Mr. Norman will receive 8,500 a year for the next 15 years from her trust. If a 7 percent interest rate is applied, what is the current value of the future payments if first receipt occurs today?
To find the current value of the future payments, we need to calculate the present value of an annuity.
The formula for the present value of an annuity is:
PV = C * [1 - (1 + r)^(-n)] / r
Where:
PV = Present Value
C = Cash flow per period
r = Interest rate per period
n = Number of periods
In this case:
C = $8,500 per year
r = 7% per year (expressed as a decimal, so r = 0.07)
n = 15 years
Plugging the values into the formula:
PV = $8,500 * [1 - (1 + 0.07)^(-15)] / 0.07
Using a calculator to simplify the expression inside the brackets:
PV = $8,500 * [1 - (1.07)^(-15)] / 0.07
= $8,500 * [1 - 0.4137] / 0.07
= $8,500 * 0.5863 / 0.07
= $5,227.05
Therefore, the current value (present value) of the future payments is $5,227.05 if the first receipt occurs today.