Please explain b in detail, especially how you get the fraction of the amount left at the end

2.1 A 50,000 loan made on January 1,2010 is to be repaid over 25 years with payments on the last day of each month, beginning January 31,2010. (a) If i(2)=10%, find the amount of the monthly payment X. (b) Starting with the first payment, the borrower decides to pay an additional 100 per month, on top of the regular payment of X, until the loan is repaid. An additional fractional payment might be necessary one month after the last regular payment of X+100. On what date will the final payment of X+100 be made, and what will be the amount of the additional fractional payment