Question

As a bright 24-year-old UNT student, you expect your next year salary (net of taxes) to be $65,000. You forecast that this salary will increase at a rate of 3% per year. You are planning to retire at the age of 65. You are planning to save 5% of your salary each year, and place these savings in investments that yield 8%. You are planning to retire in 40 years . During the 20 years of retirement, you are planning to spend equal amounts of your savings each year. How much can you spend each year?

Answer 1

P = First savings = $65,000 * 5% = $3,250

r = interest rate = 8%

g = growth rate = 3%

n = 40 years

Future Value of savings after 40 years = [P/(r-g)] * [(1+r)^n - (1+g)^n]

= [$3,250 / (8% - 3%)] * [(1+8%)^40 - (1+3%)^40]

= [$3,250 / 0.05] * [21.7245215 - 3.26203779]

= $1,200,061.44

PV = amount available for withdrawls = $1,200,061.44

r = interest rate = 8%

n = 20 years

Annual Withdrawl formula = [r*PV] / [1 - (1+r)^-n]

= [8% * $1,200,061.44] / [1 - (1+8%)^-20]

= $96,004.9152 / 0.785451793

= $122,228.9084

Therefore, the amount can be spent each year is $122,228.91