Question

John Adams plans to retire at the age of 62. He wants an annual income of $60,000 per year. He believes that he will live to be 87. He will draw the money at the end of each year. How much money will he need when he retires in order to support his $60,000 annual life style if he will average 12 percent per year on his retirement account?

Answer 1

Answer: John Adams will need approximately $452,401.18

Explanation:

To calculate how much money John Adams will need when he retires to support his desired annual income, we can use the present value of an annuity formula. The present value of an annuity is the lump sum amount needed today to generate a series of equal cash flows for a specific period, given an interest rate.

Here are the given parameters:

Desired annual income: $60,000
Years of retirement: 87 - 62 = 25 years
Interest rate: 12% per year

The present value of an annuity (PV) formula is as follows:

PV = Pmt * (1 - (1 + r)^(-n)) / r

Where:
Pmt = Desired annual payment
r = Interest rate (annual) in decimal form
n = Number of years

Plugging in the values:

PV = $60,000 * (1 - (1 + 0.12)^(-25)) / 0.12

PV = $60,000 * (1 - (1.12)^(-25)) / 0.12

PV = $60,000 * (1 - 0.097198) / 0.12

PV = $60,000 * (0.902802) / 0.12

PV ≈ $452,401.18

John Adams will need approximately $452,401.18 in his retirement account when he retires at the age of 62 to support his $60,000 annual lifestyle, assuming he earns an average of 12% per year on his retirement account.