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

$0.00626508$ .

$r = 0.07518099$