Welcome to our community

Be a part of something great, join today!

Business Math Annual Average Percentage Increase

linapril

New member
Dec 21, 2012
23
What is the simplest way of solving this?

The value of a house is doubled in 20 years. What is the annual average percentage increase, if it is assumed to be the same each year?
 

MarkFL

Administrator
Staff member
Feb 24, 2012
13,775
I would let $H_0$ be the initial value of the house, and use the relation:

$\displaystyle H=H_0(1+r)^t$

We then let $H=2H_0$, $t=20$ and solve for $r$:

$\displaystyle 2H_0=H_0(1+r)^{20}$

$\displaystyle 2=(1+r)^{20}$

Now, raise each side to a power of $\dfrac{1}{20}$, then subtract 1 from each side, and you will have isolated $r$. Then multiply by 100, and use your calculator to get a decimal approximation if you want.

edit: Please let me suggest that your topic titles be more indicative of the nature of the question. I would use something like "Computing growth rate of investment" or something similar.
 

chisigma

Well-known member
Feb 13, 2012
1,704
What is the simplest way of solving this?

The value of a house is doubled in 20 years. What is the annual average percentage increase, if it is assumed to be the same each year?

Very easy indeed...

$a= 2^{\frac{1}{20}} \sim 3.53 \text{%}$

Kind regards

$\chi$ $\sigma$
 

linapril

New member
Dec 21, 2012
23
Could please explain how you got that answer?

Very easy indeed...

$a= 2^{\frac{1}{20}} \sim 3.53 \text{%}$

Kind regards

$\chi$ $\sigma$
 

chisigma

Well-known member
Feb 13, 2012
1,704
Could please explain how you got that answer?
MarkFl has already explained that in excellent way!... an alternative explanation is that the expression of the of value of the house after N years is...

$\displaystyle v= 2^{\frac{N}{20}}$ (1)

Now all what You have to do is setting in (1) N=1...

Kind regards

$\chi$ $\sigma$