Consider an n-year loan of principal P which requires monthly payments (n 1). Two options for payments are given, constant amortization mortgage (CAM) and constant payment mortgage (CPM), both of which offer the same effective monthly interest rate is specified by i > 0. Then, we already know that the amount of monthly payments of CPM A satisfies 12n A P= . k=1 (1 + i)k Please answer the following questions. 1. (10pt) Prove that the sum of present values of the CAM payments is equal to P . 2. (5pt) Prove that the first payment of CAM is bigger than that of CPM using a). 3. (5pt) Prove that the last payment of CAM is smaller than that of CPM using a).

Problem 1 (20pt): Consider an n-year loan of principal P which requires monthly payments (n > 1). Two options for payments are given, constant amortization mortgage (CAM) and constant payment mortgage (CPM), both of which offer the same effective monthly interest rate is specified by i > 0. Then, we already know that the amount of monthly payments of CPM A satisfies 12n P= A (1 + i)k" k=1 Please answer the following questions. 1. (10pt) Prove that the sum of present values of the CAM payments is equal to P. 2. (5pt) Prove that the first payment of CAM is bigger than that of CPM using a). 3. (5pt) Prove that the last payment of CAM is smaller than that of CPM using a). Problem 1 (20pt): Consider an n-year loan of principal P which requires monthly payments (n > 1). Two options for payments are given, constant amortization mortgage (CAM) and constant payment mortgage (CPM), both of which offer the same effective monthly interest rate is specified by i > 0. Then, we already know that the amount of monthly payments of CPM A satisfies 12n P= A (1 + i)k" k=1 Please answer the following questions. 1. (10pt) Prove that the sum of present values of the CAM payments is equal to P. 2. (5pt) Prove that the first payment of CAM is bigger than that of CPM using a). 3. (5pt) Prove that the last payment of CAM is smaller than that of CPM using a)