1.各類利率之間和各類利率內(nèi)部都有一定的聯(lián)系并相互制約

今日分享那些你覺(jué)得要放棄的時(shí)候正是你最應(yīng)該努力的時(shí)候The days when you feel like giving up are the days you should try the hardest.

2.不同種類利率之間的關(guān)系

不同計(jì)息方式的利率（一）單利與復(fù)利（s美的空調(diào)服務(wù)24小時(shí)imple interest and compounding interest）在進(jìn)行資金借貸時(shí)，資金計(jì)息的方式通常有兩種：?jiǎn)卫╯imple interest) 與復(fù)利（compounding interest ）單利情形下，僅針對(duì)本金收取利息，每個(gè)計(jì)息周期支付的利息等于本金乘以期間利率。

3.各種利率之間的關(guān)系

復(fù)利情形下，沒(méi)經(jīng)過(guò)一個(gè)計(jì)息周期，必須將上一期生成的利息加入本金后再計(jì)利息，也就是俗稱的利滾利這里說(shuō)的計(jì)息周期是指相鄰兩次支付利息的時(shí)間間隔，可以是日、月、季、年When borrowing and lending funds, there are usually two ways to美的空調(diào)服務(wù)24小時(shí) 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 in美的空調(diào)服務(wù)24小時(shí)terest 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 an美的空調(diào)服務(wù)24小時(shí)nual.

4.各種利率的區(qū)分

投資者將1000元存入銀行，年化利率是10%，每年計(jì)息一次，分別計(jì)算在單利和復(fù)利情形下投資者兩年內(nèi)收到的利息總額解：?jiǎn)卫樾蜗拢顿Y者2年內(nèi)收到兩次利息，均以初始本金為基準(zhǔn)利息總額=1000*10%*2=200

5.關(guān)于不同種類的利率含義

復(fù)利情形下，2年內(nèi)收到兩次利息，每年計(jì)息基準(zhǔn)在上一年度基礎(chǔ)上滾動(dòng)上升，2年后存款資金變?yōu)?000*（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

6.這些利率之間的典型關(guān)系是什么

Investors deposit 1,000 yuan in the bank wit美的空調(diào)服務(wù)24小時(shí)h 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.

7.利率的類別

Solution: In the case of simple interest, the investor receives interest美的空調(diào)服務(wù)24小時(shí) twice in two years, all based on the initial principal.

8.幾種利率理論的異同

Total interest = 1000*10%*2=200In 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%) a美的空調(diào)服務(wù)24小時(shí)nd the principal deduction of 1000 yuan is the interest received.

9.簡(jiǎn)述利率的種類及各種利率的含義

Total interest = 1000* (1 + 10%)* (1 + 10%) - 1000 = 210（二）報(bào)價(jià)利率與有效年利率（Quoted Rate of Interest and Effective Annual Interest Rate）

10.各種利率的關(guān)系

復(fù)利的計(jì)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，計(jì)息周期越短，1年內(nèi)支付的利息總額越大這就引出兩個(gè)概念：報(bào)價(jià)利率與有效年利率The美的空調(diào)服務(wù)24小時(shí) 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 years 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: quote美的空調(diào)服務(wù)24小時(shí)d interest rate and effective annual interest rate.。

1.報(bào)價(jià)利率（Stated Annual Interest Rate /Quoted Interest rate ）銀行等金融機(jī)構(gòu)進(jìn)行利息報(bào)價(jià)時(shí)通常會(huì)提供一個(gè)年利率，并同時(shí)提供該利率每年的計(jì)息次數(shù)這個(gè)年利率就稱為報(bào)價(jià)利率。

在提供報(bào)價(jià)利率時(shí)必須同時(shí)給出1年內(nèi)的計(jì)息次數(shù)，否則是沒(méi)有意義的由報(bào)價(jià)利率可以計(jì)算出計(jì)息期利率（Periodic Interest rate ）When banks and other financial institutions quote interest rates, 美的空調(diào)服務(wù)24小時(shí)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 me美的空調(diào)服務(wù)24小時(shí)aningless. Periodic Interest Rate can be calculated from the quoted rate.。

例如,某機(jī)構(gòu)報(bào)價(jià)利率為10%，按季度計(jì)息按照此報(bào)價(jià)利率，銀行每年將支付4次利息，即每個(gè)季度支付利息10%/4=2.5%此例中，2.5%就是計(jì)息期利率，即銀行在每個(gè)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 美的空調(diào)服務(wù)24小時(shí)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(bào)價(jià)利率均是年利率的形式，這是金融行業(yè)的報(bào)價(jià)習(xí)慣值的指出的是，報(bào)價(jià)利率不是投資者1年內(nèi)獲得的真實(shí)利率收益，應(yīng)注意與后面學(xué)到的有效年利率做區(qū)分The quotation rate is in the form of annual interest rat美的空調(diào)服務(wù)24小時(shí)e, 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 Rat美的空調(diào)服務(wù)24小時(shí)e EAR）有效年利率（EAR）：是指每單位貨幣在1年內(nèi)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(bào)價(jià)利率為12%，每個(gè)月計(jì)息一次按照?qǐng)?bào)價(jià)利率，銀行每個(gè)月的計(jì)息期利率為12%/12≈1%那么美的空調(diào)服務(wù)24小時(shí)，投資者的初始投資在1年內(nèi)將按1%的利息復(fù)利12次，1元的投資在扣除本金后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 investors initial investment will be compounded 12 美的空調(diào)服務(wù)24小時(shí)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(bào)價(jià)利率，m為1年內(nèi)的計(jì)息次數(shù)Among them, r_s is the quoted rate and M is the number of interest c美的空調(diào)服務(wù)24小時(shí)ounts in one year.

若一年內(nèi)的計(jì)息次數(shù)趨于無(wú)窮，相當(dāng)于每分每秒都在計(jì)息，就能得到連續(xù)復(fù)利（Continuous Compounding）的公式

（這個(gè)公式是從上個(gè)公式通過(guò)重要極限公司轉(zhuǎn)變過(guò)來(lái)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. (thi美的空調(diào)服務(wù)24小時(shí)s formula is transformed from the previous formula through the important limit formula）

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