"Mathematics in Buying a House" uses the mathematical knowledge we have learned to understand that mathematics permeates life through the essential phenomenon of buying a house. Part I: Application of Simple Interest in Installment Example: Mr. Chen bought an ordinary apartment at a price of 84,000 yuan, which was paid off in 15 years, with an annual interest rate of 2. 143%. So how much does he pay every month, and how much does he actually pay? (It is known that interest is calculated according to simple interest) By searching information on the Internet, we get the formula for calculating interest: interest = principal * interest rate * time. Bring the above data into this formula: interest = 84,000 * 2.413% *15 = 27,000 (yuan), so the amount of money payable per month is In order to improve the family housing conditions, a resident in a certain place decided to buy a house again in 2003. One day, he came to a real estate market. Faced with the advertisements of many real estate developers, should he buy commercial housing or second-hand housing? After some investigation, the resident collected some information about housing, and then listed his family's economic situation and alternatives in the table below, ready to consult experts. The family's total monthly income is 3000 yuan, that is, the annual income is 36000 yuan. The existing deposit is 60,000, but 20,000-30,000 must be reserved for emergency use. The pre-selection plan is 1. Buy an 80-square-meter commercial house. Price per square meter 1500 yuan. 2. Buy a second-hand house with an area of 1 10 square meter and a price of142,000 yuan. Buying a house requires a down payment of 40 thousand and a loan. The resident chose a bank to apply for a housing loan. According to the information in the form, the loan evaluator of the bank provided him with the following information and suggestions: apply for a commercial loan. The down payment for house purchase shall not be less than 20% of the actual house purchase amount, and the loan amount shall not exceed 80% of the actual house purchase amount. The repayment method is equal principal repayment. According to the above loan methods, which do you think is the best choice 1, 2 (prerequisite: the area of two houses is acceptable to this resident)? This problem seems to be at a loss, but after careful analysis, it will be found that this problem can be solved with the knowledge of the content and series involved in this report. Comparing the two schemes which is the best, we mainly consider from three aspects. First, whether the down payment amount is within the economic capacity of this resident; Second, whether the annual repayment amount after the loan is within the economic capacity of residents; Third, what is the actual payment and the original value of the house? Below, we will solve these problems one by one. The down payment shall not be less than 20% of the actual total purchase price. If it is only 20%, the down payment for commercial housing needs 80 *1500 * 20% = 24,000 yuan, and the second-hand housing needs 40,000 yuan. As can be seen from the table, they are all within the economic capacity of residents. Because residents borrow money to buy a house, we assume that residents repay X yuan every year. According to the information given in the title, we can list the following tables:/kloc-principal and interest after 0/5 years and x * (1+5.04%) in the first year14 in the second year * (1+5.04%)13 in ............ in the fourteenth year. In the fifteenth year of 1, all the above data are added up, which is the actual amount payable by residents. If you buy a commercial house, you can get the following equation: (1+5.04%)14 * x+(1+5.04%)13 * x+(1+5.04%) 650. The solution of x+(1+5.04%)1* x+x = (120000-24000) * (1+5.04%)15 is x = 9273. The actual contribution of this resident is: 9273.9 *15+24000 =163108.50 yuan, which is163108.5-120. Then the following equation can be obtained: (1+5.04%)14 * x+(1+5.04%)13 * x+(1+5.04%) 65438+. For the solution of 15, x+(1+5.04%)1* x+x = (142000-40000) * (1+5.04%) x = The actual amount paid by this resident is: 9853.5 *15+40000 =187802.50 yuan, which is more than the original house price:187802.50-142000 = 45802.50 yuan. We can compare the above conclusion list as follows: comparing the down payment amount of Scheme I and Scheme II, 24,000.00,40,000.00, the payment amount of 9273.90,9853.50, and the actual payment amount of 65,438+06,365,438+008.50. The difference between 187802.50 and the original house price is 43 108.50 45802.50. According to the above table, it is easy to draw a conclusion that no matter which comparison project, scheme 2 is not as good as scheme 1. Therefore, the first plan is much better, that is, it is more cost-effective for residents to buy commercial housing. Part III: Investigation on the correlation between income level and installment (bank loan to buy a house) Question: 1, how much is your monthly income? 2. How did you buy the house? We collected the answers from 50 people and processed the data. The contingency table with the following two rows and two columns is obtained: installment payment (bank loan) with one-time payment totaling more than 5,000 yuan 71185,000 yuan and less than 24,832 total 3 1 1950 is known. The relevant formula is: among them, we substitute the data in the above table into the relevant formula: To sum up, it shows that the income level has a great relationship with whether to buy a house by stages or bank loans.