(A), the standard component modeling paper
As a meaningful attempt of inquiry learning, model essay can cultivate students' ability to find and solve problems. Generally speaking, the standard components of modeling papers are composed of title, abstract, body, conclusion, references and so on. Now, let's make a brief description of each part.
1. Title
The title is the first impression to the judges, so the title of the paper must avoid the phenomenon of unclear reference and expression. It is suggested to write the model involved in the paper or the calculation method used in the topic, such as "calculating the income of discounts and coupons in shopping malls by probability method"
2. Summary
Abstract is an important part of the paper. Concise language should be used to describe the core ideas and main viewpoints of the paper. If you have some innovations, you must explain them abstractly. Further, you must put some numerical results in the abstract, such as: "Our final calculation shows that the discount rate is 23% higher than the rebate rate of consumers." The summary should be written at the end. You shouldn't write an abstract until the rest of the paper is finished. Because the abstract is the concentrated expression of the theme and core content of the paper, you can only write the abstract if you finish all the papers and make the style of the papers clear.
Generally, it is divided into three parts, and the center of the whole paper is expressed in three sentences.
In the first sentence, what mode to use and what problems to solve.
The second sentence is how to solve the problem.
The third sentence, what is the final result?
Of course, for junior students, you don't have to write an abstract.
3. Text
The text is the core and the most important part of the paper. In the writing of the thesis, it should be carried out step by step in the way of "asking questions-analyzing problems-selecting models-establishing models-drawing conclusions". Among them, raising and analyzing problems should be clear and to the point, while selecting and establishing models should have clear objectives, detailed data, reasonable formulas and accurate calculations. In writing articles, we should try not to use simplicity.
4. Conclusion
The conclusion of this paper reflects the research results of this paper. It can be said that only when the conclusion of this paper can stand scrutiny can the paper get a higher evaluation. The writing of conclusion should pay attention to the accuracy of words and keep absolute unity with the phenomena or data described or demonstrated in this paper. It is also necessary to make self-comments on the conclusion, and it is best to extend the conclusion to social practice for testing.
5. Reference materials
If other people's materials are used in the paper, the author and application source of the cited article must be indicated at the end of the paper.
The following are two award-winning papers I found.
How should the mortgage be repaid reasonably?
Abstract and keywords:
This paper mainly discusses how to repay the mortgage reasonably.
Keywords: mortgage loan principal interest rate average capital equal principal and interest
I. Asking questions
With the development of economy, finance has increasingly entered the lives of ordinary people; Loans, insurance, pensions and credit cards; Personal housing mortgage loan is one of the important projects.
In today's society, the hottest topic is "buying a house". At present, the housing price in Beijing is around 30,000-40,000 square meters, which makes people have to choose loans. And going to the bank for a loan is actually a science. How should I repay the mortgage?
The following data is the recently announced bank loan interest rate.
Short-term loans:
Medium and long-term loans:
Within six months (including six months): 5.60
One to three years (including three years) 6. 10
Six months to one year (including one year) 6.06
Three to five years (including five years) 6.45
More than five years 6.60
Two. Model hypothesis
1. The bank interest rate remains unchanged during the loan period.
2. During this period, the influence of economic fluctuation is not considered.
3. The customer's repayment ability will remain unchanged during the repayment period, and repayment will not be made in advance.
Three. make a model
Symbolic regulation
A: The principal of the customer's loan from the bank.
B: The average principal payable by the customer in each installment.
C: The total amount that the customer should repay to the bank.
D: the total interest burden of customers.
α: the monthly interest rate of the customer's loan to the bank.
β: the annual interest rate of the customer's loan to the bank.
M: loan term
N: the total repayment period of the customer.
According to the common sense of our daily life, we can get the following relationship:
( 1) (2) (3)
Two common repayment methods
(1) Equal repayment of principal and interest
Add up the total principal and interest of the mortgage loan and distribute it evenly to each month of the repayment period. As a repayment, he pays a fixed amount to the bank every month.
(2) Repayment of equal principal
Also known as interest repayment with principal, average capital and unequal interest. The lender will allocate the principal to each month and pay off the interest from the previous trading day to the repayment date.
