Consider a mortgage loan of principal P, annual interest rate / compounded m time per year,...

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Consider a mortgage loan of principal P, annual interest rate / compounded m time per year, over a period of T years. (Note that the principal is the price minus the down payment). Let N=Tm be the number of payments and i be the monthly interest rate. Let C be the payment for each period, which is constant. The present value of the payment for the nth period is C/(1+i)^n. The value of C should be such that the sum of the present values over all N payments equals to the principal of the loan P. This value C is referred to as the present value of the annuity. Part of the amount C goes towards interest and part of it goes to principal payment (amortization). The interest is paid on the declining (remaining) balance. a) Derive formulas for the monthly payment C, as well as for the monthly interest payment R(n) and the monthly amortization A(n). We must have C=R(n)+A(n), for n=1,2, ..., N. Express your formulas in terms of P, r, m, and T. b) Choose some realistic values for P, r, m, and T, and write a computer code or create an excel spreadsheet that performs the specific computations. Consider a mortgage loan of principal P, annual interest rate / compounded m time per year, over a period of T years. (Note that the principal is the price minus the down payment). Let N=Tm be the number of payments and i be the monthly interest rate. Let C be the payment for each period, which is constant. The present value of the payment for the nth period is C/(1+i)^n. The value of C should be such that the sum of the present values over all N payments equals to the principal of the loan P. This value C is referred to as the present value of the annuity. Part of the amount C goes towards interest and part of it goes to principal payment (amortization). The interest is paid on the declining (remaining) balance. a) Derive formulas for the monthly payment C, as well as for the monthly interest payment R(n) and the monthly amortization A(n). We must have C=R(n)+A(n), for n=1,2, ..., N. Express your formulas in terms of P, r, m, and T. b) Choose some realistic values for P, r, m, and T, and write a computer code or create an excel spreadsheet that performs the specific computations.

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a The monthly payment C is the present value of the annuity which is given by C P rm 1 1rmmT where r ... View the full answer