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那些你觉得要放弃的时候正是你最应该努力的时候
The days when you feel like giving up are the days you should try the hardest.
不同计息方式的利率
（一）单利与复利（simple interest and compounding interest）
在进行资金借贷时，资金计息的方式通常有两种：单利（simple interest) 与复利（compounding interest ）单利情形下，仅针对本金收取利息，每个计息周期支付的利息等于本金乘以期间利率。复利情形下，没经过一个计息周期，必须将上一期生成的利息加入本金后再计利息，也就是俗称的利滚利。这里说的计息周期是指相邻两次支付利息的时间间隔，可以是日、月、季、年。
When borrowing and lending funds, there are usually two ways to calculate interest on funds: simple interest and compounding interest. In the case of simple interest, interest is charged only on principal, and the interest paid in each interest-bearing cycle is equal to the principal multiplied by the time interest rate. In the case of compound interest, the interest generated in the previous period must be added to the principal before the interest is calculated, which is commonly known as interest rolling. The interest-bearing period here refers to the time interval between two adjacent payments of interest, which can be daily, monthly, quarterly and annual.
投资者将1000元存入银行，年化利率是10%，每年计息一次，分别计算在单利和复利情形下投资者两年内收到的利息总额
解：单利情形下，投资者2年内收到两次利息，均以初始本金为基准
利息总额=1000*10%*2=200
复利情形下，2年内收到两次利息，每年计息基准在上一年度基础上滚动上升，2年后存款资金变为1000*（1+10%）²，扣除本金1000元即为收到利息：
利息总额=1000*（1+10%）*(1+10%)-1000=210
Investors deposit 1,000 yuan in the bank with an annual interest rate of 10%. The annual interest rate is calculated once a year. The total interest received by the investor in the case of simple interest and compound interest is calculated separately in two years.
Solution: In the case of simple interest, the investor receives interest twice in two years, all based on the initial principal.
Total interest = 1000*10%*2=200
In the case of compound interest, interest is paid twice in two years, and the annual interest base is rising on the basis of the previous year. After two years, the deposit fund becomes 1000* (1+10%) and the principal deduction of 1000 yuan is the interest received.
Total interest = 1000* (1 + 10%)* (1 + 10%) - 1000 = 210
（二）报价利率与有效年利率（Quoted Rate of Interest and Effective Annual Interest Rate）
复利的计息周期不一定是1年，也可以是半年、季度、月 、日。
相同年利率的情形下，计息周期越短，1年内支付的利息总额越大。
这就引出两个概念：报价利率与有效年利率。The interest-bearing cycle of compound interest is not necessarily one year, but also half a year, quarter, month and day. In the case of the same year's interest rate, the shorter the period of interest accrual, the larger the total amount of interest paid in one year. This leads to two concepts: quoted interest rate and effective annual interest rate.
1.报价利率（Stated Annual Interest Rate /Quoted Interest rate ）
银行等金融机构进行利息报价时通常会提供一个年利率，并同时提供该利率每年的计息次数。
这个年利率就称为报价利率
。在提供报价利率时必须同时给出1年内的计息次数，否则是没有意义的。由报价利率可以计算出计息期利率（Periodic Interest rate ）When banks and other financial institutions quote interest rates, they usually provide an annual interest rate, and at the same time provide the number of interest accruals per year. The annual interest rate is called the quoted rate. When offering the quoted interest rate, the interest counting times in one year must be given at the same time. Otherwise, it is meaningless. Periodic Interest Rate can be calculated from the quoted rate.
例如,某机构报价利率为10%，按季度计息。按照此报价利率，银行每年将支付4次利息，即每个季度支付利息10%/4=2.5%。此例中，2.5%就是计息期利率，即银行在每个支付期支付的利息率。
For example, an agency offers interest rates of 10% on a quarterly basis. According to the quoted rate, the bank will pay interest four times a year, i.e. 10%/4=2.5% per quarter. In this case, 2.5% is the interest rate of the accrual period, that is, the interest rate paid by the bank at each payment period.
报价利率均是年利率的形式，这是金融行业的报价习惯。值的指出的是，报价利率不是投资者1年内获得的真实利率收益，应注意与后面学到的有效年利率做区分。
The quotation rate is in the form of annual interest rate, which is the quotation habit of the financial industry. It is worth pointing out that the quoted rate is not the real interest rate earned by investors in one year. We should pay attention to distinguishing the quoted rate from the effective annual rate learned later.
2.有效年利率（Effective Annual Rate EAR）
有效年利率（EAR）：是指每单位货币在1年内获得的利息收益总额。
Effective Annual Interest Rate (EAR): The total amount of interest earned per unit of currency in one year.
effective annual interest rate ear: the total amount of interest earned per unit of currency in one year
例如，银行报价利率为12%，每个月计息一次。按照报价利率，银行每个月的计息期利率为12%/12
≈1%。那么，投资者的初始投资在1年内将按1%的利息复利12次，1元的投资在扣除本金后获得的利息总额即为（1+1%）
12
-1.一般的，有效年利率的公式为：
For example, the bank quotes an interest rate of 12%, which is charged once a month. According to the quoted rate, the monthly interest rate of the bank is 12%/12_1%. Then, the investor's initial investment will be compounded 12 times at 1% interest rate in one year. The total amount of interest earned by a yuan investment after deducting the principal is (1+1%)
^
12-1. Generally, the formula of effective annual interest rate is as follows:
其中，为报价利率，m为1年内的计息次数
Among them, r_s is the quoted rate and M is the number of interest counts in one year.
若一年内的计息次数趋于无穷，相当于每分每秒都在计息，就能得到连续复利（Continuous Compounding）的公式
（这个公式是从上个公式通过重要极限公司转变过来的）
If the number of interest counts in a year tends to be infinite, which is equivalent to counting interest every minute and second, the formula of continuous compound interest can be obtained. (this formula is transformed from the previous formula through the important limit formula）
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