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

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