Time Value of Money

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Time Value of Money

• Jim Bice

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Activity Plan

• Overview
• Equations and the math behind it
• Activity
• Instructions
• Reminder on Excel
• Group activity
• Summary and Homework

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Examples of Time Value of

• Were the Indians cheated in the purchase of
  Manhattan Island.
• Given 100 worth of trinkets in 1626
• What if they banked it at 7 interest

• They would have over 13,000,000,000,000 or 13
  trillion dollars today.

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What does this mean

• Why?
• What would you do with it?
• Why or why not?

• Would you rather have 100 today or 100 in a
  year?
• What if you could not spend it?
• Would you give me 100 today if I would give you
  200 in 20 years?

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Time value of money

• Time value of money - Money has the ability to
  increase over time (if it is invested)
• Interest - The amount of money that is earned
  over a certain time period
• Interest rate - The rate interest is earned

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What are all these things

• P - Present value of money
• I - Interest it earned
• i - Interest rate I/P
• F - Future value of money
• A - Annuity or uniform series
• n - number of time periods

• Relations between
• F PI P(I/P)P PiP P(1i)
• If several time periods
• F P(1i)n
• Then add A plus what A earns

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Try some examples with your calculators

• What is the value of 100 dollars in 1, 2, 3, 4
  and 5 years at an interest rate of 5
• What would I have if I saved 100 per year?
• This is how A works.

• Answers
• 1 year - 105
• 2 years - 110.25
• 3 years - 115.76
• 4 years - 121.55
• 5 years - 127.63
• 580.19

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What real life thing uses all this

• Banks
• Savings and CDs
• Car loans
• House loans
• Life Insurance
• Investors
• Loan Sharks

• Terms
• Interest rate, Inflation rate, Loan rate all are
  forms of I
• P is used for the value of the car or house etc.
• Payments on a loan are examples of A

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Assignment

• Get in your assigned groups of 3
• Grab a computer
• Put together an Excel spreadsheet that shows what
  happens over time
• Answer the questions I will post once you start.

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Reminder on how Excel works

• Formulas start with
• They are relational unless you fix the cell with
  
• Drag the formulas down to copy them

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Slide layout
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Variables
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Cells to use
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Instructions
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Spreadsheet Checks

• i 6
• Inflation 3.5
• Savings per year 100
• Starting Amount 999
• Hamburger cost 3

• What value do you have in 2009
• Should be 1900.60 in Amount Saved
• Hamburger 3.56

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Now try these

• To have a million dollars in 50 years how much
  would you need now at 6 interest?
• 8 (bonds)
• 10 (stocks)
• Now try saving different amounts at different
  times

• To save a million dollars in 50 years how much
  would you have to save per month at 8 interest?
• What if you had 100 under you mattress, how many
  burgers could you buy today?
• In 20 years?

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Estimation and error

• Rule of 70 - the number of years it will take to
  double is n70/i
• When estimating future inflation or savings rates
  these are only best guesses. You can develop a
  range by taking the high and low rates.

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Follow-up
The important equation is FP(1i)n You can
derive everything else from this. The future
value of A is FA(1i)n/i Internet
homework