Compound Interest question

Let $P_0$ be the initial balance and $I$ be the yearly interest rate compounded n times during the year. Then the future value after $m$ time steps is computed by the formula 
\[P(m)=P_0(1+\frac{i}{n})^m.\]
Here $I=4\%$, $n=4$, and $P_0=\$10,000$. Hence the future value after m quarters is 
\[P(m)=10000(1+\frac{4\%}{4})^m    \Rightarrow  P(m)=10000(1+\frac{1}{100})^m=10000(1.01)^m. \]
(a) After one year $m=4$ (after 4 quarters)
\[P(4)=10000(1.01)^4=\$10,406.04.\]
(b) To compute the effective annual rate divide the interest you receive after 1 year by the total amount, i.e. 
\[\frac{10,406.04-10,000}{10000}=.04060401=4.060401\%.\]