use matlab !1

3. Amortization is the process by which a loan is repaid by a sequence of periodic payments, each of which is part payment of interest and part payment to reduce the outstanding principal. Let p(n) represent the outstanding principal after the nth payment g(n). Suppose that interest charges compound at the rate r per payment period. The formulation of our model here is based on the fact that the outstanding principal p(n+1) after the (n+1)st payment is equal to the outstanding principal p(n) after the nth payment plus the interest rp(n) incurred during the (n+1)st period minus the nth payment g(n). 1) Write the first-order difference equation and ve for p(n), assuming initial debt p(0) = p0. 2) Solve for constant moly payment for 30-year, $300,000 morgage with 5.57% APR (Note: interest = APR/12) 3) Often paying out additional bank fees upfront can reduce the APR, is it worth paying addiotnal $1,000 upfront to lower APR from 5.57% to 5.00% over the 30 year period? What is the overall payout difference after 30 years? Plot p(n) for both cases over 30 years. Submit, 1) answer(s), 2) Matlab code, 3) graph(s) 3. Amortization is the process by which a loan is repaid by a sequence of periodic payments, each of which is part payment of interest and part payment to reduce the outstanding principal. Let p(n) represent the outstanding principal after the nth payment g(n). Suppose that interest charges compound at the rate r per payment period. The formulation of our model here is based on the fact that the outstanding principal p(n+1) after the (n+1)st payment is equal to the outstanding principal p(n) after the nth payment plus the interest rp(n) incurred during the (n+1)st period minus the nth payment g(n). 1) Write the first-order difference equation and ve for p(n), assuming initial debt p(0) = p0. 2) Solve for constant moly payment for 30-year, $300,000 morgage with 5.57% APR (Note: interest = APR/12) 3) Often paying out additional bank fees upfront can reduce the APR, is it worth paying addiotnal $1,000 upfront to lower APR from 5.57% to 5.00% over the 30 year period? What is the overall payout difference after 30 years? Plot p(n) for both cases over 30 years. Submit, 1) answer(s), 2) Matlab code, 3) graph(s)