Is My Textbook Incorrect On Explaining How To Solve Annual Interest Compounded Monthly? I doubt that the textbook solution is correct. If I have $\$100$ and put it into a bank with annual interest compounded monthly of $6\%$, how much money $y$ would I have after $t$ years?
The equation that the textbook provides is $y = 100(1+x)^{12t}$. The textbook states that for annual interest compounded monthly, the rate of $x$ equals $6\%/12$, which would equal $0.005$. But putting this into the equation with $t$ equaling $1$ for $1$ year, I get $106.1677812$ instead of the expected answer of simply $106$. Anyone know how to calculate $x$ to just get the correct exact answer of $106$? Is the equation incorrect as well?

The nominal interest rate compounded monthly is $i^{(12)}=6\%$. So the effective annual interest rate $i$ is
$$
i=\left(1+\frac{i^{(12)}}{12}\right)^{12}-1\approx 6.168\%
$$
So after $t$ years you have the amount $S(t)$
$$
S=S_0(1+i)^t=S_0\left(1+\frac{i^{(12)}}{12}\right)^{12\,t}
$$
where $S_0$ is the initial amount of money.
In general, for a nominal interest rate $i^{(m)}$ compounded $m$ times in a year, you have an effective annual interest rate
$$
i=\left(1+\frac{i^{(m)}}{m}\right)^{m}-1
$$
The quantity $i_m=\frac{i^{(m)}}{m}$ is called interest rate per conversion period.
Compounded monthy means $m=12$, quarterly $m=4$, weekly $m=52$ and so on.
