$\displaystyle (1+\frac{i}{2})^2-1 = (1+\frac{j}{m})^m - 1$

$\displaystyle (1+\frac{i}{2})^\frac{2}{m}= (1+\frac{j}{m})$

$\displaystyle (1+\frac{i}{2})^\frac{2}{m} -1=\frac{j}{m}$

$\displaystyle j=m[(1+\frac{i}{2})^\frac{2}{m} -1]$

$\displaystyle j=m(1+\frac{i}{2})^\frac{2}{m} -m$

but the correct answer is

$\displaystyle j=(1+\frac{i}{2})^\frac{2}{m} -1$

what happened to the m? this is working out effective interests payments on a mortgage so perhaps there is some assumption I I'm unaware of about the periodic interest rate (maybe they put j but they mean j/m or something) , but mathematically shouldn't the m still be there?