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 modification - often 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.)