Chapter_3_Interest_factor_in_Financing(内含中文笔记).pptVIP

Chapter 3 The Interest Factor in Financing Contents Mathematics of compound interest Present value Future value Annuity Effective annual yield for a series of cash flows assuming annual, semiannual, quarterly, monthly, and daily compounding The internal rate of return on an investment (IRR) Compound Interest (复利） Earning Interest on Interest Four basic components PV = Initial Deposit i = Interest rate n = Number of periods FVn = Value at a future time period n Future Value General equation: FV = Future Value PV = Present Value i = the interest rate per period n= the number of compounding periods is also referred to as the Future Value Interest Factor: (FVIF , i%, n) Future Value Example 3-1: What is the value at the end of year 5 of $100 deposited today if the interest rate is 10% compounded annually? FV5 = $100×(1+.10)5 = $100×(1.61051) = $161.05 Future Value When compounding periods other than annual are considered: the number of years is multiplied by the number of compounding periods the annual interest rate is divided by the number of compounding periods Future Value Future Value is also called the period rate = 100×(1.62889) = $162.89 FV5 =$161.05 Future Value Notice the difference in Future Value when multiple compounding periods are used: $162.89 $161.05 This shows the effect of earning interest on interest. p.43 Nominal annual rate NAR 名义年利率 i Effective annual yield (EAY) 实际年利率 EAYNAI, when interests are computed in semiannually, quarterly, monthly or daily compounding. It is customary in the US to use a nominal annual interest in contracts, savings accounts, mortgage notes, etc., and how payments will be made or interest accumulated (annually, semiannually, quarterly, monthly, daily) is then specified. Effective annual yield Equivalent nominal annual rate (ENAR): Given a desired EAY, when interest is compounded semiannually, quarterly, monthly or daily, what is the equivalent nominal annual ra