Calculus Examples

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

Step 1

Cancel the common factor of $10000$ and $12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12$ .

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Step 1.1

Factor $4$ out of $10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}$ .

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

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $4$ out of $12 {(1 + \frac{0.06}{12})}^{12 (6)}$ .

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

Step 1.2.2

Factor $4$ out of $- 12$ .

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

Step 1.2.3

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

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

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 $1.29613283$ .

$165.72887893$