Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Time Value of Money Main Source: BE Chapter 2 6-1 Basic Question Does TIME matter in valuing the purchasing power of every cent a person has? Answer: Yes, it DOES, as long as………. No, it DOES NOT, as long as…… 6-2 Future Value What? The real value of a unit of currency (that one has NOW) at a specific future point of time, after taking into account a specified discount rate. 6-3 Present Value What? The real value of a unit of currency (that one has in the FUTURE) at time zero, after taking into account a specified discount rate. 6-4 The Power of Compound Interest (Please open the PV-FV tables) A 20-year-old student wants to start saving for retirement. She plans to save $3 a day. Every day, she puts $3 in her drawer. At the end of the year, she invests the accumulated savings ($1,095) in an online stock account. The stock account has an expected annual return of 12%. How much money will she have when she is 65 years old? What if, today, her age is 40? 6-5 Solution If she begins saving at the age of 20 and sticks to her plan, she will have $1,487,261.89 when she is 65. If she begins saving at the age of 40 and sticks to her plan, she will have $ $146,000.59 at age 65. This is $1.3 million less than if starting at age 20. Lesson: It pays to start saving early. 6-6 Related Question How much must the 40-year old deposit annually to catch the 20-year old? Solution: To get an equal amount of $1,487,261.89, she has to invest $11,154.42 every year during the next 25 years 6-7 Classifications of Interest Rates Nominal rate (iNOM) – also called the quoted or stated rate. An annual rate that ignores compounding effects. iNOM is stated in contracts. Periods must also be given, e.g. 8% Quarterly or 8% Daily interest. Periodic rate (iPER) – amount of interest charged each period, e.g. monthly or quarterly. iPER = iNOM / m, where m is the number of compounding periods per year. m = 4 for quarterly and m = 12 for monthly compounding. 6-8 Classifications of interest rates (Continued) Effective (or equivalent) annual rate (EAR = EFF%) – the annual rate of interest actually being earned, taking into account compounding. EFF% for 10% semiannual investment EFF% = ( 1 + iNOM / m )m - 1 = ( 1 + 0.10 / 2 )2 – 1 = 10.25% An investor would be indifferent between an investment offering a 10.25% annual return and one offering a 10% annual return, compounded semiannually. 6-9 Why is it important to consider effective rates of return? An investment with monthly payments is different from one with quarterly payments. Must put each return on an EFF% basis to compare rates of return. Must use EFF% for comparisons. See following values of EFF% rates at various compounding levels. EARANNUAL EARQUARTERLY EARMONTHLY EARDAILY (365) 10.00% 10.38% 10.47% 10.52% 6-10 Can the effective rate ever be equal to the nominal rate? Yes, but only if annual compounding is used, i.e., if m = 1. If m > 1, EFF% will always be greater than the nominal rate. 6-11