Calculus Examples

$7000 {(1 + \frac{0.03}{12})}^{(12 \cdot 9)} = \frac{p ({(1 + \frac{0.03}{12})}^{(12 \cdot 9)} - 1)}{\frac{0.03}{12}}$

Step 1

Rewrite the equation as $\frac{p ({(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1)}{\frac{0.03}{12}} = 7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9}$ .

$\frac{p ({(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1)}{\frac{0.03}{12}} = 7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9}$

Step 2

Multiply both sides of the equation by $\frac{\frac{0.03}{12}}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1}$ .

$\frac{\frac{0.03}{12}}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} \cdot \frac{p ({(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1)}{\frac{0.03}{12}} = \frac{\frac{0.03}{12}}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3

Simplify both sides of the equation.

Tap for more steps...

Step 3.1

Simplify the left side.

Tap for more steps...

Step 3.1.1

Simplify $\frac{\frac{0.03}{12}}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} \cdot \frac{p ({(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1)}{\frac{0.03}{12}}$ .

Tap for more steps...

Step 3.1.1.1

Cancel the common factor of $\frac{0.03}{12}$ .

Tap for more steps...

Step 3.1.1.1.1

Cancel the common factor.

Step 3.1.1.1.2

Rewrite the expression.

$\frac{1}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (p ({(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1)) = \frac{\frac{0.03}{12}}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.1.1.2

Cancel the common factor of ${(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1$ .

Tap for more steps...

Step 3.1.1.2.1

Factor ${(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1$ out of $p ({(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1)$ .

$\frac{1}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (({(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1) p) = \frac{\frac{0.03}{12}}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.1.1.2.2

Cancel the common factor.

Step 3.1.1.2.3

Rewrite the expression.

$p = \frac{\frac{0.03}{12}}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2

Simplify the right side.

Tap for more steps...

Step 3.2.1

Simplify $\frac{\frac{0.03}{12}}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$ .

Tap for more steps...

Step 3.2.1.1

Multiply the numerator by the reciprocal of the denominator.

$p = \frac{0.03}{12} \cdot \frac{1}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.2

Divide $0.03$ by $12$ .

$p = 0.0025 \frac{1}{{(1 + \frac{0.03}{12})}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.3

Simplify the denominator.

Tap for more steps...

Step 3.2.1.3.1

Divide $0.03$ by $12$ .

$p = 0.0025 \frac{1}{{(1 + 0.0025)}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.3.2

Add $1$ and $0.0025$ .

$p = 0.0025 \frac{1}{{1.0025}^{12 \cdot 9} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.3.3

Multiply $12$ by $9$ .

$p = 0.0025 \frac{1}{{1.0025}^{108} - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.3.4

Raise $1.0025$ to the power of $108$ .

$p = 0.0025 \frac{1}{1.30952314 - 1} (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.3.5

Subtract $1$ from $1.30952314$ .

$p = 0.0025 (\frac{1}{0.30952314}) (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.4

Simplify the expression.

Tap for more steps...

Step 3.2.1.4.1

Divide $1$ by $0.30952314$ .

$p = 0.0025 \cdot 3.23077614 (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.4.2

Multiply $0.0025$ by $3.23077614$ .

$p = 0.00807694 (7000 {(1 + \frac{0.03}{12})}^{12 \cdot 9})$

Step 3.2.1.4.3

Divide $0.03$ by $12$ .

$p = 0.00807694 (7000 {(1 + 0.0025)}^{12 \cdot 9})$

Step 3.2.1.4.4

Add $1$ and $0.0025$ .

$p = 0.00807694 (7000 \cdot {1.0025}^{12 \cdot 9})$

Step 3.2.1.4.5

Multiply $12$ by $9$ .

$p = 0.00807694 (7000 \cdot {1.0025}^{108})$

Step 3.2.1.4.6

Raise $1.0025$ to the power of $108$ .

$p = 0.00807694 (7000 \cdot 1.30952314)$

Step 3.2.1.5

Multiply $0.00807694 (7000 \cdot 1.30952314)$ .

Tap for more steps...

Step 3.2.1.5.1

Multiply $7000$ by $1.30952314$ .

$p = 0.00807694 \cdot 9166.6620329$

Step 3.2.1.5.2

Multiply $0.00807694$ by $9166.6620329$ .

$p = 74.03858245$