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- 1)]= a( 1+β)^n _x[( 1+β)^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 (1+β) m _ x [(1+β) m-1]/β = 0.

x = aβ( 1+β)m/[( 1+β)m- 1]。

There are generally two ways of matching principal and interest for deferred materials: annual repayment and monthly repayment.

Annual repayment

Use the balance of the provident fund to offset the loan principal at one time. After the balance of the provident fund is used to offset the principal, the total loan amount and interest are recalculated. The total repayment amount is reduced, the interest is reduced, and the monthly payment is reduced.

For example, I borrowed 200 thousand, and I pay back 2000 every month. After one year, the balance of the provident fund is 1 1,000 yuan. After the offset, the total interest rate is recalculated, and the interest is calculated according to the principal of 20- 1 = 1.900 yuan. After recalculation, I paid back 1.900 yuan every month.

Monthly repayment

Use the balance of the provident fund to pay the monthly payment. It can alleviate the short-term financial pressure. But the total repayment amount remains unchanged, the interest remains unchanged, and the monthly payment remains unchanged.

For example, I borrowed 200 thousand, and I pay back 2000 every month. One year later, the balance of the provident fund is 654.38+0,000 yuan. In the next five months, I will pay 2000 yuan from the provident fund every month, and then pay the monthly payment five months later.

Baidu encyclopedia? Average capital plus interest