Basic Math Examples

$1381.02 = 1250 {(1 + \frac{r}{12})}^{1.33 \cdot 12}$

Step 1

Rewrite the equation as $1250 {(1 + \frac{r}{12})}^{1.33 \cdot 12} = 1381.02$ .

$1250 {(1 + \frac{r}{12})}^{1.33 \cdot 12} = 1381.02$

Step 2

Multiply $1.33$ by $12$ .

$1250 {(1 + \frac{r}{12})}^{15.96} = 1381.02$

Step 3

Divide each term in $1250 {(1 + \frac{r}{12})}^{15.96} = 1381.02$ by $1250$ and simplify.

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Step 3.1

Divide each term in $1250 {(1 + \frac{r}{12})}^{15.96} = 1381.02$ by $1250$ .

$\frac{1250 {(1 + \frac{r}{12})}^{15.96}}{1250} = \frac{1381.02}{1250}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $1250$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{1250 {(1 + \frac{r}{12})}^{15.96}}{1250} = \frac{1381.02}{1250}$

Step 3.2.1.2

Divide ${(1 + \frac{r}{12})}^{15.96}$ by $1$ .

${(1 + \frac{r}{12})}^{15.96} = \frac{1381.02}{1250}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $1381.02$ by $1250$ .

${(1 + \frac{r}{12})}^{15.96} = 1.104816$

Step 4

Convert the decimal exponent to a fractional exponent.

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Step 4.1

Convert the decimal number to a fraction by placing the decimal number over a power of ten. Since there are $2$ numbers to the right of the decimal point, place the decimal number over $10^{2}$ $(100)$ . Next, add the whole number to the left of the decimal.

${(1 + \frac{r}{12})}^{15 \frac{96}{100}} = 1.104816$

Step 4.2

Reduce the fractional part of the mixed number.

${(1 + \frac{r}{12})}^{15 \frac{24}{25}} = 1.104816$

Step 4.3

Convert $15 \frac{24}{25}$ to an improper fraction.

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Step 4.3.1

A mixed number is an addition of its whole and fractional parts.

${(1 + \frac{r}{12})}^{15 + \frac{24}{25}} = 1.104816$

Step 4.3.2

Add $15$ and $\frac{24}{25}$ .

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Step 4.3.2.1

To write $15$ as a fraction with a common denominator, multiply by $\frac{25}{25}$ .

${(1 + \frac{r}{12})}^{15 \cdot \frac{25}{25} + \frac{24}{25}} = 1.104816$

Step 4.3.2.2

Combine $15$ and $\frac{25}{25}$ .

${(1 + \frac{r}{12})}^{\frac{15 \cdot 25}{25} + \frac{24}{25}} = 1.104816$

Step 4.3.2.3

Combine the numerators over the common denominator.

${(1 + \frac{r}{12})}^{\frac{15 \cdot 25 + 24}{25}} = 1.104816$

Step 4.3.2.4

Simplify the numerator.

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Step 4.3.2.4.1

Multiply $15$ by $25$ .

${(1 + \frac{r}{12})}^{\frac{375 + 24}{25}} = 1.104816$

Step 4.3.2.4.2

Add $375$ and $24$ .

${(1 + \frac{r}{12})}^{\frac{399}{25}} = 1.104816$

Step 5

Raise each side of the equation to the power of $\frac{1}{15.96}$ to eliminate the fractional exponent on the left side.

${({(1 + \frac{r}{12})}^{\frac{399}{25}})}^{\frac{1}{15.96}} = {1.104816}^{\frac{1}{15.96}}$

Step 6

Simplify the exponent.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify ${({(1 + \frac{r}{12})}^{\frac{399}{25}})}^{\frac{1}{15.96}}$ .

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Step 6.1.1.1

Multiply the exponents in ${({(1 + \frac{r}{12})}^{\frac{399}{25}})}^{\frac{1}{15.96}}$ .

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Step 6.1.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(1 + \frac{r}{12})}^{\frac{399}{25} \cdot \frac{1}{15.96}} = {1.104816}^{\frac{1}{15.96}}$

Step 6.1.1.1.2

Cancel the common factor of $15.96$ .

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Step 6.1.1.1.2.1

Factor $15.96$ out of $399$ .

${(1 + \frac{r}{12})}^{\frac{15.96 (25)}{25} \cdot \frac{1}{15.96}} = {1.104816}^{\frac{1}{15.96}}$

Step 6.1.1.1.2.2

Cancel the common factor.

${(1 + \frac{r}{12})}^{\frac{15.96 \cdot 25}{25} \cdot \frac{1}{15.96}} = {1.104816}^{\frac{1}{15.96}}$

Step 6.1.1.1.2.3

Rewrite the expression.

${(1 + \frac{r}{12})}^{\frac{25}{25}} = {1.104816}^{\frac{1}{15.96}}$

Step 6.1.1.1.3

Divide $25$ by $25$ .

${(1 + \frac{r}{12})}^{1} = {1.104816}^{\frac{1}{15.96}}$

Step 6.1.1.2

Simplify.

$1 + \frac{r}{12} = {1.104816}^{\frac{1}{15.96}}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify ${1.104816}^{\frac{1}{15.96}}$ .

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Step 6.2.1.1

Divide $1$ by $15.96$ .

$1 + \frac{r}{12} = {1.104816}^{0.06265664}$

Step 6.2.1.2

Raise $1.104816$ to the power of $0.06265664$ .

$1 + \frac{r}{12} = 1.00626508$

Step 7

Solve for $r$ .

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Step 7.1

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

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Step 7.1.1

Subtract $1$ from both sides of the equation.

$\frac{r}{12} = 1.00626508 - 1$

Step 7.1.2

Subtract $1$ from $1.00626508$ .

$\frac{r}{12} = 0.00626508$

Step 7.2

Multiply both sides of the equation by $12$ .

$12 \frac{r}{12} = 12 \cdot 0.00626508$

Step 7.3

Simplify both sides of the equation.

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Step 7.3.1

Simplify the left side.

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Step 7.3.1.1

Cancel the common factor of $12$ .

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Step 7.3.1.1.1

Cancel the common factor.

$12 \frac{r}{12} = 12 \cdot 0.00626508$

Step 7.3.1.1.2

Rewrite the expression.

$r = 12 \cdot 0.00626508$

Step 7.3.2

Simplify the right side.

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Step 7.3.2.1

Multiply $12$ by $0.00626508$ .

$r = 0.07518099$