Assume a worker at age 25 with annual earnings of $45,000 who wants to retire at age 65 and expects to live until age 75.How much would the worker consume annually?
A)$40,000
B)$36,000
C)$32,000
D)$30,000
E)$28,000

Question

Quizplus · Accepted Answer

The worker has 40 years to save for retirement (from age 25 to 65) and expects to live for another 10 years after retirement (from age 65 to 75). Assuming the worker saves a constant amount annually and spends the rest, the total savings over 40 years will be used to fund 10 years of retirement. If the worker earns $45,000 annually, to find out how much they would consume annually, we need to calculate how much needs to be saved each year to allow for equal annual consumption during retirement. Let's denote the annual consumption by C and the annual savings by S. Since the total earnings are $45,000, we have C + S = $45,000. The total savings over 40 years, which is 40S, will be used to fund 10 years of retirement consumption, so 40S = 10C. By substituting the first equation into the second, we find that the worker needs to save $9,000 annually (which is $45,000 - C) to afford an annual consumption of $36,000 both before and after retirement.

Assume a Worker at Age 25 with Annual Earnings of $45,000