Algebra Examples

A = P {(1 + \frac{r}{n})}^{n t}

$A = P {(1 + \frac{r}{n})}^{n t}$

Step 1

Rewrite the equation as

P {(1 + \frac{r}{n})}^{n t} = A

$P {(1 + \frac{r}{n})}^{n t} = A$ .

P {(1 + \frac{r}{n})}^{n t} = A

$P {(1 + \frac{r}{n})}^{n t} = A$

Step 2

Divide each term in

P {(1 + \frac{r}{n})}^{n t} = A

$P {(1 + \frac{r}{n})}^{n t} = A$ by

P

$P$ and simplify.

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Step 2.1

Divide each term in

P {(1 + \frac{r}{n})}^{n t} = A

$P {(1 + \frac{r}{n})}^{n t} = A$ by

P

$P$ .

\frac{P {(1 + \frac{r}{n})}^{n t}}{P} = \frac{A}{P}

$\frac{P {(1 + \frac{r}{n})}^{n t}}{P} = \frac{A}{P}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of

P

$P$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{P {(1 + \frac{r}{n})}^{n t}}{P} = \frac{A}{P}$

Step 2.2.1.2

Divide

${(1 + \frac{r}{n})}^{n t}$ by

$1$ .

${(1 + \frac{r}{n})}^{n t} = \frac{A}{P}$

Step 3

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln ({(1 + \frac{r}{n})}^{n t}) = \ln (\frac{A}{P})$

Step 4

Expand

$\ln ({(1 + \frac{r}{n})}^{n t})$ by moving

$n t$ outside the logarithm.

$n t \ln (1 + \frac{r}{n}) = \ln (\frac{A}{P})$

Step 5

Divide each term in

$n t \ln (1 + \frac{r}{n}) = \ln (\frac{A}{P})$ by

$n \ln (1 + \frac{r}{n})$ and simplify.

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Step 5.1

Divide each term in

$n t \ln (1 + \frac{r}{n}) = \ln (\frac{A}{P})$ by

$n \ln (1 + \frac{r}{n})$ .

$\frac{n t \ln (1 + \frac{r}{n})}{n \ln (1 + \frac{r}{n})} = \frac{\ln (\frac{A}{P})}{n \ln (1 + \frac{r}{n})}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of

$n$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{n t \ln (1 + \frac{r}{n})}{n \ln (1 + \frac{r}{n})} = \frac{\ln (\frac{A}{P})}{n \ln (1 + \frac{r}{n})}$

Step 5.2.1.2

Rewrite the expression.

$\frac{t \ln (1 + \frac{r}{n})}{\ln (1 + \frac{r}{n})} = \frac{\ln (\frac{A}{P})}{n \ln (1 + \frac{r}{n})}$

Step 5.2.2

Cancel the common factor of

$\ln (1 + \frac{r}{n})$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{t \ln (1 + \frac{r}{n})}{\ln (1 + \frac{r}{n})} = \frac{\ln (\frac{A}{P})}{n \ln (1 + \frac{r}{n})}$

Step 5.2.2.2

Divide

$t$ by

$1$ .

$t = \frac{\ln (\frac{A}{P})}{n \ln (1 + \frac{r}{n})}$