The following formula gives the total amount of a loan \(P\) given a monthly payment \(m\), an annual interest \(r\) percent over a term of \(N\) months. Which of the following would give us the monthly payment \(m\) in terms of \(P, r,\) and \(N\)?

$$ P = \frac{\left( 1+\dfrac{r}{1{,}200} \right)^N - 1 } { \left( \dfrac{r}{1{,}200} \right) \left( 1 + \dfrac{r}{1{,}200} \right)^N} m $$

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Concentrating on the big picture,

$$ P = \dfrac{ \colorbox{aqua}{$ \left( 1+\dfrac{r}{1{,}200}\right)^N-1 $} }{ \colorbox{yellow}{ $\left( \dfrac{r}{1{,}200} \right) $} \colorbox{chartreuse} {$ \left( 1 + \dfrac{r}{1{,}200} \right)^N$}} m $$

We can do the following algebraic moves

$$ P=\frac{\colorbox{aqua}{A}}{\colorbox{yellow}{B}\colorbox{chartreuse}{C}}m $$ $$ P\cdot \colorbox{yellow}{B} \cdot \colorbox{chartreuse}{C} = \colorbox{aqua}{A}m $$ $$ \frac{\colorbox{yellow}{B}\colorbox{chartreuse}{C}}{\colorbox{aqua}{A}}P= m$$ Which gets us, $$ \boxed { m = \dfrac{ \colorbox{yellow}{ $\left( \dfrac{r}{1{,}200} \right) $} \colorbox{chartreuse} {$ \left( 1 + \dfrac{r}{1{,}200} \right)^N$}}{ \colorbox{aqua}{$ \left( 1+\dfrac{r}{1{,}200}\right)^N-1 $} } P } $$