Annuity Present Value Calculation
Calculating Present Value of Annuity
An annuity is a series of equal payments made at regular intervals. In this scenario, an annuity is set up to pay $1500 per year for ten years. To determine the present value (PV) of this annuity, we can use the formula:
PV = FV / (1 + i)^n
Where:
PV = Present Value
FV = Future Value
i = Discount rate
n = Number of years
Given information:
Cash flow = $1,500
Interest rate = 9%
Number of years = 10
Calculating Future Value
First, we need to calculate the future value (FV) of the annuity using the formula:
FV = {A * [(1 + i)^n - 1]} / i
Substitute the values:
A = $1,500
i = 9%
n = 10 years
Calculating FV:
FV = {1,500 * [(1.09^10) - 1]} / 0.09
FV = $22,789.395
Calculating Present Value
Now, we can substitute the calculated future value into the present value formula to find the present value (PV):
PV = 22,789.395 / (1.09^10)
PV = $9,626.49
Therefore, the present value (PV) of the annuity paying $1500 per year for ten years with a discount rate of 9% is $9,626.49.