# Find the percentage rate

## 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
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## 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?

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
Staff Emeritus
Homework Helper
Gold Member
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 ?

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
Staff Emeritus
Homework Helper
Gold Member
I get 1.4
That corresponds to an increase of 40% .

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
Staff Emeritus
Homework Helper
Gold Member
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.