Solve 2011.45+2011.45+2011.45+2011.45+2011.45/{left(frac{1{1+0.085}right)}^{1}+{left(1/1+0.085right)}^2+{left(1/1+0.085right)}^3+{left(1/1+0.085right)}^4+{left(frac{1}{1+0.085}right)}^5}

$$\frac{ 2011.45+2011.45+2011.45+2011.45+2011.45 }{ { \left( \frac{ 1 }{ 1+0.085 } \right) }^{ 1 } + { \left( \frac{ 1 }{ 1+0.085 } \right) }^{ 2 } + { \left( \frac{ 1 }{ 1+0.085 } \right) }^{ 3 } + { \left( \frac{ 1 }{ 1+0.085 } \right) }^{ 4 } + { \left( \frac{ 1 }{ 1+0.085 } \right) }^{ 5 } }$$

Evaluate

$$\frac{19356993596536253}{7584477216800}\approx 2552.185607949$$

Solution Steps

Add 2011.45 and 2011.45 to get 4022.9.

$$\frac{4022.9+2011.45+2011.45+2011.45}{\left(\frac{1}{1+0.085}\right)^{1}+\left(\frac{1}{1+0.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add 4022.9 and 2011.45 to get 6034.35.

$$\frac{6034.35+2011.45+2011.45}{\left(\frac{1}{1+0.085}\right)^{1}+\left(\frac{1}{1+0.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add 6034.35 and 2011.45 to get 8045.8.

$$\frac{8045.8+2011.45}{\left(\frac{1}{1+0.085}\right)^{1}+\left(\frac{1}{1+0.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add 8045.8 and 2011.45 to get 10057.25.

$$\frac{10057.25}{\left(\frac{1}{1+0.085}\right)^{1}+\left(\frac{1}{1+0.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add 1 and 0.085 to get 1.085.

$$\frac{10057.25}{\left(\frac{1}{1.085}\right)^{1}+\left(\frac{1}{1+0.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Expand \frac{1}{1.085} by multiplying both numerator and the denominator by 1000.

$$\frac{10057.25}{\left(\frac{1000}{1085}\right)^{1}+\left(\frac{1}{1+0.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Reduce the fraction \frac{1000}{1085} to lowest terms by extracting and canceling out 5.

$$\frac{10057.25}{\left(\frac{200}{217}\right)^{1}+\left(\frac{1}{1+0.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Calculate \frac{200}{217} to the power of 1 and get \frac{200}{217}.

$$\frac{10057.25}{\frac{200}{217}+\left(\frac{1}{1+0.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add 1 and 0.085 to get 1.085.

$$\frac{10057.25}{\frac{200}{217}+\left(\frac{1}{1.085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Expand \frac{1}{1.085} by multiplying both numerator and the denominator by 1000.

$$\frac{10057.25}{\frac{200}{217}+\left(\frac{1000}{1085}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Reduce the fraction \frac{1000}{1085} to lowest terms by extracting and canceling out 5.

$$\frac{10057.25}{\frac{200}{217}+\left(\frac{200}{217}\right)^{2}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Calculate \frac{200}{217} to the power of 2 and get \frac{40000}{47089}.

$$\frac{10057.25}{\frac{200}{217}+\frac{40000}{47089}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add \frac{200}{217} and \frac{40000}{47089} to get \frac{83400}{47089}.

$$\frac{10057.25}{\frac{83400}{47089}+\left(\frac{1}{1+0.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add 1 and 0.085 to get 1.085.

$$\frac{10057.25}{\frac{83400}{47089}+\left(\frac{1}{1.085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Expand \frac{1}{1.085} by multiplying both numerator and the denominator by 1000.

$$\frac{10057.25}{\frac{83400}{47089}+\left(\frac{1000}{1085}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Reduce the fraction \frac{1000}{1085} to lowest terms by extracting and canceling out 5.

$$\frac{10057.25}{\frac{83400}{47089}+\left(\frac{200}{217}\right)^{3}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Calculate \frac{200}{217} to the power of 3 and get \frac{8000000}{10218313}.

$$\frac{10057.25}{\frac{83400}{47089}+\frac{8000000}{10218313}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add \frac{83400}{47089} and \frac{8000000}{10218313} to get \frac{26097800}{10218313}.

$$\frac{10057.25}{\frac{26097800}{10218313}+\left(\frac{1}{1+0.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add 1 and 0.085 to get 1.085.

$$\frac{10057.25}{\frac{26097800}{10218313}+\left(\frac{1}{1.085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Expand \frac{1}{1.085} by multiplying both numerator and the denominator by 1000.

$$\frac{10057.25}{\frac{26097800}{10218313}+\left(\frac{1000}{1085}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Reduce the fraction \frac{1000}{1085} to lowest terms by extracting and canceling out 5.

$$\frac{10057.25}{\frac{26097800}{10218313}+\left(\frac{200}{217}\right)^{4}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Calculate \frac{200}{217} to the power of 4 and get \frac{1600000000}{2217373921}.

$$\frac{10057.25}{\frac{26097800}{10218313}+\frac{1600000000}{2217373921}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add \frac{26097800}{10218313} and \frac{1600000000}{2217373921} to get \frac{7263222600}{2217373921}.

$$\frac{10057.25}{\frac{7263222600}{2217373921}+\left(\frac{1}{1+0.085}\right)^{5}}$$

Add 1 and 0.085 to get 1.085.

$$\frac{10057.25}{\frac{7263222600}{2217373921}+\left(\frac{1}{1.085}\right)^{5}}$$

Expand \frac{1}{1.085} by multiplying both numerator and the denominator by 1000.

$$\frac{10057.25}{\frac{7263222600}{2217373921}+\left(\frac{1000}{1085}\right)^{5}}$$

Reduce the fraction \frac{1000}{1085} to lowest terms by extracting and canceling out 5.

$$\frac{10057.25}{\frac{7263222600}{2217373921}+\left(\frac{200}{217}\right)^{5}}$$

Calculate \frac{200}{217} to the power of 5 and get \frac{320000000000}{481170140857}.

$$\frac{10057.25}{\frac{7263222600}{2217373921}+\frac{320000000000}{481170140857}}$$

Add \frac{7263222600}{2217373921} and \frac{320000000000}{481170140857} to get \frac{1896119304200}{481170140857}.

$$\frac{10057.25}{\frac{1896119304200}{481170140857}}$$

Divide 10057.25 by \frac{1896119304200}{481170140857} by multiplying 10057.25 by the reciprocal of \frac{1896119304200}{481170140857}.

$$10057.25\times \frac{481170140857}{1896119304200}$$

Multiply 10057.25 and \frac{481170140857}{1896119304200} to get \frac{19356993596536253}{7584477216800}.

$$\frac{19356993596536253}{7584477216800}$$

Factor

$$\frac{821 \cdot 7 ^ {7} \cdot 31 ^ {5}}{11 \cdot 191 \cdot 271 \cdot 16651 \cdot 2 ^ {5} \cdot 5 ^ {2}} = 2552\frac{1407739262652}{7584477216800} = 2552.1856079492904$$