Chapter 2 Time Value of Money, Part 1  Learning Objectives  Calculate Future Value and Compounding of Interest  Calculate Present Value  Calculate interest rates, waiting time  Verification of solutions  Doubling your Money -- Rule of 72

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 = $  Ten Years = $100 x (1.04) 10 = $  Fifty Years = $100 x (1.04) 50 = $  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 – Formula or Equation  Method 2 -- Calculator  Method 3 – Spreadsheet  Method 4 -- FVIF Tables  End of Book Tables solve for (1+r) n  FVIF are Future Value Interest Factors

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

One Equation – Four Variables  Present Value – PV  Future Value – FV  Time – n  Interest rate (or discount rate) – r  Solve for any variable if you know the other three…page 29 for formulas  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,  Example 2.4 – Let’s Make a Deal  Original Cost of Alaska $7,200,000 (PV)  140 years ago with inflation of 4% (interest rate)  What would it cost today (FV from 1867)?  FV = $1,745,822,146

Applications  Example 2.6 – Boomtown USA  Dry Gulch population currently 94,222 (PV)  Expected to be 250,000 (FV) in 20 years  What is the growth rate (r)?  r = 5.0%  Example 2.7 – Waiting Time  Savings goal $1,000,000 (FV)  Deposit is $3, (PV) with interest rate of 15% (r)  How long will it take $3, to become $1,000,000?  n = 40 years

Doubling Your Money The Rule of 72  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  See Table 2.3 – Page 35

Homework  Problem 6 -- Future Value  Problem 8 -- Present Value  Problem 9 -- Interest Rate  Problem Waiting Period  Problem 16 – Interest Rate (Return)  Problem 19 – Growth  Problem 22 – Rule of 72