Question

Janet Woo decided to retire to Florida in 7 years. What amount should Janet invest today so she can withdraw $55,000 at the end of each year for 20 years after she retires? Assume Janet can invest money at 7% compounded annually. (Do not round intermediate calculations. Round your answer to the nearest cent.)

Answer 1

Janet should invest approximately $683,265.15 today.

Step-by-step explanation:

To determine the amount Janet should invest today, we need to calculate the present value of the $55,000 annual withdrawals for 20 years. We can use the formula for the present value of an ordinary annuity: PV = PMT * [(1 - (1 + r)^-n) / r], where PV is the present value, PMT is the annual payment, r is the interest rate, and n is the number of periods.

Given that PMT = $55,000, r = 7% (or 0.07), and n = 20, we can substitute these values into the formula as follows: PV = $55,000 * [(1 - (1 + 0.07)^-20) / 0.07]. Evaluating this expression, the present value of the annuity comes out to be approximately $683,265.15. Therefore, Janet should invest around $683,265.15 today to be able to make the desired withdrawals in the future.

Answer 2

Using an online finance calculator for the present value of ordinary annuity, the amount that Janet Woo should invest today to withdraw $55,000 at the end of each year for 20 years is $582,670.78.

N (# of periods) = 20 years

I/Y (Interest per year) = 7%

PMT (Periodic Payment) = $-55,000

FV (Future Value) = $0

Results:

PV (Present Value) = $582,670.78

Sum of all periodic payments = $-1,100,000.00

Total Interest = $517,329.22

Thus, the present value of the required investment compounded at 7% annually for 20 years is $582,670.78.