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?

Answer 1

The investment function is :

f (x) = 400(1.01)ˣ

We need to get the value of the investment between time 2 years and time 5 years

We will use integration technique whereby we will integrate the function from 2
to 5.


₂∫⁵ 400(1.01)ˣ

Using the technique for power integration :

∫bˣ = bˣ / ln b + C

Applying this in the integral:

400 ₂∫⁵ (1.01)ˣ

400 [ (1.01)ˣ / ln 1.01] from 2 to 5

ln 1.01 = 0.009950

{(1.01)⁵ / 0.009950 - (1.01)² / 0.009950} ×400

(105.63 - 102.52) = 3.11

3.11 × 400 = 1244

The answer is :

1244