Basic Math Examples

$v = 3000 (\frac{{(1 + 0.06)}^{20} - {(1 + 0.03)}^{20}}{0.06 - 0.03})$

Step 1

Multiply $3000$ by $\frac{{(1 + 0.06)}^{20} - {(1 + 0.03)}^{20}}{0.06 - 0.03}$ .

$v = 3000 (\frac{{(1 + 0.06)}^{20} - {(1 + 0.03)}^{20}}{0.06 - 0.03})$

Step 2

Simplify $3000 (\frac{{(1 + 0.06)}^{20} - {(1 + 0.03)}^{20}}{0.06 - 0.03})$ .

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Step 2.1

Simplify the numerator.

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Step 2.1.1

Add $1$ and $0.06$ .

$v = 3000 \frac{{1.06}^{20} - {(1 + 0.03)}^{20}}{0.06 - 0.03}$

Step 2.1.2

Raise $1.06$ to the power of $20$ .

$v = 3000 \frac{3.20713547 - {(1 + 0.03)}^{20}}{0.06 - 0.03}$

Step 2.1.3

Add $1$ and $0.03$ .

$v = 3000 \frac{3.20713547 - {1.03}^{20}}{0.06 - 0.03}$

Step 2.1.4

Raise $1.03$ to the power of $20$ .

$v = 3000 \frac{3.20713547 - 1 \cdot 1.80611123}{0.06 - 0.03}$

Step 2.1.5

Multiply $- 1$ by $1.80611123$ .

$v = 3000 \frac{3.20713547 - 1.80611123}{0.06 - 0.03}$

Step 2.1.6

Subtract $1.80611123$ from $3.20713547$ .

$v = 3000 \frac{1.40102423}{0.06 - 0.03}$

Step 2.2

Reduce the expression by cancelling the common factors.

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Step 2.2.1

Subtract $0.03$ from $0.06$ .

$v = 3000 (\frac{1.40102423}{0.03})$

Step 2.2.2

Cancel the common factor of $0.03$ .

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Step 2.2.2.1

Factor $0.03$ out of $3000$ .

$v = 0.03 (100000) \frac{1.40102423}{0.03}$

Step 2.2.2.2

Cancel the common factor.

$v = 0.03 \cdot 100000 \frac{1.40102423}{0.03}$

Step 2.2.2.3

Rewrite the expression.

$v = 100000 \cdot 1.40102423$

Step 2.2.3

Multiply $100000$ by $1.40102423$ .

$v = 140102.42375434$