Question

A wealthy parent is trying to fund a trust fund for his oldest son. The parent has set aside $460,300.00 today in an account that pays 7.00% annual interest. His oldest son will begin receiving the trust in 14.00 years, and the trust is set up to pay 16.00 identical annual payments. What will be the yearly withdrawal for the son from the trust?

Answer Format: Currency: Round to: 2 decimal places.

Answer 1

First we will calculate the value of the trust after 14 years, when the son will start receiving the annual payments. We will use the following formula to calculte this value:

FV = PV * ( 1 + r)ⁿ

where,FV = Future value of the trust after n years, PV = Present value of the payments = $460300, n is the time period = 14, and r is the rate of interest = 7%.

Putting the given values in the above formula, we get,

FV = $460300 * ( 1 + 7%)¹⁴

FV = $460300 * ( 1 + 0.07)¹⁴

FV = $460300 * ( 1.07)¹⁴

FV = $460300 * 2.5785341502

FV = $1186899.27

So, after 14 years, trust has $1186900 in the account.

Now, we will calculate the annual payments that the son will receive from the trust. Here, we will use the formula for present value of annuity as below:

PVA = P * (1 - (1 + r)^-n / r )

where,PVA = Present value of annuity = $1186900, P = Periodical or annual payments, n is the time period = 16, and r is the rate of interest = 7%.

Putting the given values in the above formula, we get,

$1186900 = P * (1 - (1 + 7%)^-16 / 7%)

$1186900 = P * (1 - (1 + 0.07)^-16 / 0.07)

$1186900 = P * (1 - (1.07)^-16 / 0.07)

$1186900 = P * ((1 - 0.34) / 0.07)

$1186900 = P * (0.66 / 0.07)

$1186900 = P * 9.43

P = $1186899.27 / 9.43

P = $125864.19

So, annual payments will be for $125864.19