1. 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

2. 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

3. 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)

4. 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

5. Present Value  Current Value of a future receipt -- Present Value  Present Value Equation – Four Variables

6. 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

7. 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?

8. 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

9. 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

10. Doubling Your Money The 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

11. Problems  Problem 5 -- Future Value  Problem 7 -- Present Value  Problem 9 -- Interest Rate  Problem 10 -- Waiting Period  Problem 19 -- Growth