Finite Math Examples

$v = 1500 (\frac{{(1.065)}^{n} - 1}{0.065})$

Step 1

Remove parentheses.

$v = 1500 (\frac{{1.065}^{n} - 1}{0.065})$

Step 2

Simplify $1500 (\frac{{1.065}^{n} - 1}{0.065})$ .

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Step 2.1

Multiply by $1$ .

$v = 1500 \frac{1 \cdot {1.065}^{n} - 1}{0.065}$

Step 2.2

Rewrite $- 1$ as $1 (- 1)$ .

$v = 1500 \frac{1 \cdot {1.065}^{n} + 1 (- 1)}{0.065}$

Step 2.3

Factor $1$ out of $1 \cdot {1.065}^{n} + 1 (- 1)$ .

$v = 1500 \frac{1 \cdot ({1.065}^{n} - 1)}{0.065}$

Step 2.4

Factor $0.065$ out of $0.065$ .

$v = 1500 \frac{1 \cdot ({1.065}^{n} - 1)}{0.065 (1)}$

Step 2.5

Separate fractions.

$v = 1500 (\frac{1}{0.065} \cdot \frac{{1.065}^{n} - 1}{1})$

Step 2.6

Simplify the expression.

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Step 2.6.1

Divide $1$ by $0.065$ .

$v = 1500 (15.\overline{384615} \frac{{1.065}^{n} - 1}{1})$

Step 2.6.2

Divide ${1.065}^{n} - 1$ by $1$ .

$v = 1500 (15.\overline{384615} ({1.065}^{n} - 1))$

Step 2.7

Apply the distributive property.

$v = 1500 (15.\overline{384615} \cdot {1.065}^{n} + 15.\overline{384615} \cdot - 1)$

Step 2.8

Multiply $15.\overline{384615}$ by $- 1$ .

$v = 1500 (15.\overline{384615} \cdot {1.065}^{n} - 15.\overline{384615})$

Step 2.9

Apply the distributive property.

$v = 1500 (15.\overline{384615} \cdot {1.065}^{n}) + 1500 \cdot - 15.\overline{384615}$

Step 2.10

Multiply.

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Step 2.10.1

Multiply $15.\overline{384615}$ by $1500$ .

$v = 23076.\overline{923076} \cdot {1.065}^{n} + 1500 \cdot - 15.\overline{384615}$

Step 2.10.2

Multiply $1500$ by $- 15.\overline{384615}$ .

$v = 23076.\overline{923076} \cdot {1.065}^{n} - 23076.\overline{923076}$