The annual interest rate of matching principal and interest is generally determined by the lending institution and the lender through consultation, and the interest rate will be written in the loan contract. If a daily interest rate or a monthly interest rate is given, then the annual interest rate needs to be converted. The conversion formula between them is: annual interest rate = monthly interest rate * 12= daily interest rate *30. For example, if the monthly interest rate is 0.4%, then the annual interest rate is 0.4%* 12=4.8%. The daily interest rate is 0.04%, so the annual interest rate is 0.04%*360= 14.4%.

1

The so-called matching principal and interest means that the repayment amount is the same every month, while the principal is reduced every month. Now let's assume that P is the loan principal, R is the monthly interest rate, K is the number of loan periods, and X is the monthly principal plus interest repayment amount, which is fixed. The amount owed to the bank after the first repayment is shown in the following figure:

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2

Then the money owed to the bank after the second month of repayment can be compared, and the money owed to the bank after the second month of repayment can be simplified into the form of the second formula.

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three

By analogy, the debt owed to the bank after the third month of repayment is as follows. In the second formula, the money owed to the bank is multiplied by the monthly interest rate MINUS the repayment amount in each period, and the simplified formula is in the form of Article 2.

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four

By observing the above formula and observing the law, the formula of owing bank after K period is obtained by mathematical induction, as shown in the following figure. After simplification, it can be written in the form of geometric series, and the following simplified formula form is obtained.

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five

Because there is K period, the amount of money owed to the bank after K period is 0, so the following equation holds. Then the formula of equal principal and interest can be deduced according to the following formula.

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six

The formula of monthly repayment amount obtained in the fifth step is as follows. Conversely, knowing the monthly repayment amount can also calculate the monthly interest.

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