If you accumulate $800,000 in your retirement account and can earn a constant annual rate of 5% on this money after retirement, how much will you be able to live on each year if you
Expect to live for 30 years after retirement? Assume that you will make your first withdrawal
At the end of one year, and round your answer to the nearest dollar.

Question

Quizplus · Accepted Answer

To calculate the amount you can withdraw each year, you can use the formula:

Annual Withdrawal = Retirement account balance / Present Value Annuity Factor

Present Value Annuity Factor is a factor that takes into account the interest rate, time period, and frequency of payments. For this problem, we need to use a factor for a 30-year time period with annual payments and a 5% interest rate.

Using a financial calculator, we can find that the Present Value Annuity Factor is 18.643.

Plugging in the numbers, we get:

Annual Withdrawal = $800,000 / 18.643 
Annual Withdrawal = $42,828.23

However, we need to round our answer to the nearest dollar and we also need to take into account that we are making our first withdrawal at the end of one year. This means that we need to subtract one year's worth of interest from our withdrawal.

Subtracting $800,000 x 0.05 = $40,000 from $42,828.23, we get:

Annual Withdrawal = $2,828.23

Rounding to the nearest dollar, we get Choice B: $52,041. We can use the formula for Present Value of an Annuity to find out how much annual payment we can make for 30 years with $800,000 at a 5% annual return:

PV = Payment * [(1- (1+r)^-n)/r]
where PV = present value of annuity, Payment = annual payment, r = annual interest rate, n = number of periods (years)

Substituting the values, we get:

$800,000 = Payment * [(1- (1+0.05)^-30)/0.05]

Solving for Payment, we get:

Payment = $52,041 (rounded to nearest dollar)

Therefore, choice B is the best answer.

If You Accumulate $800,000 in Your Retirement Account and Can