A state lotto has a prize that pays $1,500 each week for 25 years.
If the state can earn 5% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments?

To determine how much the state will need to deposit now in order to cover the weekly prize payments of $1,500 for 25 years, we need to use the present value formula for an annuity.

### Information:
- **Weekly prize payment (PMT)**: $1,500
- **Number of years**: 25 years
- **Payments per year**: 52 weeks
- **Total number of payments**: $ 25 \times 52 = 1300 $
- **Interest rate per year**: 5% or 0.05
- **Weekly interest rate**: $ \frac{5\%}{52} = \frac{0.05}{52} $

### Formula for the present value of an annuity:
\[
PV = PMT \times \left( \frac{1 - (1 + r)^{-n}}{r} \right)
\]
Where:
- $ PV $ = present value (amount needed now)
- $ PMT $ = payment amount ($1,500)
- $ r $ = interest rate per period (weekly interest rate)
- $ n $ = number of periods (total number of payments)

Let's calculate this now.The state will need to deposit approximately **$1,112,784** now to cover the weekly prize payments of $1,500 for 25 years, assuming a 5% annual interest rate.

Would you like more details or have any questions?

Here are five related questions you might find interesting:
1. What if the interest rate was 3% instead of 5%?
2. How would the required amount change if the prize lasted for 30 years?
3. What happens if the payments are made monthly instead of weekly?
4. How can you calculate the future value of this annuity?
5. What would the weekly payments be if the state initially deposited $1 million?

**Tip:** The present value of an annuity decreases as the interest rate increases because the money deposited now can grow more due to interest!

A state lotto has a prize that pays $1,500 each week for 25 years. If the state can earn 5% interest on investments, how much money will they need to put into an account now to cover the weekly prize payments?

Calculate how much the state needs to deposit today to cover a weekly lotto prize of $1,500 for 25 years, with an interest rate of 5%. Explore the present value of annuities, interest rates, and the time value of money.

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