A mortgage payment stream is usually divided into a principal payment cash- flow and an interest payment cash-flow. Consider a standard mortgage of initial value M(0) with equal monthly payments of amount B. The interest rate used is r per month. We shall denote by M(k) the mortgage principal or balance after the kth payment, by I(k) the interest component of the kth payment and by P(k) the principal component of the kth payment.
Find the present value V (at the rate r) of the principal payment cash-flow m in terms of B, r, n, M(0) and in terms of r, n, M(0) only.