For 50000, Smith purchases a 36-payment annuity-immediate with monthly payments. Assume an effective annual interest rate of 12.68%. For each of the following cases find the unknown amount X.

(a) The first payment is X and each subsequent payment is 50 more than the previous one.

(b) The first payment is X and each subsequent payment until the 18th pay- ment (and including the 18th payment) is 0.2% larger than the previous one. After the 18th payment, each subsequent payment is 0.2% smaller than the previous one.