Matching principal and interest repayment mode
(1) The loan term is greater than 1 year;
We assume that the principal lent by the bank to customers will be paid in one lump sum on 1 day of a month. As stipulated in the customer's contract, the repayment will start on 1 day after the principal payment, and the annual interest rate will remain unchanged during the repayment period.
Because the annual interest rate of one year is β, then the average month is (β/ 12), which is the monthly interest rate α.
That is to say, there is a relationship:
Assume that the average monthly repayment amount is X (yuan).
(I = 1...n) is the amount that the customer still owes to the bank before the first installment 1.
(i= 1…n) is the amount owed to the bank by the customer after the first installment 1 repayment.
According to the above analysis, there are
1 Amount owed to the bank before installment repayment:
1 Amount owed to the bank after installment repayment:
……
Amount owed to the bank before the first repayment:
Amount owed to the bank after the first installment repayment:
……
Amount owed to the bank before the N-th installment repayment:
Amount owed to the bank after the N-th installment repayment:
Because after the n th repayment, the money owed by the customer to the bank was paid off. That is to say:
,
Namely:
To solve this equation:
This is the formula of the total monthly repayment.
Therefore, the customer's total repayment amount is equal to:
The total interest burden is equal to:
Matching principal repayment mode
Assume that the loan term is greater than 1 year.
Assume that the customer's down payment amount is (i= 1…n) (unit: RMB).
Therefore, the amount that the customer should pay in the first payment is:
The amount payable in the second stage is:
Then, the amount payable by the customer in N period is:
The total amount of accumulated repayments payable is:
The total interest burden is:
4. Model solving
Someone borrowed 6,543,800 yuan from the bank, with a loan period of 5 years, that is, repayment in 60 installments, with a loan interest rate of 6.45. The repayment amount of each installment is shown in the following table:
Equal principal and interest repayment yuan equal principal repayment
First time 19542.7 2 19538+0
Second time 19542.7 2 1862.83
Third time 19542.7 2 1773.24
The fourth time 19542.7 2 1683.66
The fifth time 19542.7 2 1594.07
10th place19542.721146.6438+05
The 20th session 19542.7 20250.30
30th time 19542.7 19354.45
40th time 19542.7 18458.6
50th time 19542.7 17562.7
Sixtieth 19542.7 16666.89
The total repayment amount is11711160000.
Loan for 20 years
Equal principal and interest repayment equal principal repayment
First 75 14.72 9643.75
Second 75 14.72 9620.84
Third 75 14.72 9597.92
The fourth 75 14.72 9575
The fifth 75 14.72 9552.09
10th place 75 14.72 9543.5
20th 75 14.72 9208.34
No.50 75 14.72 8520.84
No.80 75 14.72 7833.34
100 No.7514.72 7375
No. 150, No.75 14. 57657.88666866667
No. 180 75 14.72 55438+0.67
200th 75 14.72 5083.33
No.265438+00th 7514th 5864866
No.220 75 14.72 4625
No.230 75 14.72 4395.83
No.240th 75 14.72 4 166.67
The total repayment amount is 654.38+0.8 million 654.38+0.66 million.
Loan for 30 years
Equal principal and interest repayment equal principal repayment
The first time 6386.59 8262.5
Second time 6386.59 8247.22
Third time 6386.59 823 1.95
The fourth time 6386.59 82 16.67
The fifth time 6386.59 820 1.39
Tenth 6386.59 8 125
Twentieth time 6386.59 7972.22
No.50 6386.59 75 13.89
The hundredth time 6386.59 6750
One hundred and fifty times, 6386.59+0438+0. 56686.5986868666 1
200th time 6386.59 5222.22
250th 6386.59 4458.33
The hundredth time 6386.59 3694.44
3rd time10 6386.59 34438+0.67
No.320 6386.59 3388.89
330th, 53660.66861
The 340th time 6386.59 3083.33
350th 6386.59 2939.55
The 360th time 2777.78
The total repayment amount is 2.29 million 1.99 million.
Verb (abbreviation of verb) model analysis
Equal principal repayment: suitable for people with higher income at present. When the borrower starts to repay the loan, the monthly burden is heavier than the equal principal and interest. As time goes on, the repayment burden will be gradually reduced. Compared with the method of equal principal and interest in the same period, the total interest expense of this repayment method is lower.
