Question

# Your client has been given a trust fund valued at \$1.58 million. She cannot access the...

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