In order to accumulate $$2,000,$ you will deposit $$100$ at the end of each month for as long as necessary. Interest is i$(12)=4\%.($a$)$ How many regular payments are required to accumulate the $$2,000?[$Keep in mind that the last of these regular payments will include the $$100$ plus an additional $$fractional$$ amount that$$s less than $$100$ to reach $$2,000$ exactly.$]($b$)$ Compute how much the fractional payment needs to be$.$