Question

1. Smart Susie began saving $5,000 a year for her retirement immediately after graduating college at age 21. She is now 30 as is Procrastinator Paul. Paul begins saving $5,000 a year at age 30, and continues doing so each year until his retirement at age 65. Smart Susie stops adding to her retirement savings after age 30, and simply lets her first 10 years of accumulated savings compound until she retires, like Paul, at age 65. Assuming each has earned and will continue to earn a 9% rate of return, how large is each savers nest egg when they reach retirement? (Hint: Assume that n = 36 for the working years, ages 30 to 65-part of the calculation and that Susie's initial contributions span 10 years, or n=10.)

Answer 1

Value of Susie's nest egg at retirement

The value of the savings at age 30 is calculated using FV function in Excel :

rate = 9% (rate of return)

nper = 10 (number of years from age 21 to 30)

pmt = -5000 (Yearly saving. This is entered with a negative sign because it is a payment into the retirement account)

FV is calculated to be $75,964.65

| Al : x x f : в =FV(9%,10,-5000) D E с 1 [Stѕ ѕвея с о 1 $75,964.65

This amount is compounded for 35 years (from age 30 to 65).

Future value = present value * (1 + rate of return)^{number of years}

Future value = $75,964.65 * (1 + 9%)³⁵

Future value = $1,550,739.90

The value of nest egg at retirement is $1,550,739.90

Value of Paul's nest egg at retirement

The value of the savings at age 65 is calculated using FV function in Excel :

rate = 9% (rate of return)

nper = 36 (number of years from age 30 to 65)

pmt = -5000 (Yearly saving. This is entered with a negative sign because it is a payment into the retirement account)

FV is calculated to be $1,180,623.61

A1 X foc =FV(9%,36,-5000) B C D 1 $1,180,623.61

The value of nest egg at retirement is $1,180,623.61