The characteristic of equal principal and interest repayment method is to repay equal principal and interest every month, which is easy to budget. Interest accounts for most of the monthly payment in the initial repayment period. With the gradual return of the principal, the proportion of the principal in the contribution is also increasing. Matching principal and interest repayment method is more suitable for borrowers with less current income, stable or increased expected income, or people with clear budget and stable income.
Application of intransitive verb model
This model can be applied in practice, and every mortgage buyer can apply this model to optimize various loan schemes according to their own conditions and affordability.
Comparison between ETC charging and parking charging costs
Are we really at a loss in the face of serious traffic jams on expressways? A few years ago, Sutong Company introduced the ETC toll collection system, which should have alleviated the congestion of expressway toll stations to a great extent, but the actual effect was not satisfactory. We think the main reason is that the cost of ETC is too high, and a machine costs 450 yuan money, so many people prefer to spend time waiting on the road.
In fact, if you calculate the cost carefully, you will have a new understanding of this problem.
Our average parameters are: vehicle weight m= 1.4t, and friction coefficient between tire and ground u=0. 17.
The calorific value of gasoline q= J/kg, the price of gasoline is 7.85 yuan/liter (10.68 yuan /kg), the engine idle power p= 17 kw, and the thermal efficiency is 23%.
Generally, one car leaves the expressway, and there are usually several cars in the driveway. We have an average of five cars. The average payment time per vehicle is 10s. In this way, each car starts to brake 5 times when charging, and waits for 50 seconds. Each starting speed ranges from 0 to 10 mph, and the starting distance is 5 meters.
From this we calculate;
1 Fuel consumption at start-up, let be, and the equation is obtained by energy conservation. After substituting the data, = 7.7g ..
2 fuel consumption when waiting 10 second, = =16.1g.
So the car consumes = 1 19g gasoline every time it goes out at high speed, which is about 1.3 yuan. If you take the expressway once a week, 52 times a year is 67.6 yuan, and the meaningless gas money spent on the expressway toll station in six years is 473.2 yuan, which is enough to buy an ETM machine. In addition to gas money, intermittent starting and braking at each payment will also cause considerable losses to the engine and brake pads, and increase additional maintenance costs. Another important point is the wasted time, averaging 50 seconds at a time. If the motorcade several kilometers long goes ahead in the rush hour, let alone delay the time. Therefore, considering the above factors, if the car often takes high speed in six years, the cost of using ETC is lower than the parking fee.
From the owner's point of view, the car is equipped with an ETC machine, which can complete the payment at a low speed. It not only saves the wasted oil money waiting for frequent starting, but also reduces the wear of engine brake pads, saving a lot of time.
From the perspective of road administration, if parking fees are charged, it is necessary to invest a lot of paper, ink and computer processing systems in toll stations and arrange corresponding staff. The money collected needs to be collected and transferred once before it can be deposited in the bank, which is both costly and troublesome. If you use the ETC system, you can charge without paper, and the money paid by the owner can be directly linked to the account, saving many steps. Therefore, from these aspects, ETC system can reduce the cost of highway departments in toll stations.
From the environmental point of view, cars will emit a lot of exhaust gas when braking and waiting, which is several times that of normal driving, especially when the toll station is congested during rush hour, and hundreds of cars are stuck on the road for several kilometers, and the exhaust gas displacement and density are amazing. The use of ETC system can effectively alleviate the congestion of toll stations, thus reducing the impact of automobile exhaust on the surrounding environment of toll stations.
Based on the above factors, the use of ETC system will play a huge positive role in the cost of car owners, highway departments and the environment. We also have two suggestions for purchasing ETC system, that is, whether the road administration department can also help car owners share some expenses, because it is beneficial to both sides; Perhaps the government can also introduce relevant policies, equip cars with ETC machines when they leave the factory, include this money in the cost of car purchase, and give corresponding subsidies.
In short, the more vehicles with ETC installed, the smoother the high-speed toll station will be.
I hope the landlord will adopt it. . . . . . . . . . . . . . . . . . . . . It's hard. .