What is the present value (or purchase price) of an annuity product which will pay you $2,000 at the end of each year for the next 15 years? Use an interest rate of 9%.
890
To calculate the present value of an annuity, we need to use the formula:
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, the cash flow per period is $2,000, the interest rate is 9% per year, and the number of periods is 15 years.
Step 1: Convert the interest rate to a decimal
r = 9% = 0.09
Step 2: Plug the values into the formula
PV = $2,000 * [(1 - (1 + 0.09)^(-15)) / 0.09]
Step 3: Calculate the present value
[(1 + 0.09)^(-15)] = 0.346;
(1 - 0.346) = 0.654;
0.654 / 0.09 = 7.27
PV = $2,000 * 7.27 ≈ $14,540.00
Therefore, the present value or purchase price of the annuity is approximately $14,540.00.