Suppose a monthly mortgage instead is modified to require that half the normal monthly payments be made every two weeks, i.e. biweekly. If monthly payments are x, on a normal mortgage, one will 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, with half the monthly payments above, when will the loan be completely repaid, and what are the savings in total interest paid over the monthly program? (Assume biweekly compounding for this part to keep it simple.