Question

Your client has been given a trust fund valued at $1.18 million. He cannot access the money until he turns 65 years old, which is in 25 years. At that time, he can withdraw $21,000 per month. If the trust fund is invested at a 4.5 percent rate, compounded monthly, how many months will it last your client once he starts to withdraw the money? (Do not round intermediate calculations and round your final answer to 2 decimal places.)

Number of months = ?

Answer 1

A	B	C	D	E	F	G	H	I	J	K	L	M
2
3
4		The number of months of withdrawals should be such that the present value of withdrawals
5		at the time of retirement should be equal to the value of fund at the time of retirement.
6
7		Current Value of Trust fund	$1,180,000
8		Interest rate	4.50%
9		Time to retirement	25	Years
10
11		Monthly interest rate	0.3750%
12		Number of months	300
13
14		Value of fund at the retirement	=$1,180,000*(P/A,0.375%,300)
15			$212,294,179.77	=D7*PV(D11,D12,-1,0)
16
17		Number of monthly withdrawals should be such that the present value of monthly withdrawals be equal to the value of fund at the retirement.
18
19		Monthly Withdrawal (P)	$21,000.00
20		Number of withdrawals (n)	?
21		Monthly Interest rate (i)	0.38%
22
23		Amount required at the retirement if the $21000 is withdrawn forever	=$21,000 / 0.38%
24			$5,600,000.00	=D19/D21
25
26		Since the amount required for withdrawal of the amount forever is lower than the value of fund at the retirement.
27		Therefore the money can be withdrawn forever.
28
29		Hence the number of months are infinite.
30