Question

$m=\frac{\left(\frac{r}{1,200}\right){(1+\frac{r}{1,200})}^N}{{(1+\frac{r}{1,200})}^N-1}P$
The formula above gives the monthly payment $m$ needed to pay off a loan of $P$ dollars at $r$ percent annual interest over $N$ months. Which of the following gives $P$ in terms of $m$, $r$, and $N$?

• A. $P=\frac{\left(\frac{r}{1,200}\right){(1+\frac{r}{1,200})}^N}{{(1+\frac{r}{1,200})}^N-1}m$
• B. $P=\frac{{(1+\frac{r}{1,200})}^N-1}{\left(\frac{r}{1,200}\right){(1+\frac{r}{1,200})}^N}m$
• C. $P=\left(\frac{r}{1,200}\right)m$
• D. $P=\left(\frac{1,200}{r}\right)m$

Answer 1

Answer: (B)

Given, $m=\frac{\left(\frac{r}{1,200}\right){(1+\frac{r}{1,200})}^N}{{(1+\frac{r}{1,200})}^N-1}P$
On cross multiplying, we get
$m[{(1+\frac{r}{1,200})}^N-1]=\left[\left(\frac{r}{1,200}\right){(1+\frac{r}{1,200})}^N\right]\times P$
$\Rightarrow P=\frac{{(1+\frac{r}{1,200})}^N-1}{\left(\frac{r}{1,200}\right){(1+\frac{r}{1,200})}^N}m$