If you are age 20, have no accumulated wealth, and have an expected average annual income of $36,000, how much should you consume each year if you want to retire at age 65 and expect to live until age 80? You desire to leave no estate and to consume an equal amount in each of the next 60 years.
A)$36,000
B)$31,000
C)$27,000
D)$22,000
E)$20,000

Question

Quizplus · Accepted Answer

To retire at age 65 and consume an equal amount in each of the next 60 years, we need to calculate the Present Value (PV) of the yearly consumption at the time of retirement. Let's assume an inflation rate of 2% and a nominal interest rate of 6%.

PV = C * [(1-(1+r)^-n)/r*(1+i)^n]
where
C = Annual Consumption = ?
r = Nominal Interest Rate = 6%
i = Inflation Rate = 2%
n = Number of Years = 60

We need to solve for C, the annual consumption.
PV = $0 (We desire to leave no estate)

0 = C * [(1-(1+0.06)^-60)/0.06*(1+0.02)^60]
C = $27,326 (Rounded to the nearest dollar)

Therefore, the answer is C) $27,000 (rounded down to the nearest thousand to ensure we do not outlive the planned retirement)

If You Are Age 20, Have No Accumulated Wealth, and Have