Originally Posted by

**earboth** Hello,

if I understand your problem correctly you have

x = 0.122222222.... then

10x = 1.22222222.... thus

9x = 1.1 Therefore

$\displaystyle x = \frac{1.1}{9}=\frac{11}{90}$

If you invest a capital of $\displaystyle C_0$ at an interest o p % then the capital grows in n years to

$\displaystyle C_n=C_0 \cdot (1+\frac{p}{100})^n$

Now plug in the values you know:

$\displaystyle 10800=10000 \cdot (1+\frac{p}{100})^4$. Divide by 10000 and calculate the 4th root:

$\displaystyle \sqrt[4]{\frac{10800}{10000}}=1+\frac{p}{100}$. Solve for p.

I got $\displaystyle p \approx 1.94~\%$