Suppose at time t = 0, you borrow $100,000 at the fixed interest rate of 0.07 per year. You repay the loan in 30 equal annual repayments so that after n = 30 years, the mortgage is paid off.
Let a denote the amount of payment each year and bt the outstanding balance in period t after your payment in period t.
Write down the first order difference equation that{bt} satisfies. What are the initial and terminal conditions for {bt}?
Use the solution to the equation in part (1) and the conditions in part (2) to find a numerical expression (3) the annual payment a.