The discussion centers on calculating the yearly growth rate required for an investment to increase by 40% over three years, with the growth occurring at a consistent rate each year. Using the formula new_value = old_value(1+r)^p, participants determined that the annual growth rate (r) is approximately 11.87%. This value was confirmed through calculations, demonstrating that (1+r)^3 yields a total increase of 40% after three years, validating the correctness of the derived rate.
PREREQUISITESStudents in finance, investment analysts, and anyone interested in understanding the mathematics of compound growth and investment returns.
What is (1+r)3 for the rate you found?HaLAA said: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.
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+0.4SammyS said:What is (1+r)3 for the rate you found?
You did get a value for r, Right?HaLAA said: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
I get 1.4SammyS said:You did get a value for r, Right?
Simple question:
With that value of r, what do you get for (1+r}3 ?
That corresponds to an increase of 40% .HaLAA said:I get 1.4
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 said:That corresponds to an increase of 40% .
At the end of three years, the investment should have increased by 40%.HaLAA said: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.
Thank you for checking my answer and help me to understand the question in more detailSammyS said: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.