a. Billy signs a note to pay $X plus 6% interest due in 8 months. On the due date the debt was commuted into 2 payments of $2,583.72 due immediately and 5 months hence with the interest rate set at 12% and the focal date set on the due date of the original debt. Find $X.

b. Jessica buys a boat for $21,500. He paid $3,000 down and signs a note to repay the reminder with interest at 8% due in 10 months. Six months before the note comes due the debt is commuted into three equal payments due 3, 6 and 9 months hence. The interest rate is set at 13% and the focal date 6 months hence. Determine the amount of the new payments.