Suppose a charity is raffling off a prize with a fair market value of $4000. According to the IRS, the winnings are subject to a 25% withholding tax on the fair market value of the prize. To encourage ticket sales, the charity has decided to pay the withholdings for the winner. The charity thought they would need to pay 0.25($4000) = $1000 to the IRS. However, the $1000 payment would be considered part of the prize, and it would also be subject to 25% withholding. The charity would have to pay 25% of the $1000, or $250. But then the $250 would also be part of the prize and subject to 25% withholding. This process would continue forever.

(a) The charity’s withholdings form an infinite geometric series with a = 1000 and r = 0.25. Determine the total withholdings due.
(b) Determine the effective withholding tax rate.