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linapril

New member
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

Staff member
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
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

Very easy indeed...

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

Kind regards

$\chi$ $\sigma$

chisigma

Well-known member
$\displaystyle v= 2^{\frac{N}{20}}$ (1)
$\chi$ $\sigma$