Answer:
The total value of the prize is $2,652,000, and the state needs to put approximately $663,938.51 into an account now to cover the weekly prize payments.
Explanation:
To find the total value of the prize, we need to calculate the sum of the weekly payments over the course of 30 years.
First, let's calculate the total number of weeks in 30 years:
30 years * 52 weeks/year = 1560 weeks
Next, we can calculate the total value of the prize:
Total value = Weekly payment * Total number of weeks
Total value = $1,700 * 1560
Total value = $2,652,000
Therefore, the total value of the prize is $2,652,000.
To determine how much money the state needs to put into an account now to cover the weekly prize payments, we need to consider the interest earned on investments.
If the state can earn a 6% interest rate on investments, we can use the present value formula to calculate the initial investment needed.
Present Value = Future Value / (1 + Interest Rate)^Number of Periods
In this case, the future value is $2,652,000, the interest rate is 6%, and the number of periods is 1560 weeks.
Present Value = $2,652,000 / (1 + 0.06)^1560
Using a financial calculator or spreadsheet software, we can find that the present value is approximately $663,938.51.
Therefore, the state will need to put approximately $663,938.51 into an account now to cover the weekly prize payments.
Thus,
The total value of the prize is $2,652,000 and the state needs to put approximately $663,938.51 into an account now to cover the weekly prize payments.