Sally deposits $100 into her savings account on the first day of every month except for each December, when she uses her money to buy holiday gifts. Define b[m] as the balance in Sally's account on the first day of month m. Assume Sally opens her account in January (m = 0), continues making monthly payments forever (except each December!), and that her monthly interest rate is 1%. Sally's account balance satisfies a simple difference equation b[m] = (1.01)b[m 1] + p[m], where p[m] designates Sally's monthly deposits. Determine a closed-form expression for b[m] that is only a function of the month m.