I know I could use a simple mortgage calculator, but I am curious to know how my mortgage payment is arrived at. Is it cumulative interest plus principal divided by years and months. Please could you supply a detailed example as I not too hot with maths. For example a £100000 mortgage at 5% over 25 years.
There is a formula for the monthly mortgage payment, M, in terms of the monthly interest rate, i, the loan amount, P, and the number of months in the repayment period, n. The formula is
M = i*P * (1+i)^n / ((1+i)^n – 1)
It will probably be less confusing with a concrete example. Take, for example, your suggestion of a 100,000 mortgage at 5% interest for 25 years. That gives a monthly interest rate (i) of .05/12 = 0041666667 and a repayment period (n) of 300 months.
The first thing to do is calculate 1.0041666667 raised to the 300th power. (You will find this MUCH easier using a calculator, but you could also do it with pen and paper.) I get
1.0041666667 ^ 300 = 3.48129
Plugging this result and the other numbers into the formula, you get
M = .0041666667 * 100000 * 3.48129 / 2.48129
M = 584.59