1. Detailed explanation of the equal principal and interest formula
(1) Equal principal and interest, detailed explanations have been given on the Internet. Let me just say that you have n installments, and the repayment amount for each installment is the same.
(2) I was distressed for a while ago, and I searched the Internet for the formula of equal principal and interest, all of which gave the result directly, without the calculation process, and I don’t know what kind of medicine is sold in the gourd. Thinking about buying a house, this formula is still If you don't understand, just calm down and figure it out.
(3) The blog post here gives a detailed derivation, assuming the following:
The loan is G yuan, the repayment period is n periods (if your loan is 30 years, then it is 360 periods), the monthly interest rate is m (if your annual interest rate is 5%, then the monthly interest rate is 5%/12=0.417%), And the repayment amount of each installment is x yuan.
Period |
Repayment amount (yuan) |
Remaining repayment amount (yuan) |
Phase one |
|
|
the second term |
|
|
.............. |
..................... |
............................ |
nth period |
|
|
According to the above formula, at the end of the nth period, the loan is repaid and the final value is 0:
Simplify it using the arithmetic progression formula:
Finally, the monthly repayment amount is obtained:
(4) Comparison of online formula with this formula:
online formula |
Derived formula |
Monthly repayment amount = [principal x monthly interest rate x (1+monthly interest rate) number of loan months] / [(1+monthly interest rate) number of repayment months - 1] |
|
After a comparison, the formulas are exactly the same. Through derivation, you can fully understand how the monthly repayment amount comes from.
2. Detailed explanation of the equal principal formula
(1) Equal amount of principal, repaying the same amount of principal every month and the interest generated by the remaining loan in that month
(2) The monthly calculation of the equivalent principal is as follows:
Period |
Repayment amount (yuan) |
Phase one |
|
the second term |
|
.............. |
..................... |
nth period |
|
3. Summary
Two ways:
(1) The monthly payment (monthly repayment) is different
等额本金每月还款额会递减，前期还款本金占比较大。
等额本息每月偿还固定金额，前期还款利息占比较大。
（2）利息不同
等额本金采用的是简单利率方法计算利息，只对剩余本金计息。
等额本息采用的是复利计算方法计息，利息制造利息，因此等额本息还款利息要高于等额本金。