You are currently 25 and would like to retire at age 45 and be able to withdraw from your savings $150,000 at the end of each year from then until age 85. You plan to save by making equal investments for the next 20 years. You believe you will earn 10% per year on your investments and will leave the money invested at 10% until it is completely used up at age 85.
Note: Present value and future value tables are needed.
How much money will you need to put into the investment at the end of each year from age 25 until age 45 to reach your goal?

Question

Quizplus · Accepted Answer

To solve this, we first calculate the present value (PV) of the withdrawals from age 45 to 85 at a 10% annual interest rate. This gives us the total amount needed at age 45. Then, we calculate how much needs to be saved annually over the next 20 years (age 25 to 45) at the same interest rate to reach this total.1. Calculate the present value of withdrawals from age 45 to 85:$$ PV = \frac{150,000}{0.10} \times \left(1 - \left(\frac{1}{(1+0.10)^{40}}\right)\right) $$$$ PV = 150,000 \times 9.077 $$$$ PV = 1,361,550 $$2. Calculate the annual savings needed to reach the PV at age 45:$$ A = \frac{PV \times 0.10}{\left(1 - \left(\frac{1}{(1+0.10)^{20}}\right)\right)} $$$$ A = \frac{1,361,550 \times 0.10}{6.728} $$$$ A \approx 25,611 $$Therefore, you need to save $25,611 annually to reach your retirement goal.

You Are Currently 25 and Would Like to Retire at Age