Congratulations. You just won the California State Lottery. The amount awarded is paid in 20 equal annual installments, at the beginning of each year. You can invest your money at 6.6%, compounded annually. You have calculated that the lottery is worth $20,975,400 today. How much was the amount awarded?

Question

Quizplus · Accepted Answer

To find the amount awarded, we need to use the present value formula for an annuity due:

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

where PV = $20,975,400 (present value), r = 6.6% (annual interest rate), and n = 20 (number of payments).

Solving for P, we get:

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

P = $36,000,000

Therefore, the amount awarded was $36,000,000.