As a key and difficult problem in senior high school mathematics, the key to effectively answer the problem of equal repayment is to clarify the relationship of equal repayment design: actual loan amount+loan interest generated during repayment = repayment amount per installment+loan interest generated during repayment. Whether it is a collective or a member of society, after a one-time loan of H yuan, it is necessary to choose the repayment method according to factors such as interest rate and equal repayment within the time limit stipulated by the loan bank. It can be said that the selected equal repayment method is closely related to the interests of units and individuals. Here is an example to illustrate the problem of equal repayment.

Second, the calculation of equal repayment

Example 1: At the beginning of the year, someone borrowed 654.38 million yuan from the bank to buy a house.

(1) If the annual interest rate of the bank he borrowed is 5%, he intends to divide it into 10 times, and repay it in equal amount from the second year after the loan, excluding compound interest. So, how much does he need to pay back to the bank every year?

(2) If the annual interest rate of the bank he borrowed is 4%, he still intends to repay the loan in installments of 10. Then, if the interest of the previous year is included in the principal interest of the second year, how much does he need to repay to the bank every year? Analysis: Whether calculating simple interest or compound interest, a common algorithm is to replace deposits, but in real life, this algorithm has no practical significance, and even brings unnecessary economic losses to both borrowers and borrowers. Therefore, when calculating the equal repayment problem, we should avoid the algorithm of replacing deposits. Taking (1) in the example as an example, if it is calculated by saving, assuming that X yuan needs to be repaid every year, the following equation can be obtained:105 (1+10 * 5%) = X (1+9 * 5). It is obviously unreasonable for the lender, and the final conclusion calculated based on this equation naturally does not have the accuracy it deserves, so the calculation of equal repayment of loans loses its original meaning. Through the rational use of the knowledge points mastered at this stage, the correct calculation method can be obtained as follows: divide all loans into n shares on average, and the amount of each loan is a 1, a2, ..., an. Assuming that the total loan amount is H and it is paid off in ***n years, the following equation can be obtained: A 1+A2+...+An = H assuming a single loan. X represents the sum of the principal and interest that the lender needs to repay when the loan expires in K years, that is, x=ak( 1+kr). AK = X/ 1+krH =(X/ 1+R)+(X/ 1+2r)+(X/ 1+3r)+……(X/ 1+NR)X = H(X/ 1+R)+(X/ 1+2r)+(X/ 1+3r)+……(X/65438)

(1) Suppose you need to repay X yuan every year, then: X =105 (11+5%)+(11+10%.

(2) Assuming that X yuan needs to be repaid every year, then: X =105 (11+4%)+(1+4%) 2+(1/). The remaining 6,543,800+0.5 million yuan was loaned in a commercial bank for five years in the name of individual housing, and the annual interest rate of the commercial bank was 4.77%. Then, in the two repayment methods that can be selected, which one needs to pay less loan interest? Analysis: According to the topic, the annual interest rate of this commercial bank is 4.77%, so the monthly interest rate should be 4.77%/12 = 0.3975% (1). Choose the average capital repayment method. The monthly interest is: monthly principal = 15000/60=2500 (yuan), the first month interest = 15000 * 0.3975% = 596.25 (yuan), and the second month interest = (15000-) 0.3975% = 576.38 (yuan) ... interest of 60th month = 2500 * 0.3975% = 99.94 (yuan). The total interest is 18 185.55 yuan. (2) Choose the repayment method of equal principal and interest. The monthly repayment amount is:15000 * 0.3975% * (1+0.3975%) 60 (1+0.3975%) 60-1= 2814.995. 2814.91-15000 =18894.6 (yuan) Through calculation, it can be found that the average principal repayment method is more affordable than the equal principal repayment method, but in the first few months of repayment, the repayment person needs to bear greater pressure.

Three. Concluding remarks

Through the analysis of the above contents, it can be seen that in order to accurately and efficiently calculate and solve the problem of equal repayment of loans, the formulas involved in this paper must be reasonably applied, and the calculation formulas and methods that meet the characteristics of different topics must be selected according to their characteristics. It should be noted that in real life, most banks in China follow the principle of "equal repayment of principal and interest". Therefore, when combining theory with practice, we need to pay attention to this aspect to avoid unnecessary problems.

References:

Wu Min. Excel-based analysis of repayment of principal and interest in advance [J]. Modern commercial trade industry, 2015,3624:18-119.28.