Applications - A Guide to MATLAB for Beginners and Experienced Users - page 145

Mortgage Payments
We want to understand the relationships among the mortgage payment rate
of a fixed rate mortgage, the principal (the amount borrowed), the annual
interest rate, and the period of the loan. We are going to assume (as is
usually the case in the United States) that payments are made monthly,
even though the interest rate is given as an annual rate. Let's define
peryear = 1/12; percent = 1/100;
So the number of payments on a 30-year loan is
30*12
ans =
360
and an annual percentage rate of 8% comes out to a monthly rate of
8*percent*peryear
ans =
0.0067
Now consider what happens with each monthly payment. Some of the
payment is applied to interest on the outstanding principal amount, P , and
some of the payment is applied to reduce the principal owed. The total
amount, R , of the monthly payment remains constant over the life of the
loan. So if J denotes the monthly interest rate, we have R = J ∗ P + (amount
applied to principal), and the new principal after the payment is applied is
P + J ∗ P − R = P ∗ (1 + J ) − R = P ∗ m − R ,
where m = 1 + J . So a table of the amount of the principal still outstanding
after n payments is tabulated as follows for a loan of initial amount A , for n
from0to6:
symsmJPRA
P=A;
for n = 0:6,
disp([n, P]),
P = simplify(-R + P*m);
end