Have you been passed by bank routines? | Yiwen teaches you to calculate the true annualized interest rate
Code Ape Stone 
background
You must also often receive phone promotions from various banks, you can apply for microloans/credit card bill installment/universal funds, or other products with messy names.
Or you may receive a call saying, "Mr. Stone, we have noticed that your bill this month is X million yuan. Please rest assured that I am not calling this time to urge you to repay. Based on your high quality in our bank credit, our side can help you apply for deferment, but also do not have the money this month, next month installments also, just a month repayment xx yuan to ...... "(have the impression it?)
then asked electricity Sales staff, how much is your final annualized interest? At
this time, the general bank customer service will directly avoid this question. The beautiful name is: "We don't charge interest, we only charge a certain fee. Based on your good credit, Now you have a limit of 50,000 that can be withdrawn immediately, which can be repaid in 12 installments, and only XXXX yuan per month." 
Students who may not understand, heard the promotion of bank customer service classmates, and felt that the interest rate is not too expensive, and it is quite cost-effective to lack money in an emergency. It is possible to get caught up in the routine directly, so he accepted the deception and applied for this loan/instalment product.
Case interpretation
Let me use the actual example of Shanghai Pudong Development Bank to calculate the final annualized interest rate of similar products. 
As shown in the picture above, it is a product of Shanghai Pudong Development Bank called "Universal Gold". It can be seen that withdrawing 10,000 yuan, repaying the money in 12 installments (that is, 12 months), the repayment method of equal principal and interest, monthly The repayment is 929.51 yuan.
Fudge you, no discussion
In preliminary calculations, you may simply think that this interest rate is that the total amount of money to be repaid is 929.51 12, and the loan principal is 10,000 yuan, then the annualized interest rate is: (929.51 12-10000 )/10000*100%=11.54%, It feels okay, not an exaggeration. 
But in fact, this algorithm is problematic, because you borrowed the principal of 10,000 yuan, and did not enjoy the one-year period, and you will repay the principal every month thereafter.
Actual annualized interest rate
Let's use the common online mortgage/borrowing calculator[1] to calculate. If calculated at an annualized 11.54%, the monthly repayment situation should be as follows, that is, only 886.34 equal principal and interest repayments are required each month, which is 929.51 yuan. A lot less. 
And if the monthly repayment is 929.51 yuan, the interest rate is far more than 11.54%. Just use the loan calculator to estimate it.
It seems that the existing online tools can only be calculated forward, that is, the known interest rate and loan principal are calculated in the repayment schedule. There is no tool that can reverse the loan interest rate from the monthly repayment amount. Initial attempts to obtain the following approximate result. (Note: This article was originally an article written in 2017. Now there are similar calculators on the Internet. You can directly use the method in the following article to calculate.) As 
you can see, the annualized interest rate has reached 20.66%, which is better than previously expected. Too much.
Therefore, when telemarketing is promoting sales, it often does not tell you the annualized interest rate directly, because it is too high and you may not accept it.
In fact, you borrowed the principal of 10,000, and did not enjoy the whole year, but only enjoyed one month, because after one month, you will have to return part of the principal (and interest).
And how is this interest rate calculated? Why is there such a big difference between before and after? Let's continue.
How to calculate the annualized interest rate
Applet method
Here is a small program that I wrote about 17 years ago (it was difficult to find it on the market at the beginning). You can use it directly by clicking the small program below.
As shown in the figure above, directly enter the total loan amount, monthly repayment amount and the number of repayment months to calculate the annualized interest rate. Later, there was feedback from users, hoping to have a function of calculating the repayment plan with a known borrowing rate, so this function was added before. The forward calculation function can be divided into equal principal and interest, equal principal and pre-interest There are three repayment methods for the latter. 
If
you want to see how to derive the calculation process, please remember to experience the applet and come back and continue to read the analysis later.
How Excel calculates
With the help of Excel, we can also easily calculate the correct annualized interest rate. 
Excel calculates the annualized interest rate
directly by using the IRR function in Excel, or directly using the RATE function.
- IRR function: Enter the total number of direct installments and the number of repayments in each subsequent installment.
- RATE function: input as three parameters, which respectively represent: the number of installments, monthly repayment amount, and total loan amount.
