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## Chapter 2 Time Value of Money

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**Chapter 2 Time Value of Money**• Time Value of Money, Part 1 • Topics • Future Value and Compounding of Interest • Present Value • Four Variables -- One Equation • Applications • Doubling your Money -- Rule of 72s • Problems**Future Value**• What would you rather have, $100 today or $100 in one year? • Why $100 today? • Preference for money today implies that there is time value in money • Old Adage, save for a rainy day • How much will you have at the rainy day? • Future Value is the value at a future date of money earning interest • FV = Amount put away plus interest earned FV = PV x (1 + r)n 2.2**Future Value and Compounding of Interest**• Simple Lump Sum Investment • Put Away $100 today • Earn 4% interest • Value in • One Year = $100 x 1.04 = $104 • Three Years = $100 x (1.04)3 = $112.49 • Ten Years = $100 x (1.04)10 = $148.02 • Fifty Years = $100 x (1.04)50 = $710.67 • Why is money growing? Compounding of Interest (interest is earning interest)**Four Methods to Find FV**• What is the Future Value of $325 earning 5% interest annually after seven years? • Method 1 -- FVIF Tables • End of Book Tables solve for (1+r)n • FVIF are Future Value Interest Factors • Method 2 -- Equation • Method 3 -- Calculator • Method 4 -- Spreadsheet**Present Value**• Current Value of a future receipt -- Present Value • Present Value Equation – Four Variables**Four Variables -- One Equation**• Present Value – PV • Future Value – FV • Time – n • Interest rate (or discount rate) – r • Solve for any variable if you know the other three… • Mathematics Principle – One Equation, One Unknown**Applications**• Solving for Present Value – What is today’s value of a future payment? • Solving for Future Value – What Will I have in the future? • Solving for interest rate or discount rate – How fast is my money growing or what is the cost of my loan? • Solving for time – How long must I wait?**Applications**• Example 2.3 – Saving for Retirement • Want Future Value of $2,000,000 • Will Wait 40 years with 6% interest rate • How much do I need to put away today? • PV = $194,444.38 • Example 2.4 – Seward’s Foley • Original Cost of Alaska $7,200,000 (PV) • 135 years ago with inflation of 4% (interest rate) • What would it cost today (FV from 1867)? • FV = $1,434,938,545.32**Applications**• Example 2.7 – What is the growth rate • Boomtown population currently 94,222 (PV) • Expected to be 250,000 (FV) in 20 years • What is the growth rate (r)? • r = 5.0% • Example 2.8 – Waiting Time • Savings goal $1,000,000 (FV) • Deposit is $228.10 (PV) with interest rate of 15% (r) • How long will it take $228.10 to become $1,000,000? • n = 60 years**Doubling Your MoneyThe Rule of 72s**• Before calculators and spreadsheets a quick estimate of doubling your money was found by using 72… • Time estimate = 72 / interest rate • Example, with 8% interest how long to double your money? • Time = 72 / 8 = 9 years • Actual time is 9.01 years… • Estimate also good to find interest rate needed to double money in a given period, 72 / n = interest rate**Problems**• Problem 5 -- Future Value • Problem 7 -- Present Value • Problem 9 -- Interest Rate • Problem 10 -- Waiting Period • Problem 19 -- Growth