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

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

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

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P = (\frac{r}{1, 200}) m

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P = (\frac{1, 200}{r}) m

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Solution

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

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m=(r1,200)(1+r1,200)N(1+r1,200)N−1PThe 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?

The correct option is B P=(1+r1,200)N−1(r1,200)(1+r1,200)NmGiven, m=(r1,200)(1+r1,200)N(1+r1,200)N−1POn cross multiplying, we getm[(1+r1,200)N−1]=[(r1,200)(1+r1,200)N]×P⇒P=(1+r1,200)N−1(r1,200)(1+r1,200)Nm

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