$6.($The biweekly mortgage $)$ Here is a proposal that has been advanced as a way for homeowners to save thousands of dollars on mortgage payments: pay biweekly instead of monthly Specifically, if monthly payments are x$,$ it is suggested that one instead pay x$/2$ every two weeks $($for a total of $26$ payments per year$).$ This will pay down the mortgage faster, saving interest. The savings are surprisingly dramatic for this seemingly minor modificationoften cutting the total interest payment by over one$-$third. Assume a loan amount of $$100,000$ for $30$ years at $10\%$ interest, compounded monthly

$($a$)$ Under a monthly payment program, what are the monthly payments and the total interest paid over the course of the $30$ years?

$($b$)$ Using the biweekly program, when will the loan be completely repaid, and what are the savings in total interest paid over the monthly program? $($You may assume biweekly compounding for this part.