Calculus Examples

\frac{10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}}{12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12}

$\frac{10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}}{12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12}$

Step 1

Cancel the common factor of

10000

$10000$ and

12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12

$12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12$ .

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Step 1.1

Factor

4

$4$ out of

10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}

$10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}$ .

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor

4

$4$ out of

12 {(1 + \frac{0.06}{12})}^{12 (6)}

$12 {(1 + \frac{0.06}{12})}^{12 (6)}$ .

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) - 12}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) - 12}$

Step 1.2.2

Factor

4

$4$ out of

- 12

$- 12$ .

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) + 4 (- 3)}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) + 4 (- 3)}$

Step 1.2.3

Factor

4

$4$ out of

4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) + 4 (- 3)

$4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) + 4 (- 3)$ .

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3)}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3)}$

Step 1.2.4

Cancel the common factor.

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3)}$

Step 1.2.5

Rewrite the expression.

$\frac{2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

Step 2

Simplify the numerator.

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Step 2.1

Multiply

$2500$ by

$0.06$ .

$\frac{150 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

Step 2.2

Multiply

$150$ by

${(1 + \frac{0.06}{12})}^{12 (6)}$ .

$\frac{214.80664177}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

Step 3

Simplify the denominator.

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Step 3.1

Divide

$0.06$ by

$12$ .

$\frac{214.80664177}{3 {(1 + 0.005)}^{12 (6)} - 3}$

Step 3.2

Add

$1$ and

$0.005$ .

$\frac{214.80664177}{3 \cdot {1.005}^{12 (6)} - 3}$

Step 3.3

Multiply

$12$ by

$6$ .

$\frac{214.80664177}{3 \cdot {1.005}^{72} - 3}$

Step 3.4

Raise

$1.005$ to the power of

$72$ .

$\frac{214.80664177}{3 \cdot 1.43204427 - 3}$

Step 3.5

Multiply

$3$ by

$1.43204427$ .

$\frac{214.80664177}{4.29613283 - 3}$

Step 3.6

Subtract

$3$ from

$4.29613283$ .

$\frac{214.80664177}{1.29613283}$

Step 4

Divide

$214.80664177$ by

$1.29613283$ .

$165.72887893$