There are generally two kinds of interest rate calculation, one is simple interest and the other is compound interest. The change of loan interest with time is equivalent to compound interest, and the calculation of simple interest does not need to include interest when calculating the principal; And compound interest should be incorporated into the principal for repeated interest calculation.

The difference between compound interest calculation and simple interest calculation

The difference between compound interest calculation and simple interest calculation is that the items in the simple interest calculation method are directly multiplied by the annual interest rate in brackets; In the calculation of compound interest, the term is used as an index outside the brackets. If the investment period is the same and the investment annual interest rate is the same, then the value of the former is greater than the value of the latter. Therefore, the amount of due principal and interest calculated under compound interest method is greater than that calculated under simple interest method, and the longer the term, the greater the difference between the two values.

The same fund 100 yuan, with an annual interest rate of 2.00%. The longer the term, the greater the gap. The reason is that the interest income obtained under the compound interest method is continuously reinvested and new income is continuously obtained.

So why is there a difference between simple interest method and compound interest law? Simple interest method calculation is simple, easy to operate and understand. Therefore, whether it is a bank deposit or a one-time debt service, it is calculated according to simple interest. But for investors, the interest received in each period will be reinvested, and no one will put the interest income in the wallet intact, at least in the bank, it will also get the income from demand deposits. Therefore, the compound interest method is a more scientific method to calculate the investment income.

Especially the present value calculation of compound interest method, this formula determines how much money you should pay now to get a fixed income in the future. All the analysis of bond pricing revolves around this issue.

Simple interest situation

The bank's savings deposit interest rate is calculated according to simple interest. The so-called simple interest means only calculating the time value (interest) of the principal within the investment period, and not calculating the interest of interest. This is the simplest way to calculate interest.

The calculation formula of simple interest is:

I=P0×r×n

Where: I is the interest due, P0 is the principal, R is the annual interest rate, and n is the term;

Example: Peter's return on investment. ※

Peter now has a sum of 65,438 yuan+0,000 yuan. If he makes a time deposit in the bank with a term of 3 years and an annual interest rate of 2.00%, then according to the calculation rules of bank deposit interest, the sum of the principal and interest due to Peter is:

1000+1000× 2.00 %× 3 =1060 (yuan).

According to the simple interest rate of 2.00% per year, the interest on the principal of 65,438+0,000 yuan within three years is 60 yuan. On the other hand, if calculated according to simple interest, how much is 1060 yuan equivalent to now after three years? This is the so-called "present value" problem.

Present value is the value of future funds discounted to the present moment at a given interest rate level, which is the inverse process of the time value of funds.

According to simple interest method, the method of calculating present value from future value is simple. We use Vp to represent the present value and Vf to represent the future value, so there is

Vf=Vp×( 1+r×n) where r represents the interest rate of the investment and n represents the term, usually in years. Turn this formula upside down, and you get the formula for calculating the present value:

Example: Peter's return on investment. ※

Peter wants to earn 65,438+0,060 yuan in three years, so how much money should he deposit in the bank now? At present, the annual interest rate of three-year bank deposits is 2.00%. Then according to the calculation formula of the present value of simple interest,

Peter needs to save 65,438+0,000 yuan now to ensure an income of 65,438+0,060 yuan in three years.

Compound interest situation

The so-called compound interest means that the interest generated after each interest period is added to the principal to calculate the interest of the next period. In this way, in each interest-bearing period, the interest of the previous interest-bearing period should become the principal of interest-bearing, that is, interest-bearing at interest, which is also commonly known as "rolling interest".

Example: Peter's return on investment. ※

Peter's money is 65,438+0,000 yuan, and the interest rate of the bank's 65,438+0-year fixed deposit is 2.00%. At the beginning of each year, Peter will withdraw the principal and interest of the previous year, and then deposit them together as the principal in the 1 year time deposit for three years. So how much principal and interest can he get at the end of the third year? The calculation method of interest on this investment is compound interest.

At the end of the first year, * * * has principal and interest, which are:

1000+1000× 2.00% =1020 (yuan)

Subsequently, the principal and interest received at the end of the first year and the investment principal at the beginning of the second year, that is, interest, have been incorporated into the principal. Therefore, at the end of the second year, * * * has repaid the principal and interest as follows:

1020+1020× 2.00% =1040.40 (yuan)

By analogy, at the end of the third year, * * * has principal and interest, which are:

1040.40+1040.40× 2.00% =1061.21(yuan)

This is the calculation principle of the sum of principal and interest due under the compound interest method. The calculation process of this method seems too complicated on the surface, but it is not. The calculation process of the above sum of Peter's capital principal and interest can actually be expressed as:

1 000× ( 1+2.00% )× ( 1+2.00% )× ( 1+2.00%) = 1 000× ( 1+2.00%)

Like simple interest method, we use Vp to represent the present value and Vf to represent the future value, so there is

Vf=Vp×( 1+r)n

Where r represents the interest rate of investment and n represents the term, usually in years.

Turn this formula upside down, and you get the formula for calculating the present value:

Example: Peter's return on investment. ※

Peter wants to earn 65,438 yuan in three years. How much money should he deposit in the bank now according to the compound interest investment law? The current interest rate of the bank's 1 year deposit is 2.00%. Then, according to the formula for calculating the present value of compound interest:

Peter needs to deposit 65,438+0,000 yuan now, so as to guarantee the income of 65,438+0,066,5438+0.265,438+0 yuan in three years. Of course, Peter must combine the annual principal and interest income to make new investments, so as to get the result of 1.06 1.225438+0 yuan.

Please understand this example carefully, it is the basis of all future bond pricing analysis. The present value formula of compound interest method determines how much you should pay at present to get the expected return in the future, and the pricing analysis of bonds is centered around this problem.

The interest change you mentioned, the interest in the second month is higher than that in the first month, is legal. But at present, China's banks practice simple interest, and private lending is usury, which is actually simple interest, but the interest is relatively high.

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