Personal Finance
Time Value of Money
Bill Klinger
Personal Finance
• Review
– Opportunity cost
– Cash flow statement
• Changes over time
• Factors affecting
– Balance sheet
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Assets
Liabilities
Net worth
Factors affecting
– Analysis
• Ratios
Interest
• Interest is the cost of money
• When you borrow
– You pay interest to get the money
• When you invest or loan
– Others pay you interest to get the money
Time Value of Money
• A dollar today is worth less than a dollar in the future
– Why?
• If you give up money today, you expect to receive more
in the future
– You have opportunity costs
– What is opportunity cost?
Future Value
• Simple future value (FV)
– FV = amount x (1 + interest rate)
• Example
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Assume interest rate of 3%
If invest $1000 today, how much will you have next year?
FV = 1000 x (1 + .04)
FV = $1040
Future Value
• Compound interest
– Earn interest on the interest on the interest …
– Einstein said was the most powerful force in the universe
• FV formula too complex for this class
– Will use tables in text
– Can also use Excel function, FV
• FV = PV x FVIF
– FV = Future value, amount you will have in the future
– PV = Present value, amount you have today
– FVIF = Future value interest factor, found in text Appendix C.1
Future Value
• Problems
– You invest $100 today at 4% interest.
in 4 years?
– You invest $100 today at 4% interest.
in 10 years?
– You invest $100 today at 9% interest.
in 4 years?
– You invest $100 today at 9% interest.
in 10 years?
How much will you have
How much will you have
How much will you have
How much will you have
• What can you say about the length of time you invest?
– What does that say about your investment plans?
• What can you say about the difference the interest rate
makes?
Future Value
• Compounding rule of thumb
• Rule of 72
– Calculate how long it will take money to double
Years to double = 72 / (interest rate)
Present Value
• Present value represents the value of future payments to
you now
– For example
– What is $1000 next year worth to you now?
• Can also think of it as willingness to pay
– For example
– What would you pay today for $10,000 in 5 years?
• To calculate PV, need to know
– Future amount
– Interest rate
– Number of years
Present Value
• PV formula too complex for this class
– Will use tables in text
– Can also use Excel function, PV
• PV = FV x PVIF
– PV = Present value, amount you have today
– FV = Future value, amount you will have in the future
– PVIF = Present value interest factor, found in text Appendix C.2
Text Error
• Table C.2 has an error
• Heading is incorrect
• Should read
PV = FV x PVIFi,n
Present Value
• Problems
– What is $10,000 five years from now worth today if interest rates
are 4%?
– What is $10,000 ten years from now worth today if interest rates
are 4%?
– What is $10,000 five years from now worth today if interest rates
are 10%?
– What is $10,000 ten years from now worth today if interest rates
are 10%?
• What can you say about the effect of the length of time?
• What can you say about the difference the interest rate
makes?
Present Value
• Problems
– How much are you willing to pay for $5,000 next year if interest
rates are 6%?
– How much are you willing to pay for $50,000 in 20 years if
interest rates are 6%?
In Class
• In groups of two
– Chapter 3 Financial Planning Problems
• In groups of two
– Create a simple budget with one or two problems
– Exchange with another group and find problems