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