A loan of $2,000 is paid by the following series of payments, beginning one year after the loan is made: 100; 105; 110; 115; .... 145; 150; 145; 140, ...., 105; 100; 100; 100; ..., The payments of $100 continue for as long as necessary, and then a smaller payment is made one year after the last payment of $100. Determine the total number of payments needed to repay this loan, and the size of the last payment, if the effective annual rate is 4%