The mathematical principle of personal housing loan calculator

1. The deduction of the formula for calculating the monthly amount of equal principal and interest law

In the previous essay "Use C # write personal housing Loan calculator" mentioned that, such as interest rate unchanged in the case of the monthly repayment amount is fixed, so also known as the "matching method", the calculation formula is as follows:

Monthly Return amount =	Loan amount x Month rate x (1 + month rate) period
(1 + monthly interest rate) number of periods -1

Now let's deduce the formula.

We know that the method of equal principal and interest is calculated as follows:

Monthly interest rate = Last month's remaining loan balance X-month interest

This month also the principal = monthly amount-The month also interest

Remaining loan balance of the month = remaining loan balance last month-month return principal

So:

Remaining loan balances for the month

= remaining loan balance last month-monthly return principal

= remaining loan balance of last month-(monthly amount-monthly interest)

= Last month's remaining loan balance-monthly payment + month interest

= Last month remaining loan balance-monthly amount + last month's remaining loan amount of X-month interest rate

= Last month remaining loan balance X (1 + monthly interest rate)-monthly return amount

Set

A = Loan Amount

R = Monthly interest rate

n = number of periods

z = Monthly return amount