Question

Find both the arithmetic growth rate and the geometric growth rate of the dividends for Alexander's Markets.

Year	2001	2002	2003	2004	2005	2006	2007	2008	2009	2010
Dividend	​$1.46	​$2.43	​$3.08	​$4.41	​$5.25	​$6.49	​$7.11	​$8.36	​$7.87	​$6.84

What is the arithmetic growth rate of the dividends for Alexander's Markets?

​(Round to two decimal​ places.)

What is the geometric growth rate of the dividends for Alexander's Markets?

Answer 1

Year   Dividend    Change (in percentage)
2010   ​$6.84        =(6.84-7.87)/7.87=-13.09%
2009   ​$7.87        =(7.87-8.36)/8.36=-5.86%
2008   ​$8.36        =(8.36-7.11)/7.11=17.58%
2007   ​$7.11        =(7.11-6.49)/6.49=9.55%
2006   ​$6.49        =(6.49-5.25)/5.25=23.62%
2005   ​$5.25        =(5.25-4.41)/4.41=19.05%
2004   ​$4.41        =(4.41-3.08)/3.08=43.18%
2003   ​$3.08        =(3.08-2.43)/2.43=26.75%
2002   ​$2.43        =(2.43-1.46)/1.46=66.44%
2001   ​$1.46

Now, arithmetic growth rate (is the average of the dividend growth rates as we calculated above) and is given by:
(-13.09%+(-5.86%)+17.58%+9.55%+23.62%+19.05%+43.18%+26.75%+66.44%)/9=1.87/9=0.2080 or 20.80%

Geometric growth rate of the dividends=[(Final year dividend/Initial year dividend)^1/number of years we calculated the change in dividends]-1
Final year dividend or dividend paid in year 2010 is $6.84
Dividend paid in year 2001 is ​$1.46
Number of years we calculated the percentage change in dividends=9

Geometric growth rate=(6.84/1.46)^1/9 - 1 =4.6849315^1/9 -1 =1.1871964-1=0.1871964 or 18.72%