Question 1172845
Let's break down this problem. We need to find the present value of an annuity, where Ron Sample receives $3,000 at the beginning of each year for 5 years, and the interest rate is 8% compounded annually.

Since the payments are made at the beginning of each year, this is an annuity due.

**Formula for Present Value of an Annuity Due:**

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

Where:

* PV = Present Value
* PMT = Payment per period ($3,000)
* r = Interest rate per period (8% or 0.08)
* n = Number of periods (5 years)

**Calculation:**

PV = 3000 * [(1 - (1 + 0.08)^-5) / 0.08] * (1 + 0.08)

1.  Calculate (1 + 0.08)^-5:
    * (1.08)^-5 ≈ 0.6805832

2.  Calculate 1 - (1 + 0.08)^-5:
    * 1 - 0.6805832 ≈ 0.3194168

3.  Divide by 0.08:
    * 0.3194168 / 0.08 ≈ 3.99271

4.  Multiply by 1.08:
    * 3.99271 * 1.08 ≈ 4.3121268

5.  Multiply by 3000:
    * 4.3121268 * 3000 ≈ 12936.3804

6. Round to the nearest cent.
    * 12936.38

Therefore, approximately $12,936.38 should be invested at 8% interest compounded annually to award the prize.