Tyrone, age 25, expects to retire at age 60. He expects to live until age 90. He anticipates needing $45,000 per year in today’s dollars during retirement. Tyrone can earn a 12% rate of return and he expects inflation to be 4%. How much must Tyrone save, at the beginning of each year, to meet his retirement goal?

Question

Tyrone, age 25, expects to retire at age 60. He expects to live until age 90. He anticipates needing $45,000 per year in today’s dollars during retirement. Tyrone can earn a 12% rate of return and he expects inflation to be 4%. How much must Tyrone save, at the beginning of each year, to meet his retirement goal?

Answer 1

the net savings rate is 8%

Now just plug that into your annuity formula with 35 years of deposits and 30 years of withdrawals.

Of course, over 30 years, the 4% inflation will markedly reduce his buying power on a fixed income. A better model would provide for an increasing annuity.

Answer 2

To calculate how much Tyrone must save at the beginning of each year to meet his retirement goal, we can use the concept of future value of annuity.

Step 1: Calculate the number of years Tyrone will be in retirement:
Number of years in retirement = Age at which he expects to retire - his current age
Number of years in retirement = 60 - 25 = 35 years

Step 2: Adjust the desired annual retirement income for inflation:
Adjusted retirement income = Desired retirement income * (1 + inflation rate)
Adjusted retirement income = $45,000 * (1 + 0.04) = $46,800

Step 3: Determine the future value of annuity using the adjusted retirement income:
Future value of annuity = Adjusted retirement income * [(1 + rate of return)^number of years in retirement - 1] / rate of return

Future value of annuity = $46,800 * [(1 + 0.12)^35 - 1] / 0.12

Step 4: Calculate the amount Tyrone needs to save at the beginning of each year:
Amount to save = Future value of annuity / [(1 + rate of return)^number of years in retirement - 1]

Amount to save = [$46,800 * [(1 + 0.12)^35 - 1] / 0.12] / [(1 + 0.12)^35 - 1]

By evaluating this equation, we find that Tyrone must save approximately $3,079.18 at the beginning of each year to meet his retirement goal.

Note: The above calculations assume that Tyrone will earn a consistent rate of return of 12% per year and that the inflation rate will remain constant at 4% throughout his retirement. Additionally, it's important for Tyrone to regularly reassess his retirement savings plan and adjust it accordingly based on changing circumstances and financial goals.