Question

Your great aunt left you an inheritance in the form of a trust. The trust agreement states that you are to receive $2,400 on the first day of each year, starting immediately and continuing for 20 years. What is the value of this inheritance today if the applicable discount rate is 6.75 percent

Answer 1

The value of this inheritance today is $30,541.12.

Step-by-step explanation:

Since the $2,400 is to be received the first day of each year, this is shows that this an annuity due and the relevant formula to use is the formula for calculating the present value (PV) of an annuity due given as follows:

PV = P * [{1 - [1 / (1 + r)]^n} / r] * (1 + r) .................................. (1)

Where ;

PV = Present value or the value of this inheritance today =?

P = Annual receipt = $2,400

r = discount rate = 6.75%, or 0.0675

n = number of years = 20

Substituting the values into equation (1) above, we have:

PV = $2,400 * [{1 - [1 / (1 + 0.0675)]^25} / 0.0675] * (1 + 0.0675)

PV = $2,400 * 11.9208107635642 * 1.0675

PV = $30,541.12

Therefore, the value of this inheritance today is $30,541.12.