Questions: Find the cash value of the following lottery jackpot. Yearly jackpot payments begin immediately. Assume the lottery can invest at the given interest rate. 14,000,000 jackpot, 6% interest, 20 annual payments (Round to the nearest dollar as needed.)

Solution Steps

To find the annual payment, divide the total jackpot amount by the number of payments. Given a jackpot amount of $14000000 to be paid out over 20 years, the annual payment \(P\) is calculated as: \[ P = \frac{FV}{n} = \frac{14000000}{20} = 700000 \]

Using the present value of an annuity formula, we can calculate the present value of the lottery winnings. The formula is: \[ PV = P \times \left(1 - (1 + r)^{-n}\right) / r \] Substituting the values, we get: \[ PV = 700000 \times \left(1 - (1 + 0)^{-20}\right) / 0 = 8028945 \]

Final Answer: