Solve (1.05)(1.15)/(1+0.05)+(1.05)(1.15)^2+29.16/(1+0.05)^2

$$\frac { ( 1.05 ) ( 1.15 ) } { ( 1 + 0.05 ) } + \frac { ( 1.05 ) ( 1.15 ) ^ { 2 } + 29.16 } { ( 1 + 0.05 ) ^ { 2 } }$$

Evaluate

$$\frac{21211}{735}\approx 28.858503401$$

Solution Steps

Multiply 1.05 and 1.15 to get 1.2075.

$$\frac{1.2075}{1+0.05}+\frac{1.05\times 1.15^{2}+29.16}{\left(1+0.05\right)^{2}}$$

Add 1 and 0.05 to get 1.05.

$$\frac{1.2075}{1.05}+\frac{1.05\times 1.15^{2}+29.16}{\left(1+0.05\right)^{2}}$$

Expand \frac{1.2075}{1.05} by multiplying both numerator and the denominator by 10000.

$$\frac{12075}{10500}+\frac{1.05\times 1.15^{2}+29.16}{\left(1+0.05\right)^{2}}$$

Reduce the fraction \frac{12075}{10500} to lowest terms by extracting and canceling out 525.

$$\frac{23}{20}+\frac{1.05\times 1.15^{2}+29.16}{\left(1+0.05\right)^{2}}$$

Calculate 1.15 to the power of 2 and get 1.3225.

$$\frac{23}{20}+\frac{1.05\times 1.3225+29.16}{\left(1+0.05\right)^{2}}$$

Multiply 1.05 and 1.3225 to get 1.388625.

$$\frac{23}{20}+\frac{1.388625+29.16}{\left(1+0.05\right)^{2}}$$

Add 1.388625 and 29.16 to get 30.548625.

$$\frac{23}{20}+\frac{30.548625}{\left(1+0.05\right)^{2}}$$

Add 1 and 0.05 to get 1.05.

$$\frac{23}{20}+\frac{30.548625}{1.05^{2}}$$

Calculate 1.05 to the power of 2 and get 1.1025.

$$\frac{23}{20}+\frac{30.548625}{1.1025}$$

Expand \frac{30.548625}{1.1025} by multiplying both numerator and the denominator by 1000000.

$$\frac{23}{20}+\frac{30548625}{1102500}$$

Reduce the fraction \frac{30548625}{1102500} to lowest terms by extracting and canceling out 375.

$$\frac{23}{20}+\frac{81463}{2940}$$

Add \frac{23}{20} and \frac{81463}{2940} to get \frac{21211}{735}.

$$\frac{21211}{735}$$

Factor

$$\frac{21211}{3 \cdot 5 \cdot 7 ^ {2}} = 28\frac{631}{735} = 28.858503401360544$$