Applications of Logarithmic Functions

-- Section 4.4 --
 
Annual Growth Rate

  

 An investment is growing continuously for t years.
P = current value, P0 = original amount
 
A $10,000 stock investment in 1993 was worth $22,400 in 2000. Find the average annual growth rate of the stock.

Solve

            Step

     Calculator Help

Annual Growth Rate Find your ln key.  (Natural log)
 Identify each part
  HINT: use these key strokes

P = 22,400

 current amount = 22,400 1 ÷ 7 × ln (2.24) [enter or =]
Po= 10,000
initial amount = 10,000 Some calculators do not require the parentheses
t = 7
t = 2000 - 1993 = 7  
Annual Growth Rate


Interpret Þ The investment earn about 12% a year for 7 years.
  
A $5,000 stock investment in 1992 was worth $32,500 in 1998. Find the average annual growth rate of the stock.

[Solution]

If $10,000 is invested each year in an annuity earning 10% annual interest, when will the account be worth $1,000,000?
 
*Annuities:

P is amount invested each year. 
r  is the annual interest rate.
A is the amount after n  years.
 

Solve

            Step

     Calculator Help

annuity formula Find your log key.  (common log)
 Identify each part
  HINT: use these key strokes
P = 10,000
invested each year log(1000000×.1÷10000 + 1)÷log(1 + .1)  [enter or =]
r = 0.1
annual interest rate  parentheses are need here
A = 1,000,000
amount after n years

plug in the parts

and simplify
Interpret Þ It will take about 25 years to have 1,000,000 by investing 10,000 a year at 10% annual interest.
*An annuity is an invested or loan with a fixed payment and interest rate.  There can be variations.

If $5,000 is invested each year in an annuity earning 8% annual interest, when will the account be worth $500,000?

[Solution]

Tutorials and Applets by
Joe McDonald
Community College of Southern Nevada