Finite Math Examples

$(3600 \cdot ({1.03}^{n} - 1)) = 1762.24045614$

Step 1

Divide each term in $3600 \cdot ({1.03}^{n} - 1) = 1762.24045614$ by $3600$ and simplify.

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Step 1.1

Divide each term in $3600 \cdot ({1.03}^{n} - 1) = 1762.24045614$ by $3600$ .

$\frac{3600 \cdot ({1.03}^{n} - 1)}{3600} = \frac{1762.24045614}{3600}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $3600$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{3600 \cdot ({1.03}^{n} - 1)}{3600} = \frac{1762.24045614}{3600}$

Step 1.2.1.2

Divide ${1.03}^{n} - 1$ by $1$ .

${1.03}^{n} - 1 = \frac{1762.24045614}{3600}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $1762.24045614$ by $3600$ .

${1.03}^{n} - 1 = 0.48951123$

Step 2

Move all terms not containing $n$ to the right side of the equation.

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Step 2.1

Add $1$ to both sides of the equation.

${1.03}^{n} = 0.48951123 + 1$

Step 2.2

Add $0.48951123$ and $1$ .

${1.03}^{n} = 1.48951123$

Step 3

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

$\ln ({1.03}^{n}) = \ln (1.48951123)$

Step 4

Expand $\ln ({1.03}^{n})$ by moving $n$ outside the logarithm.

$n \ln (1.03) = \ln (1.48951123)$

Step 5

Divide each term in $n \ln (1.03) = \ln (1.48951123)$ by $\ln (1.03)$ and simplify.

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Step 5.1

Divide each term in $n \ln (1.03) = \ln (1.48951123)$ by $\ln (1.03)$ .

$\frac{n \ln (1.03)}{\ln (1.03)} = \frac{\ln (1.48951123)}{\ln (1.03)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $\ln (1.03)$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{n \ln (1.03)}{\ln (1.03)} = \frac{\ln (1.48951123)}{\ln (1.03)}$

Step 5.2.1.2

Divide $n$ by $1$ .

$n = \frac{\ln (1.48951123)}{\ln (1.03)}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$n = \frac{\ln (1.48951123)}{\ln (1.03)}$

Decimal Form:

$n = 13.47984382 \dots$