FUTURE VALUE PROBLEMS
A future value problem is one where PERIOD 0 1 2 3
we know the cash flow amount we are investing $100 ? ? ?
today and wish to determine how much it will grow to in
n periods
Example 1
Bob invests $100 today at 4%.  How much will this investment Answer
grow to in one year?
Take .04 * 100 and add it to the $100 =100*(1+.04) 104
Example 2
Bob invests $100 today at 4%  How much will this investment =100*(1.04)^2 108.16
grow to in 2 years?
Example 3
Bob invests $100 today at 4%.  How much will this investment =100*(1+.04)^3 112.4864
grow to in 3 years?
How would you build a Future Value table from the data in Future Value of $1
Examples 1-3?  Can you fill in the 6% column? Rate
Periods 0.04 0.06
MEMORIZE THE GENERAL FORMULA:  FV=PV*(1+i)^n 1 1.04  
In the table to the right, Future Value of $1, the PV is set 2 1.0816  
to 1.00.  3 1.124864  
PRESENT VALUE PROBLEMS PERIOD 0 1 2 3
A present value problem is one in which we know the future ? $104
cash flow to be received…but we need to figure out how
much to pay for it today to earn a given interest rate.
Example 1a.  How much would Bob have to invest today in
order to receive a cash flow of $104 in one year, assuming the
interest rate is 4%?
Answer
Method:  PV = 104 * 1/(1.04)^1 =104 * 1/(1+.04)^1 100
GENERAL FORMULA:    PV = FV* 1/(1+i)^n
Example 1b.  How much would Bob have to invest today to =108.16 * 1/(1+.04)^2 100
receive $108.16 after two years, assuming a 4% interest rate?
Example 1c.  How much would Bob have to invest today to =112.4864 * 1/(1+.04)^3 100
receive $112.48 after 3 years, assuming a 4% interest rate?
Using the General Formula above, and setting FV to 1.00, Rate
can you fill in the table on the right for the .06 column? Periods 0.04 0.06
1 0.961538  
2 0.924556  
3 0.888996