for retirement, Nick plans to put money every month into a 401k plan at work. If Nick is currently 24, how much will need to be saved each month to meet the retirement goal, assuming the retirement accounts earn an average of 6.8% per year.

Pleas show your work, starting formula and not in excel or shortcuts on a calculator.

Answer 1

Number of months in 28 years = 28 x 12 = 336

Number of months in (67 - 24) = 43 years = 43 x 12 = 516

Monthly (nominal) interest rate = 6.8%/12 = 0.57%

Monthly income after retirement = 63,600/12 = 5,300

PW of monthly income at time of retirement (after 516 months) = 5,300 x P/A(0.57%, 336) = 5,300 x 149.4534** = 792,103.05

Required monthly savings = 792,103.05 / F/A(0.57%, 516) = 792,103.05 / 3,119.4855 = $253.92

**P/A(0.57%, 336) = [1 - (1.0057)^-336] / 0.0057 = (1 - 0.1481) / 0.0057 = 0.8519 / 0.0057 = 149.4534

**F/A(0.57%, 516) = [(1.0057)⁵¹⁶ - 1] / 0.0057 = (18.7811 - 1) / 0.0057 = 17.7811 / 0.0057 = 3,119.4855