Finite Math Examples

$21000 = 3000 {(1 + (\frac{0.07}{12}))}^{n}$

Step 1

Rewrite the equation as $3000 {(1 + \frac{0.07}{12})}^{n} = 21000$ .

$3000 {(1 + \frac{0.07}{12})}^{n} = 21000$

Step 2

Simplify.

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Step 2.1

Divide $0.07$ by $12$ .

$3000 {(1 + 0.0058\overline{3})}^{n} = 21000$

Step 2.2

Add $1$ and $0.0058\overline{3}$ .

$3000 \cdot {1.0058\overline{3}}^{n} = 21000$

Step 3

Divide each term in $3000 \cdot {1.0058\overline{3}}^{n} = 21000$ by $3000$ and simplify.

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Step 3.1

Divide each term in $3000 \cdot {1.0058\overline{3}}^{n} = 21000$ by $3000$ .

$\frac{3000 \cdot {1.0058\overline{3}}^{n}}{3000} = \frac{21000}{3000}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3000$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3000 \cdot {1.0058\overline{3}}^{n}}{3000} = \frac{21000}{3000}$

Step 3.2.1.2

Divide ${1.0058\overline{3}}^{n}$ by $1$ .

${1.0058\overline{3}}^{n} = \frac{21000}{3000}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $21000$ by $3000$ .

${1.0058\overline{3}}^{n} = 7$

Step 4

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln ({1.0058\overline{3}}^{n}) = \ln (7)$

Step 5

Expand $\ln ({1.0058\overline{3}}^{n})$ by moving $n$ outside the logarithm.

$n \ln (1.0058\overline{3}) = \ln (7)$

Step 6

Divide each term in $n \ln (1.0058\overline{3}) = \ln (7)$ by $\ln (1.0058\overline{3})$ and simplify.

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Step 6.1

Divide each term in $n \ln (1.0058\overline{3}) = \ln (7)$ by $\ln (1.0058\overline{3})$ .

$\frac{n \ln (1.0058\overline{3})}{\ln (1.0058\overline{3})} = \frac{\ln (7)}{\ln (1.0058\overline{3})}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $\ln (1.0058\overline{3})$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{n \ln (1.0058\overline{3})}{\ln (1.0058\overline{3})} = \frac{\ln (7)}{\ln (1.0058\overline{3})}$

Step 6.2.1.2

Divide $n$ by $1$ .

$n = \frac{\ln (7)}{\ln (1.0058\overline{3})}$

Step 7

The result can be shown in multiple forms.

Exact Form:

$n = \frac{\ln (7)}{\ln (1.0058\overline{3})}$

Decimal Form:

$n = 334.55660887 \dots$