Analysis Beispiele

\frac{10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}}{12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12}

$\frac{10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}}{12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12}$

Schritt 1

Kürze den gemeinsamen Teiler von

10000

$10000$ und

12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12

$12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12$ .

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Schritt 1.1

Faktorisiere

4

$4$ aus

10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}

$10000 (0.06) {(1 + \frac{0.06}{12})}^{12 (6)}$ heraus.

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{12 {(1 + \frac{0.06}{12})}^{12 (6)} - 12}$

Schritt 1.2

Kürze die gemeinsamen Faktoren.

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Schritt 1.2.1

Faktorisiere

4

$4$ aus

12 {(1 + \frac{0.06}{12})}^{12 (6)}

$12 {(1 + \frac{0.06}{12})}^{12 (6)}$ heraus.

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) - 12}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) - 12}$

Schritt 1.2.2

Faktorisiere

4

$4$ aus

- 12

$- 12$ heraus.

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) + 4 (- 3)}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) + 4 (- 3)}$

Schritt 1.2.3

Faktorisiere

4

$4$ aus

4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) + 4 (- 3)

$4 (3 {(1 + \frac{0.06}{12})}^{12 (6)}) + 4 (- 3)$ heraus.

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3)}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3)}$

Schritt 1.2.4

Kürze den gemeinsamen Faktor.

\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3)}

$\frac{4 (2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)})}{4 (3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3)}$

Schritt 1.2.5

Forme den Ausdruck um.

\frac{2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}

$\frac{2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

\frac{2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}

$\frac{2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

\frac{2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}

$\frac{2500 \cdot 0.06 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

Schritt 2

Vereinfache den Zähler.

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Schritt 2.1

Mutltipliziere

2500

$2500$ mit

0.06

$0.06$ .

\frac{150 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}

$\frac{150 {(1 + \frac{0.06}{12})}^{12 (6)}}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

Schritt 2.2

Mutltipliziere

150

$150$ mit

{(1 + \frac{0.06}{12})}^{12 (6)}

${(1 + \frac{0.06}{12})}^{12 (6)}$ .

\frac{214.80664177}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}

$\frac{214.80664177}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

\frac{214.80664177}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}

$\frac{214.80664177}{3 {(1 + \frac{0.06}{12})}^{12 (6)} - 3}$

Schritt 3

Vereinfache den Nenner.

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Schritt 3.1

Dividiere

0.06

$0.06$ durch

12

$12$ .

\frac{214.80664177}{3 {(1 + 0.005)}^{12 (6)} - 3}

$\frac{214.80664177}{3 {(1 + 0.005)}^{12 (6)} - 3}$

Schritt 3.2

Addiere

1

$1$ und

0.005

$0.005$ .

\frac{214.80664177}{3 \cdot {1.005}^{12 (6)} - 3}

$\frac{214.80664177}{3 \cdot {1.005}^{12 (6)} - 3}$

Schritt 3.3

Mutltipliziere

12

$12$ mit

6

$6$ .

\frac{214.80664177}{3 \cdot {1.005}^{72} - 3}

$\frac{214.80664177}{3 \cdot {1.005}^{72} - 3}$

Schritt 3.4

Potenziere

1.005

$1.005$ mit

72

$72$ .

\frac{214.80664177}{3 \cdot 1.43204427 - 3}

$\frac{214.80664177}{3 \cdot 1.43204427 - 3}$

Schritt 3.5

Mutltipliziere

3

$3$ mit

1.43204427

$1.43204427$ .

\frac{214.80664177}{4.29613283 - 3}

$\frac{214.80664177}{4.29613283 - 3}$

Schritt 3.6

Subtrahiere

3

$3$ von

4.29613283

$4.29613283$ .

\frac{214.80664177}{1.29613283}

$\frac{214.80664177}{1.29613283}$

\frac{214.80664177}{1.29613283}

$\frac{214.80664177}{1.29613283}$

Schritt 4

Dividiere

214.80664177

$214.80664177$ durch

1.29613283

$1.29613283$ .

165.72887893

$165.72887893$