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 13? 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 







