Time Value of Money
Outline
Time value of money Future value and present value Single payments Multiple payments
TVM
Two choices $1000 now $1000 in ten years $1 at one date is not the same as $1 at another date Things to consider: Interest Inflation What underlies interest? Productive real assets - Impatience
Questions
How much is $1 today worth in T years? How much is $1 in T years worth today? How do we move cash flows back and forth in time?
FV
Example 1: Have a bank account that pays 10% per year. Invest $1 today How much is in the account one year later? What is the FV after two years? After three? Timeline What about if you invested $100 today? Suppose instead of compounding, the bank only paid simple interest Meaning?
At an interest rate of r per year, $100 grows to
At the end of
Compound interest
Simple interest
One year
Two years
Three years
T years
How much is $C worth if invested at T years at an interest rate of r per year? Compound interest: Simple interest:
Compounding
Invest$100 at 10% annual rate
2000
180
1600
1400
1200
1000
80