Basic Math Examples

$3000 = \frac{y}{1 + 0.07} + \frac{y}{{(1 + 0.07)}^{2}} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}}$

Step 1

Rewrite the equation as $\frac{y}{1 + 0.07} + \frac{y}{{(1 + 0.07)}^{2}} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$ .

$\frac{y}{1 + 0.07} + \frac{y}{{(1 + 0.07)}^{2}} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$

Step 2

Simplify $\frac{y}{1 + 0.07} + \frac{y}{{(1 + 0.07)}^{2}} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}}$ .

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Step 2.1

Find the common denominator.

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Step 2.1.1

Add $1$ and $0.07$ .

$\frac{y}{1.07} + \frac{y}{{(1 + 0.07)}^{2}} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$

Step 2.1.2

Multiply $\frac{y}{1.07}$ by $\frac{{(1 + 0.07)}^{4}}{{(1 + 0.07)}^{4}}$ .

$\frac{y}{1.07} \cdot \frac{{(1 + 0.07)}^{4}}{{(1 + 0.07)}^{4}} + \frac{y}{{(1 + 0.07)}^{2}} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$

Step 2.1.3

Multiply $\frac{y}{1.07}$ by $\frac{{(1 + 0.07)}^{4}}{{(1 + 0.07)}^{4}}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y}{{(1 + 0.07)}^{2}} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$

Step 2.1.4

Multiply $\frac{y}{{(1 + 0.07)}^{2}}$ by $\frac{1.225043}{1.225043}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y}{{(1 + 0.07)}^{2}} \cdot \frac{1.225043}{1.225043} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$

Step 2.1.5

Multiply $\frac{y}{{(1 + 0.07)}^{2}}$ by $\frac{1.225043}{1.225043}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{{(1 + 0.07)}^{2} \cdot 1.225043} + \frac{y}{{(1 + 0.07)}^{3}} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$

Step 2.1.6

Multiply $\frac{y}{{(1 + 0.07)}^{3}}$ by $\frac{1.1449}{1.1449}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{{(1 + 0.07)}^{2} \cdot 1.225043} + \frac{y}{{(1 + 0.07)}^{3}} \cdot \frac{1.1449}{1.1449} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$

Step 2.1.7

Multiply $\frac{y}{{(1 + 0.07)}^{3}}$ by $\frac{1.1449}{1.1449}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{{(1 + 0.07)}^{2} \cdot 1.225043} + \frac{y \cdot 1.1449}{{(1 + 0.07)}^{3} \cdot 1.1449} + \frac{y}{{(1 + 0.07)}^{4}} = 3000$

Step 2.1.8

Multiply $\frac{y}{{(1 + 0.07)}^{4}}$ by $\frac{1.07}{1.07}$ .

Step 2.1.9

Multiply $\frac{y}{{(1 + 0.07)}^{4}}$ by $\frac{1.07}{1.07}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{{(1 + 0.07)}^{2} \cdot 1.225043} + \frac{y \cdot 1.1449}{{(1 + 0.07)}^{3} \cdot 1.1449} + \frac{y \cdot 1.07}{{(1 + 0.07)}^{4} \cdot 1.07} = 3000$

Step 2.1.10

Reorder the factors of ${(1 + 0.07)}^{2} \cdot 1.225043$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{1.225043 {(1 + 0.07)}^{2}} + \frac{y \cdot 1.1449}{{(1 + 0.07)}^{3} \cdot 1.1449} + \frac{y \cdot 1.07}{{(1 + 0.07)}^{4} \cdot 1.07} = 3000$

Step 2.1.11

Multiply $1.225043$ by ${(1 + 0.07)}^{2}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{1.40255173} + \frac{y \cdot 1.1449}{{(1 + 0.07)}^{3} \cdot 1.1449} + \frac{y \cdot 1.07}{{(1 + 0.07)}^{4} \cdot 1.07} = 3000$

Step 2.1.12

Reorder the factors of ${(1 + 0.07)}^{3} \cdot 1.1449$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{1.40255173} + \frac{y \cdot 1.1449}{1.1449 {(1 + 0.07)}^{3}} + \frac{y \cdot 1.07}{{(1 + 0.07)}^{4} \cdot 1.07} = 3000$

Step 2.1.13

Multiply $1.1449$ by ${(1 + 0.07)}^{3}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{1.40255173} + \frac{y \cdot 1.1449}{1.40255173} + \frac{y \cdot 1.07}{{(1 + 0.07)}^{4} \cdot 1.07} = 3000$

Step 2.1.14

Reorder the factors of ${(1 + 0.07)}^{4} \cdot 1.07$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{1.40255173} + \frac{y \cdot 1.1449}{1.40255173} + \frac{y \cdot 1.07}{1.07 {(1 + 0.07)}^{4}} = 3000$

Step 2.1.15

Multiply $1.07$ by ${(1 + 0.07)}^{4}$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043}{1.40255173} + \frac{y \cdot 1.1449}{1.40255173} + \frac{y \cdot 1.07}{1.40255173} = 3000$

Step 2.2

Combine the numerators over the common denominator.

