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.