Solve 27.5+27.5/(1+12%)^4+27.5/(1+12%)^8

$$27.5 + \frac { 27.5 } { ( 1 + 12 \% ) ^ { 4 } } + \frac { 27.5 } { ( 1 + 12 \% ) ^ { 8 } }$$

Evaluate

$$\frac{42376943892855}{755603996672}\approx 56.083535926$$

Solution Steps

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

$$27.5+\frac{27.5}{\left(1+\frac{3}{25}\right)^{4}}+\frac{27.5}{\left(1+\frac{12}{100}\right)^{8}}$$

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

$$27.5+\frac{27.5}{\left(\frac{28}{25}\right)^{4}}+\frac{27.5}{\left(1+\frac{12}{100}\right)^{8}}$$

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

$$27.5+\frac{27.5}{\frac{614656}{390625}}+\frac{27.5}{\left(1+\frac{12}{100}\right)^{8}}$$

Divide 27.5 by \frac{614656}{390625} by multiplying 27.5 by the reciprocal of \frac{614656}{390625}.

$$27.5+27.5\times \frac{390625}{614656}+\frac{27.5}{\left(1+\frac{12}{100}\right)^{8}}$$

Multiply 27.5 and \frac{390625}{614656} to get \frac{21484375}{1229312}.

$$27.5+\frac{21484375}{1229312}+\frac{27.5}{\left(1+\frac{12}{100}\right)^{8}}$$

Add 27.5 and \frac{21484375}{1229312} to get \frac{55290455}{1229312}.

$$\frac{55290455}{1229312}+\frac{27.5}{\left(1+\frac{12}{100}\right)^{8}}$$

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

$$\frac{55290455}{1229312}+\frac{27.5}{\left(1+\frac{3}{25}\right)^{8}}$$

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

$$\frac{55290455}{1229312}+\frac{27.5}{\left(\frac{28}{25}\right)^{8}}$$

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

$$\frac{55290455}{1229312}+\frac{27.5}{\frac{377801998336}{152587890625}}$$

Divide 27.5 by \frac{377801998336}{152587890625} by multiplying 27.5 by the reciprocal of \frac{377801998336}{152587890625}.

$$\frac{55290455}{1229312}+27.5\times \frac{152587890625}{377801998336}$$

Multiply 27.5 and \frac{152587890625}{377801998336} to get \frac{8392333984375}{755603996672}.

$$\frac{55290455}{1229312}+\frac{8392333984375}{755603996672}$$

Add \frac{55290455}{1229312} and \frac{8392333984375}{755603996672} to get \frac{42376943892855}{755603996672}.

$$\frac{42376943892855}{755603996672}$$

Factor

$$\frac{3 \cdot 5 \cdot 11 \cdot 19 \cdot 37 \cdot 709 \cdot 3049 \cdot 13 ^ {2}}{2 ^ {17} \cdot 7 ^ {8}} = 56\frac{63120079223}{755603996672} = 56.08353592556552$$