2. Suppose you take out an n-year mortgage of $L with monthly payments, with nominal annual interest rate of i convertible monthly. Show that the total amount you will pay in interest to the bank over the course of the loan is X 12n k=1 Ik = 12nQ L =niL 1 (1 + i/12)12n L. Compute these amounts explicitly for a 15-year mortgage and a 30-year mortgage with i = 3% and L = 100, 000; also compare the monthly payments for both. (Hint: for each k we know Ik = Q Pk, and the sum of all principal payments must be the total loan amount.)