Finite Math Examples

$75000 = p {(1 + \frac{0.051}{12})}^{18 \cdot 12}$

Step 1

Rewrite the equation as $p {(1 + \frac{0.051}{12})}^{18 \cdot 12} = 75000$ .

$p {(1 + \frac{0.051}{12})}^{18 \cdot 12} = 75000$

Step 2

Simplify.

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Step 2.1

Multiply $18$ by $12$ .

$p {(1 + \frac{0.051}{12})}^{216} = 75000$

Step 2.2

Divide $0.051$ by $12$ .

$p {(1 + 0.00425)}^{216} = 75000$

Step 2.3

Add $1$ and $0.00425$ .

$p \cdot {1.00425}^{216} = 75000$

Step 3

Divide each term in $p \cdot {1.00425}^{216} = 75000$ by ${1.00425}^{216}$ and simplify.

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Step 3.1

Divide each term in $p \cdot {1.00425}^{216} = 75000$ by ${1.00425}^{216}$ .

$\frac{p \cdot {1.00425}^{216}}{{1.00425}^{216}} = \frac{75000}{{1.00425}^{216}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of ${1.00425}^{216}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{p \cdot {1.00425}^{216}}{{1.00425}^{216}} = \frac{75000}{{1.00425}^{216}}$

Step 3.2.1.2

Divide $p$ by $1$ .

$p = \frac{75000}{{1.00425}^{216}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $1.00425$ to the power of $216$ .

$p = \frac{75000}{2.49941013}$

Step 3.3.2

Divide $75000$ by $2.49941013$ .

$p = 30007.08000452$