A loan is an annuity pointed the other way: you hold the balance, and equal payments grind it to exactly zero on the last one. The level payment is $M = \dfrac{P\,i}{1 - (1+i)^{-n}}$ — M equals P i over, one minus, one plus i to the minus n. $P$ is the principal borrowed in dollars, $i$ is the rate per PAYMENT period as a decimal (an annual rate divided by 12 for monthly payments), $n$ is the number of payments (years times 12), and $M$ is the payment itself. Both $i$ and $n$ must speak the same period or the formula answers a question nobody asked.

Then the line the advertisement never prints: $I = M\,n - P$, the total interest — everything handed over across the whole term, minus the amount actually borrowed. On a 30-year mortgage it routinely exceeds the price of the house. That is not a scandal; it is a rental fee for a very large sum over a very long time. But it deserves to be computed rather than assumed.

Finally, the only fair way to compare two quoted rates: $\mathit{EAR} = \left(1 + \dfrac{r}{m}\right)^{m} - 1$, the effective annual rate, where $r$ is the nominal annual rate as a decimal and $m$ is the number of compoundings per year. 12% compounded monthly is 12.68% effective, so it loses to 12.5% compounded annually. The bigger headline was the cheaper loan, and only the EAR could have told you.