Loan Repayment I: basic concepts of loan repayment

In today's society, early consumption is no longer a new term. The following is the repayment of loans.

However, can you tell me what is going on with the loan repayment? What are the loan repayment methods? How is the monthly loan repayment calculated? How do I calculate the principal amount and interest of the monthly loan amount? How can I select a repayment method? What other loan repayment methods can financial institutions offer? This seriesArticleThis is the topic of "repaying loans.

First, for convenience. Define some variables. In subsequent articles, the meaning of variables will not change unless otherwise specified.

1. Initial principal (in a broad sense, the principal is actually multiplied by a multiple)

P. (Monthly interest rate, calculated at an annual rate of 12)

N period. (Number of times of repayment, for example, 10 years of loan, n = 120)

Y (m) period m repayment amount

X (m) principal in the M-th repayment amount

Interest in S (m) period m repayment amount

T (m) remaining principal after period m

^ Power operation, for example, 3 ^ 4 = 3 × 3 × 3 × 3 = 81

According to the above definition, the variables above are correlated and meet the following conditions:

1 ≤ m ≤ n

Y (m) = x (m) + S (m)

T (0) = 1

T (n) = 0

S (m) = T (S-1) × P

T (m) = m-1)-X (m)

X (1) + X (2) + X (3) + ...... + X (n) = 1

There are several concepts that you may not pay attention.

I. The annual interest rate is not the actual annual interest rate. The actual annual interest rate is slightly higher than the annual interest rate, which many people will neglect.

For example, if the annual interest rate of your loan is 5.31%. The monthly interest rate is 5.31% usd12 = 0.004425

12 months a year, you calculate compound interest when repaying the loan. The actual interest rate for a year is (1 + 0.004425) ^ 12-1 = 5.44%

2. No matter what method of repayment is selected, it is actually the same. There is no cost-effectiveness or no cost-effectiveness. Many people do not understand this.

There are many articles on the Internet discussing the most cost-effective way to repay loans and the most interest-saving expenses. This idea is correct, but it is time to neglect it. How is interest generated? There is a time factor in it. Let's look at the problem from another perspective. Assume that an ideal state is that the Bank will be able to borrow the principal in a timely manner. For the bank, no matter how much principal you pay each month, it can borrow money in a timely manner and bring interest income in the next month. At this time, the monthly income of the bank is the same, because the cash is out, and the interest is the same. Since the bank has the same benefits as the method you choose to repay the loan, it should be the same for you. Although the actual situation is far from complex, the basic principle remains unchanged.

Although, the method used for loan repayment is the same. However, for the actual situation, it is also a financial management method and a plan for your own life.

The following articles will introduce the features of various repayment methods and calculation formulas. We also hope that you will participate in the discussion.