An amount of $500 was invested in 1970 and the investment grew as shown in the following table. The average rate of change of the investment between 1975 and 1980 is ___ per year.
Year 1970 1975 1980 1985
Capital 500 966 1856 3578
There are two ways of doing this, and they give different answers. The change between 1975 and 1980 is $890 in 5 years, or $178 per year. That is 18.4% of the INITIAL amount per year. But it is not the average annual rate of change during the five year peiod
The best way to compute the annual rate of change, r, for that five year period is to use the formula
(1 +r)^5 = 1856/966 = 1.9213
This leads to
1 + r = 1.1395
r = 13.95 % per year