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 b_t the outstanding balance in period t after your payment in period t. Write down the first order difference equation that{b_t} satisfies. What are the initial and terminal conditions for {b_t}? 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. 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 b_t the outstanding balance in period t after your payment in period t. Write down the first order difference equation that{b_t} satisfies. What are the initial and terminal conditions for {b_t}? 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