You are considering a lottery prize that will pay you ₹10,000 per year for the next 15 years. If the discount rate is 5%, what is the present value of this annuity?
Question
You are considering a lottery prize that will pay you ₹10,000 per year for the next 15 years. If the discount rate is 5%, what is the present value of this annuity?
Solution
To calculate the present value of the annuity, we need to discount each future payment to its present value using the discount rate of 5%.
Step 1: Determine the discount factor The discount factor can be calculated using the formula: Discount Factor = 1 / (1 + Discount Rate)^Number of Years
In this case, the discount rate is 5% (or 0.05) and the number of years is 15. Plugging these values into the formula, we get: Discount Factor = 1 / (1 + 0.05)^15
Step 2: Calculate the present value of each payment To calculate the present value of each payment, we multiply the annual payment of ₹10,000 by the discount factor.
Present Value of each payment = Annual Payment * Discount Factor
Step 3: Calculate the total present value To find the total present value of the annuity, we sum up the present value of each payment over the 15-year period.
Total Present Value = Present Value of Payment 1 + Present Value of Payment 2 + ... + Present Value of Payment 15
By performing these calculations, we can determine the present value of the annuity.
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