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{y \cdot 1.225043 + y \cdot 1.1449 + y \cdot 1.07}{1.40255173} = 3000$

Step 2.3

Simplify each term.

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Step 2.3.1

Move $1.225043$ to the left of $y$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{1.225043 \cdot y + y \cdot 1.1449 + y \cdot 1.07}{1.40255173} = 3000$

Step 2.3.2

Move $1.1449$ to the left of $y$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{1.225043 y + 1.1449 \cdot y + y \cdot 1.07}{1.40255173} = 3000$

Step 2.3.3

Move $1.07$ to the left of $y$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{1.225043 y + 1.1449 y + 1.07 y}{1.40255173} = 3000$

Step 2.4

Simplify by adding terms.

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Step 2.4.1

Add $1.225043 y$ and $1.1449 y$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{2.369943 y + 1.07 y}{1.40255173} = 3000$

Step 2.4.2

Add $2.369943 y$ and $1.07 y$ .

$\frac{y {(1 + 0.07)}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.4.3

Add $1$ and $0.07$ .

$\frac{y \cdot {1.07}^{4}}{1.07 {(1 + 0.07)}^{4}} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5

Simplify each term.

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Step 2.5.1

Cancel the common factor of ${1.07}^{4}$ and $1.07$ .

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Step 2.5.1.1

Factor $1.07$ out of $y \cdot {1.07}^{4}$ .

$\frac{1.07 (y \cdot {1.07}^{3})}{1.07 {(1 + 0.07)}^{4}} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.1.2

Cancel the common factors.

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Step 2.5.1.2.1

Factor $1.07$ out of $1.07 {(1 + 0.07)}^{4}$ .

$\frac{1.07 (y \cdot {1.07}^{3})}{1.07 ({(1 + 0.07)}^{4})} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.1.2.2

Cancel the common factor.

$\frac{1.07 (y \cdot {1.07}^{3})}{1.07 {(1 + 0.07)}^{4}} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.1.2.3

Rewrite the expression.

$\frac{y \cdot {1.07}^{3}}{{(1 + 0.07)}^{4}} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.2

Raise $1.07$ to the power of $3$ .

$\frac{y \cdot 1.225043}{{(1 + 0.07)}^{4}} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.3

Simplify the denominator.

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Step 2.5.3.1

Add $1$ and $0.07$ .

$\frac{y \cdot 1.225043}{{1.07}^{4}} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.3.2

Raise $1.07$ to the power of $4$ .

$\frac{y \cdot 1.225043}{1.31079601} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.4

Move $1.225043$ to the left of $y$ .

$\frac{1.225043 \cdot y}{1.31079601} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.5

Factor $1.225043$ out of $1.225043 \cdot y$ .

$\frac{1.225043 (y)}{1.31079601} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.6

Factor $1.31079601$ out of $1.31079601$ .

$\frac{1.225043 (y)}{1.31079601 (1)} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.7

Separate fractions.

$\frac{1.225043}{1.31079601} \cdot \frac{y}{1} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.8

Divide $1.225043$ by $1.31079601$ .

$0.93457943 \frac{y}{1} + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.9

Divide $y$ by $1$ .

$0.93457943 y + \frac{3.439943 y}{1.40255173} = 3000$

Step 2.5.10

Factor $3.439943$ out of $3.439943 y$ .

$0.93457943 y + \frac{3.439943 (y)}{1.40255173} = 3000$

Step 2.5.11

Factor $1.40255173$ out of $1.40255173$ .

$0.93457943 y + \frac{3.439943 (y)}{1.40255173 (1)} = 3000$

Step 2.5.12

Separate fractions.

$0.93457943 y + \frac{3.439943}{1.40255173} \cdot \frac{y}{1} = 3000$

Step 2.5.13

Divide $3.439943$ by $1.40255173$ .

$0.93457943 y + 2.45263181 \frac{y}{1} = 3000$

Step 2.5.14

Divide $y$ by $1$ .

$0.93457943 y + 2.45263181 y = 3000$

Step 2.6

Add $0.93457943 y$ and $2.45263181 y$ .

$3.38721125 y = 3000$

Step 3

Divide each term in $3.38721125 y = 3000$ by $3.38721125$ and simplify.

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Step 3.1

Divide each term in $3.38721125 y = 3000$ by $3.38721125$ .

$\frac{3.38721125 y}{3.38721125} = \frac{3000}{3.38721125}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3.38721125$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3.38721125 y}{3.38721125} = \frac{3000}{3.38721125}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{3000}{3.38721125}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $3000$ by $3.38721125$ .

$y = 885.68435$