Your client has been given a trust fund valued at $1.07 million. He cannot access the money until he turns 65 years old, which is in 30 years. At that time, he can withdrawal $28,500 per month. If the trust fund is invested at a 5.0 percent rate, how many months will it last your client once he starts to withdraw the money?

285 Months

Explanation:

n = 30 years * 12 = 360

percent rate = 5.0 % divided by 12 = 0.417.

Now recalling the statement of time value for money,

We have future value = present value * (1 + rate) ∧ n

future value = 1, 070,000 * (1 + 0.417) ∧ 360

future value = 3.33065667 E 60

At age 65, the value 3.33065667 E 60 will be the present monthly withdrawal at $28,500.

present value of ordinary annuity, = annuity (1 - (1 + r) ∧ - n : r

= 3.33065667 E 60 = 28500 (1 - (1 + 0.417) ∧ - n : 0.417

= 3.33065667 E 60 : 28500 = (1 - (1 + 0.417) ∧ - n : 0.417

1.168651462 E 56 = (1 - (1 + 0.417) ∧ - n : 0.417

we now introduce logs to determine the value of n

Solving further, we discovered that n = 285.

Therefore, the number of months it will last one he start to withdraw the money is 285 month