# Thread: Investment average rate increase?

1. ## Investment average rate increase?

An investment of $1000 increases 16% each year. Find the average rate at which the investment has grown over the first 5 years. I have already found the amount after the first year is$1160, and after the 5 years is $2100.30. Can someone please help me/teli me how find the average rate of increase? The answer is$220.07 per year.
Thank you.

2. Originally Posted by overduex
An investment of $1000 increases 16% each year. Find the average rate at which the investment has grown over the first 5 years. I have already found the amount after the first year is$1160, and after the 5 years is $2100.30. Can someone please help me/teli me how find the average rate of increase? The answer is$220.07 per year.
Thank you.
After 1st year, A1 = 1000(1 +0.16) = 1160.
After 2nd year, A2 = 1160(1 +0.16) = A1(1 +0.16) = 1000(1 +0.16)^2
.
.
After 5th year, A5 = 1000(1 +0.16)^5 = 2100.34 -----you got that right.

Meaning, after 5 years it gained 2100.34 -1000 = 1100.34 dollars.
So average gain per year 1100.34 /5 = 220.07 dollars. ----the book says.

But that is not yet the average rate of increase, even if the book says so.
Gain is not rate.
The average rate of increase then is
220.07/1000 = 0.22007 or 22% per year ------answer.