You and 11 co-workers have just won $12 million ($1 million each) from the state lottery. Assuming that you each receive your share over 20 years and that the state lottery earns a 4% return on its funds, what is the present value of your prize before taxes, if you request the “up-front cash” option?


To calculate the present value of the prize, we can use the formula for the present value of an annuity, as the $1 million will be paid out over 20 years. Since the lottery earns a 4% return on its funds, we treat this as the discount rate. 

The present value of an annuity formula is:

\[
PV = P \times \left(1 - (1 + r)^{-n}\right) \div r
\]

Where:
- $ P $ = Payment per period ($1 million ÷ 20 years = $50,000 per year),
- $ r $ = Annual discount rate (4% = 0.04),
- $ n $ = Number of periods (20 years).

Let's calculate this.

The present value of your $1 million prize, assuming you request the “up-front cash” option and the state lottery earns a 4% return, is approximately **$679,516.32** before taxes.

Would you like more details or have any questions? 

Here are five related questions to consider:
1. How does increasing the discount rate affect the present value of the prize?
2. What would the present value be if the prize was distributed over 30 years instead of 20?
3. How does inflation affect the real value of the prize over time?
4. How would the present value change if the annual payment was $60,000 instead of $50,000?
5. What is the future value of this prize if invested at 4% for 20 years?

**Tip:** Always consider the time value of money when comparing cash flows across different periods.

You and 11 co-workers have just won $12 million ($1 million each) from the state lottery. Assuming that you each receive your share over 20 years and that the state lottery earns a 4% return on its funds, what is the present value of your prize before taxes, if you request the 'up-front cash' option?

Find out how to calculate the present value of a lottery prize of $1 million, paid out over 20 years, with a 4% return. Learn the present value of an annuity formula, and discover how factors like the discount rate affect your prize. Suitable for finance and economics students.

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