1. Computing mortgage payments and balances Suppose you borrow L dollars, which you are to repay over a period of 20 years at 6% interest, compounded monthly. How much will your monthly payments be? To answer that, let p be the monthly payment and Ax be the balance remaining filling on the loan at the end of & months. (a) The key formula is - - - Ak = 1.005Ak-1 - P. (27) Explain in words what this says and where it comes from. - - - - - (b) Fork = 1, we have to take Ak-1 = Lin (27). Applying formula (27) recursively for k = 1, 2, 3 gives A1 = 1.005L - p A2 = 1.005Al - p = (1.005)2L - 1.005p - p A3 = 1.005 A2 - p = (1.005)3 L - (1.005)2p - 1.005p - p. - - Continuing in this way, write a formula for Ak in terms of L and p. (c) To simplify your formula, use the following formula, known as the geometric series formula: For any number t * 1 and any positive integer m, 1+ t+t? + ... f fm_ tit - 1 t - 1