I. The meaning of equal principal and interest
1, equal principal and interest, refers to a loan repayment method. Matching principal and interest means paying the same amount of loans (including principal and interest) every month during the repayment period.
2. It is not the same concept as average capital. Although the monthly repayment amount may be lower than the average capital repayment method at the beginning, the interest paid in the end will be higher than the average capital repayment method commonly used by banks.
2. Calculation formula of monthly repayment of equal principal and interest
[loan principal × monthly interest rate ×( 1+ monthly interest rate) repayment months ]=[( 1+ monthly interest rate) repayment months-1]
The following example illustrates the equal principal and interest repayment method.
Suppose the borrower obtains a personal housing loan of 200,000 yuan from the bank, with a loan term of 20 years and an annual interest rate of 4.2%, and pays the principal and interest on a monthly basis. According to the above formula, the monthly repayment of principal and interest is 1233.5438+04 yuan.
The above results only give the sum of the principal and interest payable each month, so it is necessary to decompose this sum of principal and interest.
Refund method
That is to add up the total principal and interest of the mortgage loan, and then distribute it evenly to each month of the repayment period. The monthly repayment amount is fixed, but the proportion of principal in the monthly repayment amount increases month by month, and the proportion of interest decreases month by month. This method is the most common and recommended by most banks for a long time.
Matching principal and interest repayment method refers to the borrower's equal repayment of loan principal and interest every month, in which the monthly loan interest is calculated according to the remaining loan principal at the beginning of the month and settled every month.
The average capital repayment method means that the borrower repays the loan principal with the same amount (loan amount/loan months) every month, calculates the loan interest according to the remaining loan principal at the beginning of the month, and settles it every month, and the sum of the two is the monthly repayment amount.
computing formula
Monthly repayment amount = [loan principal × monthly interest rate ×( 1+ monthly interest rate) repayment months ]=[( 1+ monthly interest rate) repayment months-1]
Deduction of repayment formula
Assuming that the total loan amount is A, the monthly interest rate of the bank is β, the total number of installments is M (months) and the monthly repayment amount is X, the monthly loan owed to the bank is:
The first month A( 1+β)-X
Second month (a (1+β)-x) (1+β)-x = a (1+β) 2-x [1+β)]
The third month ((a (1+β)-x) (1+β)-x)-x = a (1+β) 3-x [1+(.
It can be concluded that the loan owed to the bank after the nth month is a (1+β) n–x [1+(1+β)+(1+β) 2+…+(1+β) (n
Because the total repayment period is m, that is, all bank loans have just been repaid in the m th month.
So there is a (1+β) m–x [(1+β) m-1]/β = 0.
x = aβ( 1+β)m/[( 1+β)m- 1]。
Repayment method and calculation of average capital
1. Repayment amount of equal principal and interest repayment method:
Monthly repayment amount: a * [I * (1+I) n]/[(1+I) n-1]
(Note: A: loan principal, I: monthly loan interest rate, n: loan months)
2. Average capital repayment method repayment amount:
Monthly principal repayment: None
Monthly interest payable: 30 days
Total monthly payable: a/n+ an*i/30*dn.
(Note: a: loan principal, i: monthly loan interest rate, n: loan months, an: remaining loan principal in the nth month, a 1=a, a2=a-a/n, a3 = a-2 * a/n ... The actual number of days in the nth month of dn and so on, for example, February in a normal year is 20.
Interest calculation of repayment method
Interest calculation of equal principal and interest repayment method:
Repay the loan with equal principal and interest. Calculate the monthly repayment principal and interest first: bx = a * I (1+I) n/[(1+I) n-1].
Repay the loan with equal principal and interest. Repayment of loan principal in the nth month:
b=a*i( 1+i)^(n- 1)/[( 1+i)^n- 1]
Repay the loan with equal principal and interest: interest for repayment in the nth month:
x = bx-b = a*i( 1+i)^n/[( 1+i)^n- 1]- a*i( 1+i)^(n- 1)/[( 1+i)^n- 1]
(Note: BX= the total amount of principal and interest repaid each month when the loan is repaid with equal principal and interest.
B= equal repayment of principal and interest, monthly repayment of principal,
A= total loans
I= monthly loan interest rate,
N= total repayment months,
N= the nth month
X= monthly interest paid to repay the loan with equal principal and interest)
Interest calculation of average capital repayment method
Monthly interest payable: 30 days
3. Repay in advance with equal principal and interest.
Early repayment refers to the behavior of the borrower to repay the loan before the repayment period. In some cases, prepayment is beneficial to the borrower and unfavorable to the lender, so whether prepayment is allowed and the conditions for prepayment should be clearly stipulated. Prepayment includes full prepayment, partial prepayment with unchanged loan term and partial prepayment with shortened loan term.
