Solve 275+275/(1+12%)^4+275/(1+12%)^8

$$275 + \frac { 275 } { ( 1 + 12 \% ) ^ { 4 } } + \frac { 275 } { ( 1 + 12 \% ) ^ { 8 } }$$

Evaluate

$$\frac{211884719464275}{377801998336}\approx 560.835359256$$

Solution Steps

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$275+\frac{275}{\left(1+\frac{3}{25}\right)^{4}}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Add 1 and \frac{3}{25} to get \frac{28}{25}.

$$275+\frac{275}{\left(\frac{28}{25}\right)^{4}}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Calculate \frac{28}{25} to the power of 4 and get \frac{614656}{390625}.

$$275+\frac{275}{\frac{614656}{390625}}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Divide 275 by \frac{614656}{390625} by multiplying 275 by the reciprocal of \frac{614656}{390625}.

$$275+275\times \frac{390625}{614656}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Multiply 275 and \frac{390625}{614656} to get \frac{107421875}{614656}.

$$275+\frac{107421875}{614656}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Add 275 and \frac{107421875}{614656} to get \frac{276452275}{614656}.

$$\frac{276452275}{614656}+\frac{275}{\left(1+\frac{12}{100}\right)^{8}}$$

Reduce the fraction \frac{12}{100} to lowest terms by extracting and canceling out 4.

$$\frac{276452275}{614656}+\frac{275}{\left(1+\frac{3}{25}\right)^{8}}$$

Add 1 and \frac{3}{25} to get \frac{28}{25}.

$$\frac{276452275}{614656}+\frac{275}{\left(\frac{28}{25}\right)^{8}}$$

Calculate \frac{28}{25} to the power of 8 and get \frac{377801998336}{152587890625}.

$$\frac{276452275}{614656}+\frac{275}{\frac{377801998336}{152587890625}}$$

Divide 275 by \frac{377801998336}{152587890625} by multiplying 275 by the reciprocal of \frac{377801998336}{152587890625}.

$$\frac{276452275}{614656}+275\times \frac{152587890625}{377801998336}$$

Multiply 275 and \frac{152587890625}{377801998336} to get \frac{41961669921875}{377801998336}.

$$\frac{276452275}{614656}+\frac{41961669921875}{377801998336}$$

Add \frac{276452275}{614656} and \frac{41961669921875}{377801998336} to get \frac{211884719464275}{377801998336}.

$$\frac{211884719464275}{377801998336}$$

Factor

$$\frac{3 \cdot 5 ^ {2} \cdot 11 \cdot 13 ^ {2} \cdot 19 \cdot 37 \cdot 709 \cdot 3049}{2 ^ {16} \cdot 7 ^ {8}} = 560\frac{315600396115}{377801998336} = 560.8353592556551$$