Compared with the average capital, although the amount of early repayment is less than the average capital, the total interest of final repayment is higher than that of equal principal and interest repayment. But the two repayment methods have their own advantages and disadvantages, and we can't say which one is better.
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.
The calculation formula of monthly repayment amount is as shown on the right:
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 one installment, the balance of the first loan is 200,000 yuan, the interest payable is 700 yuan (200,000× 4.2%/12), the principal is 533. 14 yuan, and the bank loan is still 19466.86 yuan; The interest payable in the second phase is (199466.86× 4.2%/12).
Add up the total principal and interest of the mortgage loan and 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.
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] (1+β)-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)+(n-65).
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]。