Question 1176067
Absolutely! Let's calculate the total value of the prize and the amount needed to cover the weekly payments.

**1. Total Value of the Prize**

* Weekly prize: $1,700
* Years: 40
* Weeks per year: 52

Total value = Weekly prize * Weeks per year * Years
Total value = $1,700 * 52 * 40
Total value = $3,536,000

**2. Present Value Calculation**

To determine how much money the state needs to invest now, we need to calculate the present value of the annuity.

* Weekly payment: $1,700
* Interest rate: 3% per year
* Years: 40

Since the payments are weekly, we need to adjust the interest rate to a weekly rate.

* Annual interest rate: 0.03
* Weekly interest rate: 0.03 / 52 ≈ 0.000576923

We'll use the present value of an ordinary annuity formula, but since it is weekly, we will use the weekly interest rate, and total number of weeks.

Total number of weeks = 40 years * 52 weeks/year = 2080 weeks

Using the present value of an annuity formula:

PV = PMT * [1 - (1 + r)^-n] / r

Where:

* PV = Present Value
* PMT = Weekly payment ($1,700)
* r = Weekly interest rate (0.03 / 52)
* n = Total number of weeks (2080)

PV = 1700 * [1 - (1 + 0.03/52)^-2080] / (0.03/52)

PV = 1700 * [1 - (1.000576923)^-2080] / 0.000576923

PV = 1700 * [1 - 0.301131] / 0.000576923

PV = 1700 * 0.698869 / 0.000576923

PV = 1700 * 1211.37

PV = 2059329

Therefore, the state needs to put approximately $2,059,329 into an account now to cover the weekly prize payments.

**Answers:**

* Total value of the prize: $3,536,000
* Amount needed to cover the prize payments: $2,059,329 (approximately)