Basic Math Examples

v = 2700 (\frac{{(1 + 0.06)}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05})

$v = 2700 (\frac{{(1 + 0.06)}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05})$

Step 1

Multiply

2700

$2700$ by

\frac{{(1 + 0.06)}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05}

$\frac{{(1 + 0.06)}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05}$ .

v = 2700 (\frac{{(1 + 0.06)}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05})

$v = 2700 (\frac{{(1 + 0.06)}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05})$

Step 2

Simplify

2700 (\frac{{(1 + 0.06)}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05})

$2700 (\frac{{(1 + 0.06)}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05})$ .

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Add

1

$1$ and

0.06

$0.06$ .

v = 2700 \frac{{1.06}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05}

$v = 2700 \frac{{1.06}^{30} - {(1 + 0.05)}^{30}}{0.06 - 0.05}$

Step 2.1.2

Raise

1.06

$1.06$ to the power of

30

$30$ .

v = 2700 \frac{5.74349117 - {(1 + 0.05)}^{30}}{0.06 - 0.05}

$v = 2700 \frac{5.74349117 - {(1 + 0.05)}^{30}}{0.06 - 0.05}$

Step 2.1.3

Add

1

$1$ and

0.05

$0.05$ .

v = 2700 \frac{5.74349117 - {1.05}^{30}}{0.06 - 0.05}

$v = 2700 \frac{5.74349117 - {1.05}^{30}}{0.06 - 0.05}$

Step 2.1.4

Raise

1.05

$1.05$ to the power of

30

$30$ .

v = 2700 \frac{5.74349117 - 1 \cdot 4.32194237}{0.06 - 0.05}

$v = 2700 \frac{5.74349117 - 1 \cdot 4.32194237}{0.06 - 0.05}$

Step 2.1.5

Multiply

- 1

$- 1$ by

4.32194237

$4.32194237$ .

v = 2700 \frac{5.74349117 - 4.32194237}{0.06 - 0.05}

$v = 2700 \frac{5.74349117 - 4.32194237}{0.06 - 0.05}$

Step 2.1.6

Subtract

$4.32194237$ from

$5.74349117$ .

$v = 2700 \frac{1.42154879}{0.06 - 0.05}$

Step 2.2

Reduce the expression by cancelling the common factors.

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Step 2.2.1

Subtract

$0.05$ from

$0.06$ .

$v = 2700 (\frac{1.42154879}{0.01})$

Step 2.2.2

Cancel the common factor of

$0.01$ .

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Step 2.2.2.1

Factor

$0.01$ out of

$2700$ .

$v = 0.01 (270000) \frac{1.42154879}{0.01}$

Step 2.2.2.2

Cancel the common factor.

$v = 0.01 \cdot 270000 \frac{1.42154879}{0.01}$

Step 2.2.2.3

Rewrite the expression.

$v = 270000 \cdot 1.42154879$

Step 2.2.3

Multiply

$270000$ by

$1.42154879$ .

$v = 383818.17539589$