Your client has been given a trust fund valued at $1.58 million. She cannot access the money until she turns 65 years old, which is in 15 years. At that time, she can withdraw $24,000 per month.
If the trust fund is invested at a 5.5 percent rate, how many months will it last your client once she starts to withdraw the money
Calculation accumulated amount at 65:
PV = Trust value invested = $1,580,000
n = 15 years
r = interest rate = 5.5%
Accumulated amount at 65 = PV * (1+r)^n
= $1,580,000 * (1+5.5%)^15
= $1,580,000 * 2.23247649
= $3,527,312.85
Accumulated balance at 65 is $3,527,312.85
Caluculation of Number of monthly withdrawals
PV = Accumulated value = $3,527,312.85
r = monthly interest rate = 5.5%/12 = 0.45833333%
P = Monthly withdrawl amount = $24,000
Let n = number of withdrawls
PV = P * [1 - (1+r)^-n] / r
$3,527,312.85 = $24,000 * [1 - (1+0.45833333%)^-n] / 0.45833333%
[1 - (1+0.45833333%)^-n] = 0.673618767
(1+0.45833333%)^-n = 0.326381233
(1.0045833333%)^n = 3.06390166
n = log(3.06390166) / log(1.0045833333)
n = 0.486274822 / 0.00198596865
n = 244.855236
n = 244.85 months
Therefore, the money will last for 244.85 months once she starts withdrawing money
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