When choosing the loan term and repayment method, we should fully consider the operation of funds and the subsequent sources of funds. It is suggested that the term should be as long as possible, and the prepayment should be as little as possible (preferably lower than the amount of repayment funds that can be determined), so as to increase flexibility and prevent bad credit records or financial difficulties caused by insufficient repayment funds. At the same time, when the funds are abundant, you can choose to use these funds for investment (it is recommended to choose products with lower risks, such as capital-guaranteed wealth management products, government bonds, corporate bonds, etc. ), and you can choose to repay in advance (if the yield of low-risk investment is lower than the bank loan interest rate, you will generally choose to repay in advance). However, it is necessary to agree with the bank not to charge liquidated damages for early repayment (agreed in the loan contract).
In short, so choose the repayment method that suits you, and choose to repay in advance when the funds are abundant. If the expected income in the future decreases gradually and you want to save interest, then my suggestion is to choose the repayment method of average capital. The final repayment interest of this repayment method will be less than that of the repayment method with equal principal and interest, because whether the interest is reduced or increased, the repayment interest is related to the loan principal and is not affected by other variables. It should be noted that the total amount of repayment is actually the same when the interest rate remains unchanged.
Collection of liquidated damages for prepayment
At the beginning of this century, some banks in the United States restricted the prepayment of loan customers by some means, such as requiring prepayment to pay liquidated damages, or only allowing partial prepayment, or limiting prepayment to less than three years. The reason is that a large number of bank loans are lent through third parties, and banks have to pay a large commission in advance for this; In addition, the initial interest rates of many loans issued by banks themselves are set at low levels to attract customers. The high initial cost of banks, once customers optimize loans or prepay, will inevitably lead to the disaster of bank loan costs.
In order to limit prepayment, some lending institutions put forward a concept called substantial prepayment. Different lending institutions have different standards for substantive behavior, but generally it means that the prepayment amount of the borrower exceeds 20% of the principal balance within 12 months. Under this concept, some banks require borrowers to repay in advance to pay liquidated damages.
Liquidated damages for early repayment are the terms agreed in the contract between the borrower and the lender. Once the borrower pays off all the loans or most of the principal in advance within the specified time, the borrower will pay the liquidated damages. Liquidated damages are generally calculated according to the percentage of the outstanding balance at the time of prepayment (generally 2% to 5%); Or agree on interest for several months. However, the maximum liquidated damages are subject to contract or law.
The validity period of liquidated damages usually does not exceed 3 years (some are 5 years). After the validity period, the penalty rate will be cancelled, or gradually reduced, or only 1% of the balance. As long as the annual prepayment does not exceed 20% of the loan balance, there is no need to pay liquidated damages.
As far as personal housing loans are concerned, under the current circumstances, commercial banks do not want personal housing loans to be repaid in advance, because they have always regarded such loans as the best loans for banks, and the competition among banks for personal housing loans is fierce, so commercial banks certainly do not want personal housing loans to be repaid in advance. The reason why some commercial banks dare not charge liquidated damages for personal housing credit prepayment is not because they don't want to get this profit, but because of the competition among banks.
At present, there is no uniform regulation on the collection of liquidated damages for prepayment in China, and whether to collect liquidated damages for prepayment is still controversial, and the handling methods of banks are not the same. The common practice is to cancel the 30% interest discount for personal loan customers who repay their mortgages in advance, which increases the interest amount of customers, and many customers have given up the idea of prepayment.
abstract
Whether it is equal principal and interest repayment method or average capital repayment method, the nature of interest will not change. Interest rates are determined by the impatience of countless people. Because of impatience, that is, impatience, people always want to enjoy it early, so there is an exchange of "spot" and "futures"; It is precisely because of impatience that the "futures" farther away from today, the lower their value. Therefore, in order to realize the transaction between "spot" and "futures", the number of "futures" must be greater than "spot", and the difference between them determines the interest rate.
Many people mistakenly think that the average capital repayment method can save interest because they don't understand the principle of bank interest calculation. Actually, it's not. As we all know, every day you deposit money in the bank, you will get interest. The more money you save, the more interest you will get. Similarly, the same is true for loans. If the bank loan exceeds one day, it will pay interest for one more day. The larger the loan amount, the more interest will be paid to the bank. Therefore, the amount of interest, under the condition of constant interest rate, can only be determined by the time and amount of funds actually occupied, but not by which repayment method. This is the unchangeable truth. Different repayment methods are only set to meet the different needs or consumption preferences of people with different incomes, different ages and different consumption concepts. Its essence is nothing more than "chop and change" or "chop and change" to repay the loan principal first, which leads to the long-term use of the loan principal and short-term use, and then affects the increase and decrease of interest with the change of the actual amount of funds occupied and the length of the term. It can be seen that no matter which repayment method is adopted, banks do not do business at a loss, and customers do not have the benefit of saving interest expenses.
The time value of funds determines that the loan must pay interest, and it is understandable for bankers to take various ways to maximize profits. Only by choosing appropriate loan and repayment methods reasonably can we reach the balance point of the game with bankers and gain greater benefits. Therefore, careful analysis is needed to make the most appropriate and appropriate choice.