chapter4-1無文字金融工程專業(yè)(文件)
【正文】 tment ? R: Nominal interest rate per annum ? m: Compounding frequency 6 Continued ? When the interest is pounded once a year for T years: ? What if interest is paid more frequently? Here are a few examples of the formula: TRPVFV )1( ??) )41( 4 gc o m p o u n d i nq u a r t e r l yRPVFV T（???) )121( 12 gc o m p o u n d i nm o n t h l yRPVFV T（???m=1 m=4 m=12 7 continued ? Consider an amount PV invested for T years at an interest rate of R per annum. Compounding frequency(m) m=1 m1 m→ Future value after n years (FV) mT)mRPV ( 1 ? RTPV e?TR)1P V ( ?The limit as m tends to infinity is known as continuous pounding 8 示例 ? 例：假設(shè)存款金額為 100，名義年利率為 10%，存款期限為 1年，在年度計(jì)息的條件下，明年的期末存款余額為： 100 = 110 ? 半年計(jì)息一次： 100 = ? 每季度計(jì)息一次： 100 ＝ ? 連續(xù)復(fù)利： 100 = 9 實(shí)際利率與計(jì)息次數(shù) 0 100 200 300 400系列110 continued ? The limit as m tends to infinity is known as continuous pounding ? The standard future and present value formulas are: ? PV→ FV： PV* eRT＝ FV ? FV→ PV： FV* eRT ＝ PV ? For example, if your discount rate is 8%, and you are going to receive $200 in 2 years, the present value of that cash flow is: . 0 8 ( 2 )2 0 0 1 7 0 . 4 3P V e ???11 continued ? You should be aware of how to convert between interest rates of different pounding frequency. For example, if ry is the annually pounded rate of return what is the equivalent quarterly pounded rate of return? ? You can set this up easily enough by realizing that if you invest in both for a given time period (say 1 year) , you wind up with the same amount of cash, that is: ? ?41 / 4q( 1 ) 1 so r 4 1 14qyyrrr?? ??? ? ? ? ? ??? ??????12 continued ? In general to convert between a rate r1 that has pounding frequency m1 and rate r2 that has pounding frequency m2, you use this formula: ? So, if you had a semiannual rate of 6% and wanted to know the equivalent quarterly rate: 12122111mmrrmm??????? ? ?????????24 1 1 .0 5 9 5 5 6 , o r 5 .9 5 5 6 %2qr??????? ? ? ???????13 continued ? To convert between a discrete rate, rd with pounding frequency md and a continuously pounded rate rc, use: (this assumes t=1) cd rmdd emr ?? )1(? ?1dl n 1orr1ddmdcdr mdrrmem????????????????????????A deposit
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