Question

Your father has $400000 invested at 7 percent, and he wants to retire. He plans to withdraw $55000 at the beginning of each year, starting now. How long will it take to exhaust his funds, i.e., run the account down to zero? Your Answer: Answer units

Answer 1

It would take 10 years and 5 months to run the account down to zero for a Sum of $400000 invested at 7% interest rate and $55000 withdrawn at the beginning of each year.

Assuming that the Sum of $400000 has generated 7% interest before the first withdrawal.

Years	[1] Current investment ($)	[2] Annual Withdrawals ($)	[1]-[2] Balance amount ($)	Rate of interest (%)	Balance amount at the end of the year
	400,000	-	400,000	7	428,000
1	428000	55000	373,000	7	399,110
2	399,110	55000	344,110	7	368,198
3	368,198	55000	313,198	7	335,122
4	335,122	55000	280,122	7	299,730
5	299,730	55000	244,730	7	261,861
6	261,861	55000	206,861	7	221,341
7	221,341	55000	166,341	7	177,985
8	177,985	55000	122,985	7	131,594
9	131,594	55000	76594	7	81,955
10	81,955	55000	26,955	7	28,842

After 10 withdrawals, an amount of $28,842  would be left in account for withdrawal. This can be withdrawn in 5 months. [55000 in 12 months i.e. 4583 per month. 28842/4583= 4.98 (5months approx)]