Question

Diana invested some money in a bank at a fixed rate of interest compounded annually. The equation below shows the value of her investment after x years:

f(x) = 400(1.01)x

What was the average rate of change of the value of Diana's investment from the second year to the fifth year?

1.01 dollars per year
2.47 dollars per year
4.12 dollars per year
12.36 dollars per year

Answer 1

4.12

Explanation:

Answer 2

$4.12 per year

Explanation:

Diana's investment value after 5 years is ...

... 400·1.01^5 = 420.40

After 2 years, it is ...

... 400·1.01^2 = 408.04

So, the difference in the three years of concern is ...

... 420.40 -408.04 = 12.36

Then the average per year is ...

... 12.36/3 = 4.12 . . . . . dollars per year