Yikes! I know an index of 1.18404 for the equation "1.18404=(1+i)^4", but not how to solve for i.

Question

Calculate the compound interest rate. Compound interest is calculated based on the change in the cost index over the 4-yr period:
PV=FV(1+i)
4362=3684(1+i)^4
4362/3684=(1+i)^4
1.18404=(1+i)^4
i=4.31%

Answer 1

If $(1+i)^4=1.18404$, then $1+i=1.18404^{1/4}$, so $i=1.18404^{1/4}-1=0.0431.$

Answer 2

You have $1.18404=(1+i)^4$.

Now, take the fourth root of each side

$\sqrt[4]{1.18404}=1+i$.

So now, $\sqrt[4]{1.18404}=1.0431=1+i$.

Then $i=0.0431=4.31\%$