What Is the Yearly Growth Rate for a 40% Increase Over Three Years?

[HaLAA]

Homework Statement

If an investment increased by 40% over 3 years and rose by the same percentage rate each of those years, what was the rate?

Homework Equations

new_value = old_value(1+r)^p

The Attempt at a Solution

Let value of the investment be 1000, then we have 1000(1+0.4) = 1000(1+r)^3, r = 0.1187

r seems reasonable to me, but I am not sure that is right.

 

[SammyS]

Homework Statement

If an investment increased by 40% over 3 years and rose by the same percentage rate each of those years, what was the rate?

Homework Equations

new_value = old_value(1+r)^p

The Attempt at a Solution

Let value of the investment be 1000, then we have 1000(1+0.4) = 1000(1+r)^3, r = 0.1187

r seems reasonable to me, but I am not sure that is right.

What is (1+r)³ for the rate you found?

 

[HaLAA]

What is (1+r)³ for the rate you found?

the investment is increasing at the same rate in 3 years, and we are looking for the rate,r. In order to get the value after 3 years which is already increase 40%, I think (1+r)^3 is the rate increase over 4 years. Thus, this would equal to 1+0.4

 

[SammyS]

the investment is increasing at the same rate in 3 years, and we are looking for the rate,r. In order to get the value after 3 years which is already increase 40%, I think (1+r)^3 is the rate increase over 4 years. Thus, this would equal to 1+0.4

You did get a value for r, Right?

Simple question:

With that value of r, what do you get for (1+r}³ ?

 

[HaLAA]

You did get a value for r, Right?

Simple question:

With that value of r, what do you get for (1+r}³ ?

I get 1.4

 

[SammyS]

I get 1.4

That corresponds to an increase of 40% .

 

[HaLAA]

That corresponds to an increase of 40% .

I am getting confusing about the question, the investment increased 0.4 in 3 years, and in this 3 years increasing by the same rate, that is how I understand the question.

 

[SammyS]

I am getting confusing about the question, the investment increased 0.4 in 3 years, and in this 3 years increasing by the same rate, that is how I understand the question.

At the end of three years, the investment should have increased by 40%.

You were to find the yearly rate necessary for that growth.

Checking your answer, it seems the % you found is correct.

 

[HaLAA]

At the end of three years, the investment should have increased by 40%.

You were to find the yearly rate necessary for that growth.

Checking your answer, it seems the % you found is correct.

Thank you for checking my answer and help me to understand the question in more detail