Question

How much should be deposited now at 10% compounded semiannually to make possible

withdrawals of $3,000 every 6 months for the next 10 years? Also, how much free cash will you

have withdrawn (ie money the bank gave you as interest)?

Answer 1

i. Calculation of Deposit amount:

Annual rate is 10%. So that, semi-annual rate is 5%. and total withdrawals = 10 years x 2 = 20 times.

Present value = $3,000 x 12.46221 present value annuity factor at 5% for 20 years

Present value = $37,387

Now the Deposit amount should be $37,387 to make possible withdrawals of $3,000 every 6 months for the next 10 years.

ii. Calculation of free cash withdrawn:

Total amount withdrawn (3,000 x 20 times)	$60,000
Less: Amount deposited	($37,387)
Free cash withdrawn	$22,613