Finite Math Examples

$y = \frac{300 (1 - {(1 + \frac{0.0375}{12})}^{- 120})}{\frac{0.0375}{12}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$y = 300 (1 - {(1 + \frac{0.0375}{12})}^{- 120}) \frac{12}{0.0375}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Cancel the common factor of $0.0375$ .

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Step 2.1.1

Factor $0.0375$ out of $300 (1 - {(1 + \frac{0.0375}{12})}^{- 120})$ .

$y = 0.0375 (8000 (1 - {(1 + \frac{0.0375}{12})}^{- 120})) \frac{12}{0.0375}$

Step 2.1.2

Cancel the common factor.

$y = 0.0375 (8000 (1 - {(1 + \frac{0.0375}{12})}^{- 120})) \frac{12}{0.0375}$

Step 2.1.3

Rewrite the expression.

$y = 8000 (1 - {(1 + \frac{0.0375}{12})}^{- 120}) \cdot 12$

Step 2.2

Multiply $12$ by $8000$ .

$y = 96000 (1 - {(1 + \frac{0.0375}{12})}^{- 120})$

Step 3

Simplify each term.

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Step 3.1

Divide $0.0375$ by $12$ .

$y = 96000 (1 - {(1 + 0.003125)}^{- 120})$

Step 3.2

Add $1$ and $0.003125$ .

$y = 96000 (1 - {1.003125}^{- 120})$

Step 3.3

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = 96000 (1 - \frac{1}{{1.003125}^{120}})$

Step 3.4

Raise $1.003125$ to the power of $120$ .

$y = 96000 (1 - \frac{1}{1.4541409})$

Step 3.5

Divide $1$ by $1.4541409$ .

$y = 96000 (1 - 1 \cdot 0.68769126)$

Step 3.6

Multiply $- 1$ by $0.68769126$ .

$y = 96000 (1 - 0.68769126)$

Step 4

Simplify the expression.

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Step 4.1

Subtract $0.68769126$ from $1$ .

$y = 96000 \cdot 0.31230873$

Step 4.2

Multiply $96000$ by $0.31230873$ .

$y = 29981.6382862$