Calculation formula of equal principal and interest repayment
Suppose the loan amount is A, the monthly interest rate is I, the annual interest rate is I, the number of repayment months is N, the monthly repayment amount is B, and the total repayment interest is Y.
1:I= 12×i
2:Y=n×b-a
3. The interest for repayment in the first month is: a× i.
The repayment interest of the second month is [a-(b-a× i) ]× i = (a× i-b )× (1+i)1+b.
The repayment interest of the third month is {a-(b-a× i)-[b-(a× i-b )× (1+i)1-b] }× i = (a× i-b )× (1+).
The repayment interest of the fourth month = (a× I-b )× (1+I) 3+B.
.....
The repayment interest of the nth month = (a× I-b )× (1+I) (n-1)+B.
The above sum is: y = (a× I-b )× [(1+I) n-1] ÷ I+n× b.
4. The above two y values are equal.
Average monthly repayment: b = a× I× (1+I) n ÷ [(1+I) n-1]
Pay interest: y = n× a× I× (1+I) n ÷ [(1+I) n-1]-a.
Total repayment amount: n× a× I× (1+I) n ÷ [(1+I) n-1]
Note: a b stands for the power of a.