you have one state lottery prize quoted at $36 million lottery but this means is that if you take the monthly payments of $150,000 for 20 years, you will have a total payout of $36 million if the appropriate interest rate is assumed to be 4.08% APR what would be the cash payout on this lottery today?

The cash payout of a lottery today, also called the "lump sum," can be determined by calculating the present value of the monthly payments using the given interest rate.

Here, the key details are:
- Monthly payments = $150,000
- Duration = 20 years = 240 months (20 years × 12 months/year)
- Interest rate = 4.08% APR (Annual Percentage Rate)
- The cash payout is the present value (PV) of the monthly annuity.

We will use the present value of an annuity formula to compute this:

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

Where:
- $P$ = monthly payment = $150,000
- $r$ = monthly interest rate = $ \frac{4.08\%}{12} = \frac{0.0408}{12} $
- $n$ = number of months = 240

Now let's calculate the lump sum payout.The cash payout (lump sum) of the lottery today, assuming a 4.08% APR and monthly payments of $150,000 for 20 years, would be approximately **$24.58 million**.

Would you like more details on how this was calculated, or have any further questions?

Here are 5 follow-up questions you might find interesting:
1. How does increasing the interest rate affect the cash payout?
2. What would happen if the monthly payment period was reduced to 15 years instead of 20?
3. How do lotteries typically decide between cash payouts and annuities?
4. How is the APR determined in real-world lottery payouts?
5. How would inflation impact the value of these payments over 20 years?

**Tip**: Understanding present value is crucial when comparing long-term payments to lump sums. The higher the interest rate, the lower the present value of future payments.

You have one state lottery prize quoted at $36 million lottery but this means is that if you take the monthly payments of $150,000 for 20 years, you will have a total payout of $36 million. If the appropriate interest rate is assumed to be 4.08% APR, what would be the cash payout on this lottery today?

Find out how to calculate the lump sum payout of a $36 million lottery prize, given monthly payments of $150,000 over 20 years and an interest rate of 4.08% APR. Learn about the present value of annuities and the time value of money with a step-by-step solution. Suitable for Grades 11-12 or finance students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation