Let's suppose I have $3$ flowers in a field initially and that the number of flowers doubles every month. I can then write that $$N=3(1+0.5/12)^{12t}$$
where $t$ is the time in years. Right? But then if I want to know the number of flowers after $3$ months, which should be the $24$, I use this formula and it does not give me $24$. Why?
If $t$ is the number of years, then $12t$ is the number of months, and that is the number of times that one multiplies by $2$. Thus
$$ N= 3\cdot \underbrace{2\cdot2\cdot2\cdots2}_{\begin{smallmatrix} \text{just as many 2s} \\ \text{as the number} \\ \text{of months} \end{smallmatrix}} = 3\cdot 2^{\text{number of months}} = 3\cdot 2^{12t}. $$
After three months, you have $t = \frac 1 4$ (since $3 \text{ months} = \frac 1 4 \text{ year}$).