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那些你覺得要放棄的時候正是你最應該努力的時候
The days when you feel like giving up are the days you should try the hardest.
不同計息方式的利率
（一）單利與複利（simple interest and compounding interest）
在進行資金借貸時，資金計息的方式通常有兩種：單利（simple interest) 與複利（compounding interest ）單利情形下，僅針對本金收取利息，每個計息週期支付的利息等於本金乘以期間利率。複利情形下，沒經過一個計息週期，必須將上一期生成的利息加入本金後再計利息，也就是俗稱的利滾利。這裡說的計息週期是指相鄰兩次支付利息的時間間隔，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.
投資者將1000元存入銀行，年化利率是10%，每年計息一次，分別計算在單利和複利情形下投資者兩年內收到的利息總額
解：單利情形下，投資者2年內收到兩次利息，均以初始本金為基準
利息總額=1000*10%*2=200
複利情形下，2年內收到兩次利息，每年計息基準在上一年度基礎上滾動上升，2年後存款資金變為1000*（1+10%）²，扣除本金1000元即為收到利息：
利息總額=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）報價利率與有效年利率（Quoted Rate of Interest and Effective Annual Interest Rate）
複利的計息週期不一定是1年，也可以是半年、季度、月 、日。
相同年利率的情形下，計息週期越短，1年內支付的利息總額越大。
這就引出兩個概念：報價利率與有效年利率。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.報價利率（Stated Annual Interest Rate /Quoted Interest rate ）
銀行等金融機構進行利息報價時通常會提供一個年利率，並同時提供該利率每年的計息次數。
這個年利率就稱為報價利率
。在提供報價利率時必須同時給出1年內的計息次數，否則是沒有意義的。由報價利率可以計算出計息期利率（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,某機構報價利率為10%，按季度計息。按照此報價利率，銀行每年將支付4次利息，即每個季度支付利息10%/4=2.5%。此例中，2.5%就是計息期利率，即銀行在每個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.
報價利率均是年利率的形式，這是金融行業的報價習慣。值的指出的是，報價利率不是投資者1年內獲得的真實利率收益，應注意與後面學到的有效年利率做區分。
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）：是指每單位貨幣在1年內獲得的利息收益總額。
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，銀行報價利率為12%，每個月計息一次。按照報價利率，銀行每個月的計息期利率為12%/12
≈1%。那麼，投資者的初始投資在1年內將按1%的利息複利12次，1元的投資在扣除本金後獲得的利息總額即為（1+1%）
12
-1.一般的，有效年利率的公式為：
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，為報價利率，m為1年內的計息次數
Among them, r_s is the quoted rate and M is the number of interest counts in one year.
若一年內的計息次數趨於無窮，相當於每分每秒都在計息，就能得到連續複利（Continuous Compounding）的公式
（這個公式是從上個公式通過重要極限公司轉變過來的）
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）
內容來源於網絡公開信息。
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