Final answer:
To calculate the present value of an annuity to receive fixed annual payments of $250,000 for 15 years at an interest rate of 10%, you need to use the present value of an annuity formula, which considers the payment amount, interest rate, and number of payments.
Step-by-step explanation:
Calculating the Present Value of an Annuity
To determine the present value of an annuity that you wish to receive in the form of fixed payments of $250,000 for 15 years with an interest rate of 10 percent per annum, we utilize the formula for the present value of an annuity. The formula takes into account the periodic payment amount, the interest rate, and the total number of payments.
It's essential in finance to understand how to calculate the present value of an annuity since it helps in evaluating the amount needed to invest today to achieve a certain future financial goal.
The present value of an annuity (PVA) formula is:
PVA = P * [(1 - (1 + r)^-n) / r]
Where:
- P = Periodic payment ($250,000)
- r = Periodic interest rate (0.10)
- n = Total number of payments (15)
Inserting the values into the formula:
PVA = 250,000 * [(1 - (1 + 0.10)^-15) / 0.10]
Calculating this will give the present value of the annuity required to ensure 15 years of $250,000 annual payments.