Finite Math Examples

$12500 \cdot {(1 + 0.027)}^{\frac{11}{12}} + 14000 \cdot {(1 + 0.027)}^{\frac{3}{12}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1

Simplify each term.

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Step 1.1

Add $1$ and $0.027$ .

$12500 \cdot {1.027}^{\frac{11}{12}} + 14000 \cdot {(1 + 0.027)}^{\frac{3}{12}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.2

Raise $1.027$ to the power of $\frac{11}{12}$ .

$12500 \cdot 1.02472242 + 14000 \cdot {(1 + 0.027)}^{\frac{3}{12}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.3

Multiply $12500$ by $1.02472242$ .

$12809.03029964 + 14000 \cdot {(1 + 0.027)}^{\frac{3}{12}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.4

Add $1$ and $0.027$ .

$12809.03029964 + 14000 \cdot {1.027}^{\frac{3}{12}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.5

Cancel the common factor of $3$ and $12$ .

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Step 1.5.1

Factor $3$ out of $3$ .

$12809.03029964 + 14000 \cdot {1.027}^{\frac{3 (1)}{12}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.5.2

Cancel the common factors.

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Step 1.5.2.1

Factor $3$ out of $12$ .

$12809.03029964 + 14000 \cdot {1.027}^{\frac{3 \cdot 1}{3 \cdot 4}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.5.2.2

Cancel the common factor.

$12809.03029964 + 14000 \cdot {1.027}^{\frac{3 \cdot 1}{3 \cdot 4}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.5.2.3

Rewrite the expression.

$12809.03029964 + 14000 \cdot {1.027}^{\frac{1}{4}} + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.6

Raise $1.027$ to the power of $\frac{1}{4}$ .

$12809.03029964 + 14000 \cdot 1.00668271 + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.7

Multiply $14000$ by $1.00668271$ .

$12809.03029964 + 14093.5579831 + 25000 \cdot {(1 + 0.027)}^{- \frac{10}{12}}$

Step 1.8

Add $1$ and $0.027$ .

$12809.03029964 + 14093.5579831 + 25000 \cdot {1.027}^{- \frac{10}{12}}$

Step 1.9

Cancel the common factor of $10$ and $12$ .

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Step 1.9.1

Factor $2$ out of $10$ .

$12809.03029964 + 14093.5579831 + 25000 \cdot {1.027}^{- \frac{2 (5)}{12}}$

Step 1.9.2

Cancel the common factors.

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Step 1.9.2.1

Factor $2$ out of $12$ .

$12809.03029964 + 14093.5579831 + 25000 \cdot {1.027}^{- \frac{2 \cdot 5}{2 \cdot 6}}$

Step 1.9.2.2

Cancel the common factor.

$12809.03029964 + 14093.5579831 + 25000 \cdot {1.027}^{- \frac{2 \cdot 5}{2 \cdot 6}}$

Step 1.9.2.3

Rewrite the expression.

$12809.03029964 + 14093.5579831 + 25000 \cdot {1.027}^{- \frac{5}{6}}$

Step 1.10

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

$12809.03029964 + 14093.5579831 + 25000 \cdot \frac{1}{{1.027}^{\frac{5}{6}}}$

Step 1.11

Raise $1.027$ to the power of $\frac{5}{6}$ .

$12809.03029964 + 14093.5579831 + 25000 \cdot \frac{1}{1.02244989}$

Step 1.12

Divide $1$ by $1.02244989$ .

$12809.03029964 + 14093.5579831 + 25000 \cdot 0.97804303$

Step 1.13

Multiply $25000$ by $0.97804303$ .

$12809.03029964 + 14093.5579831 + 24451.07581939$

Step 2

Simplify by adding numbers.

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Step 2.1

Add $12809.03029964$ and $14093.5579831$ .

$26902.58828275 + 24451.07581939$

Step 2.2

Add $26902.58828275$ and $24451.07581939$ .

$51353.66410214$