In fact, according to the official Excel document, Excel's IRR and other functions are also calculated by the iterative method. For details, please refer to the Excel IRR function description [2]
If you just want to know how to calculate the repayment interest rate with ready-made tools, you can go here. ended.
If you are more curious, what is the calculation behind this, let's continue.
Especially for programmers, you can try it yourself. Can you implement the following RATE function in Excel?
Derivation method
If there is no idea, let's follow my rhythm. Let's derive forward the calculation process of this equal principal and interest rate. 
Assuming that the total borrowing amount is A, the monthly interest rate is R, and the monthly repayment amount is M, grasp one point, the total amount of arrears principal* (1+monthly interest rate) is: the 
derivation process (enlarge the view),
so you can get the first For the arrears of month i, the above formula can be simplified, because after the subtracted number M is a geometric series, after the i-th month is obtained, the total arrears is:
If you know the monthly interest rate R, you can calculate the monthly repayment amount directly through the above formula,
Still based on the above example of Shanghai Pudong Development Bank, where A=10000, M=929.51, the value of R can be calculated by substituting the above formula. 
but! How to solve the above equation?
We can also learn from Excel. People say that iterative method is used. We can too.
I wrote a small code and searched iteratively to figure it out. It seems that there is an interview question for programmers here, haha.
Dear programmers, see what methods can be calculated? I will not publish the code I wrote here for the time being. See if you have any ideas? (knock on the blackboard) It 
is calculated by calculation. With a loan of 10,000 yuan and a monthly repayment amount of 929.51 yuan, the monthly interest rate is 0.017, which is 1.7% , The annualized interest rate is 20.65%, which is basically the same as that found at the beginning of the article.
After the monthly interest rate comes out, the repayment schedule will naturally come out.
>>> monthRate = calcMonthRate(12, 10000, 929.51)
>>> print monthRate
0.0172138214111
>>> print monthRate * 12
0.206565856934
>>> schedules = repaymentSchedules(12, 10000, monthRate)
>>> for s in schedules: print s
...
[1， '929.49'， '172.14'， '757.35'， '9242.65']
[2， '929.49'， '159.10'， '770.39'， '8472.26']
[3， '929.49'， '145.84'， '783.65'， '7688.61']
[4， '929.49'， '132.35'， '797.14'， '6891.47']
[5， '929.49'， '118.63'， '810.86'， '6080.61']
[6， '929.49'， '104.67'， '824.82'， '5255.79']
[7， '929.49'， '90.47'， '839.02'， '4416.77']
[8， '929.49'， '76.03'， '853.46'， '3563.31']
[9， '929.49'， '61.34'， '868.15'， '2695.16']
[10， '929.49'， '46.39'， '883.10'， '1812.06']
[11， '929.49'， '31.19'， '898.30'， '913.76']
[12， '929.49'， '15.73'， '913.76'， '0.00'
It can be seen that the above repayment schedule is consistent with the initial online mortgage calculator. Let’s take a look again. China Merchants Bank has a cash installment business. 
The above instalment rate is 12 installments, 0.75% (surface monthly interest = (3270 12-36000)/36000/12), application installment 36000, monthly repayment 3270. Through the above formula, let's take a look at the actual rate. The monthly interest rate is equivalent to 1.35% and the annual interest rate is 16.2%, which is much higher than the apparent annual interest rate (0.75% 12=9%).
>>> calcMonthRate(12, 36000, 3270)
0.013513565063476562
>>> calcMonthRate(12, 36000, 3270)*12
0.16216278076171875Small science
Finally, here is a small science popularization. For the annualized loan interest rate, there are two numbers as the dividing line, 24% and 36%.
- If the interest rate agreed by the borrower and lender does not exceed 24% of the annual interest rate, and the lender requests the borrower to pay interest at the agreed interest rate, the people's court shall support it.
- The interest rate agreed by the borrower and lender exceeds the annual interest rate by 36%, and the interest agreement for the excess part is invalid. Where the borrower requests the lender to return the interest that has been paid in excess of 36% of the annual interest rate, the people's court shall support it.
Conclusion
So, friends, next time the bank will call you, do you know how to deal with it? No longer have to be confused by the so-called handling fee interest rate (surface phenomenon)!
In addition, the majority of programmers friends are invited to think about the problems left before, and see what methods everyone has to calculate. Welcome to leave a message for discussion.
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