Solve 20(1+0.03)^11/(1+0.05)^11

$$\frac { 20 ( 1 + 0.03 ) ^ { 11 } } { ( 1 + 0.05 ) ^ { 11 } }$$

Evaluate

$$\frac{55369354828977823124188}{3420678716232626953125}\approx 16.186657509$$

Solution Steps

Add 1 and 0.03 to get 1.03.

$$\frac{20\times 1.03^{11}}{\left(1+0.05\right)^{11}}$$

Calculate 1.03 to the power of 11 and get 1.3842338707244455781047.

$$\frac{20\times 1.3842338707244455781047}{\left(1+0.05\right)^{11}}$$

Multiply 20 and 1.3842338707244455781047 to get 27.684677414488911562094.

$$\frac{27.684677414488911562094}{\left(1+0.05\right)^{11}}$$

Add 1 and 0.05 to get 1.05.

$$\frac{27.684677414488911562094}{1.05^{11}}$$

Calculate 1.05 to the power of 11 and get 1.7103393581163134765625.

$$\frac{27.684677414488911562094}{1.7103393581163134765625}$$

Expand \frac{27.684677414488911562094}{1.7103393581163134765625} by multiplying both numerator and the denominator by 10000000000000000000000.

$$\frac{276846774144889115620940}{17103393581163134765625}$$

Reduce the fraction \frac{276846774144889115620940}{17103393581163134765625} to lowest terms by extracting and canceling out 5.

$$\frac{55369354828977823124188}{3420678716232626953125}$$

Factor

$$\frac{2 ^ {2} \cdot 103 ^ {11}}{3 ^ {11} \cdot 5 ^ {10} \cdot 7 ^ {11}} = 16\frac{6.384953692557861 \times 10^{20}}{3.420678716232627 \times 10^{21}} = 16.18665750929073$$