If the average capital is used for repayment, the first monthly payment will be 6208.33 yuan, and the monthly payment will gradually decrease in the future.
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.
Repayment 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] (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]。
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].