Matching principal and interest means paying interest first, then paying principal. In the first half of the whole loan, interest accounts for the largest proportion, and in the second half, principal accounts for the largest proportion.

Therefore, the borrower only needs to repay before 1/2, which can effectively reduce the interest; When the repayment period exceeds 1/2, it is not so cost-effective to choose early repayment.

Assuming that the borrower chooses a repayment period of 30 years, it is best to repay in advance in the 15 year. If you choose a repayment period of 20 years, it is best to choose early repayment in the first 10 year.

Matching principal and interest refers to a loan repayment method, that is, repaying the same amount of loans (including principal and interest) every month during the repayment period.

Equal principal and interest and average capital are not the same concept. Although the monthly repayment amount may be lower than that in average capital at the beginning, the interest paid in the end will be higher than that in average capital, which is also a method often used by banks.

Calculation method

Calculation formula of monthly repayment amount:

P: loan principal

R: monthly interest rate

N: number of repayment periods

Attachment: monthly interest rate = annual interest rate/12

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. Still on the basis of the above example, one month is the first installment, and the balance of the first installment loan is 200,000 yuan, and the interest payable is 700 yuan (200,000× 4.2%/12), the principal is 533. 14 yuan, and the loan owed to Yan Hui Bank is 19466.86 yuan; The interest payable in the second phase is (199466.86× 4.2%/12).

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]

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( 1β)-X

Second month (a (1β)-x) (1β)-x = a (1β) 2-x [1β]]

The third month [a (1β)-x) (1β)-x] (1β)-x = a (1β) 3-x [1β) (.

It can be concluded that the loan owed to the bank after the nth month is a (1β) n _ x [1β) (1β) 2? ( 1β)^(n- 1)]=a( 1β)^n_x[( 1β)^n- 1]/β

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 (1β) m _ x [(1β) m-1]/β = 0.

X = a β (1β) m/[(1β) m-1].

Repayment method and calculation of average capital

1. Repayment amount of equal principal and interest repayment method:

Monthly repayment amount: a [I (1I) n]/[(1I) n-1]

(Note: A: loan principal, I: monthly loan interest rate, N: monthly loan amount)

2. Average capital repayment method repayment amount:

Monthly principal repayment: None

Monthly interest payable: ani/30dn

Total monthly payable: a/nani/30dn

(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-2a/n ... The actual number of days in the nth month is analogized, for example, February in a normal year is 28,3.

Which year is the most cost-effective mortgage in 20 years?

If you apply for a 20-year mortgage, as long as the lender's economic conditions permit, the sooner you repay the mortgage, the more cost-effective it will be, and the more interest expenses you can save. If the repayment time has exceeded one-third of the loan period, it is not cost-effective to repay in advance.

However, if the lender prepays for less than one year, the bank will charge liquidated damages. Due to the existence of liquidated damages, it is sometimes not cost-effective to repay the loan in advance, and the lender can apply for early repayment after one year of repayment.

The loan is 700,000 yuan, with equal principal and interest. In which year is it appropriate to pay off the 20-year mortgage?

In the first seven years.

For commercial loans, if the repayment method is equal principal and interest, it is reasonable for the bank staff to suggest paying off the loan within the first third of the total repayment time. Because of the repayment method of equal principal and interest, the monthly mortgage payment in previous years was almost always to pay interest, and the principal was very small. The sooner you pay back the money in advance, the more money you save, and you don't have to pay so much interest.

Matching principal and interest means that the borrower repays the loan principal and interest with the same amount every month. Because the monthly repayment amount is equal, in the early stage of the loan, the repayment interest is more and the loan principal is less, while in the later stage of the loan, the loan interest decreases and the loan principal is more. Therefore, it can be simply understood as the way to pay interest first and then repay the principal.

Extended data:

Precautions:

1. Handle the cancellation of house mortgage in time: house mortgage during the loan period. This house cannot be rented or resold. Therefore, after paying off the loan, you must go to the bank to handle the mortgage cancellation business in time, otherwise the mortgage record will still be filed in the real estate department, laying a hidden danger for the future.

2. Don't repay the provident fund first for partial loan repayment: If you choose a portfolio loan when handling the loan, it will involve the question of which part of the loan will be repaid first. I suggest you pay back the commercial loan first, because everyone knows that the interest of commercial loan is higher than that of provident fund loan. If that part of the commercial loan is paid off first, then for individuals and families, the monthly mortgage pressure will definitely be reduced and the interest will be saved.

3. Understand the bank's policy of repaying loans in advance: Be sure to understand the bank's policy in advance before repaying loans in advance. Not all banks have the same policies, and some even affect their credit records and even pay fines. Therefore, it is necessary to know clearly in advance, and it is recommended to be cautious when handling bank loans.