Question

You plan on saving $12,300 at the end of each of the next 20 years and investing your savings at an annual interest rate of 8%. At the end of year 20 you plan on retiring. You plan on leaving your savings in investments yielding an annual rate of 8% and withdrawing from savings a constant amount for the next 30 years commencing at the end of your first year of retirement. How large a withdrawal can you afford to make?
Select one:
a. $68,000
b. $27,500
c. $39,300
d. $50,000
e. None of the above

Answer 1

- Saving at the end of each year for next 20 years = $12,300

Calculating the Future Value of the periodic deposit:-

Where, C= Periodic Deposits = $12,300

r = Periodic Interest rate = 8%

n= no of periods = 20

Future Value = $ 562,872.16

So, Accumulated amount at the end of 20 year = $562,872.16

Now, you will withdraw commencing at the end of your first year of retirement from the accumulated amout.

Calculating the periodic withdrawal from accumulated amount using Present Value of Ordinary Annuity:-

Where, C= Periodic withdrawal

r = Periodic Interest rate = 8%

n= no of periods = 30

Present Value = $562,872.16

C = $49,998.49

So, the large withdrawal can make is $50,000 (approx).

Hence, Option D. $50,000