Solve 6000[frac{(1+0.011)^{5}-1}{0.011(1+0.011)^{5}}]+1100[(1+0.1011)^5-0.011^45-1/(0.01)^2(1+0.011)^5]

$$6000 [ \frac { ( 1 + 0.011 ) ^ { 5 } - 1 } { 0.011 ( 1 + 0.011 ) ^ { 5 } } ] + 1100 [ \frac { ( 1 + 0.1011 ) ^ { 5 } - 0.011 ^ { 4 } 5 - 1 } { ( 0.01 ) ^ { 2 } ( 1 + 0.011 ) ^ { 5 } } ]$$

Evaluate

$$\frac{6835031878107541765610}{1056223383366051}\approx 6471199.166529674$$

Solution Steps

Add 1 and 0.011 to get 1.011.

$$6000\times \frac{1.011^{5}-1}{0.011\left(1+0.011\right)^{5}}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Calculate 1.011 to the power of 5 and get 1.056223383366051.

$$6000\times \frac{1.056223383366051-1}{0.011\left(1+0.011\right)^{5}}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Subtract 1 from 1.056223383366051 to get 0.056223383366051.

$$6000\times \frac{0.056223383366051}{0.011\left(1+0.011\right)^{5}}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Add 1 and 0.011 to get 1.011.

$$6000\times \frac{0.056223383366051}{0.011\times 1.011^{5}}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Calculate 1.011 to the power of 5 and get 1.056223383366051.

$$6000\times \frac{0.056223383366051}{0.011\times 1.056223383366051}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Multiply 0.011 and 1.056223383366051 to get 0.011618457217026561.

$$6000\times \frac{0.056223383366051}{0.011618457217026561}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Expand \frac{0.056223383366051}{0.011618457217026561} by multiplying both numerator and the denominator by 1000000000000000000.

$$6000\times \frac{56223383366051000}{11618457217026561}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Reduce the fraction \frac{56223383366051000}{11618457217026561} to lowest terms by extracting and canceling out 11.

$$6000\times \frac{5111216669641000}{1056223383366051}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Multiply 6000 and \frac{5111216669641000}{1056223383366051} to get \frac{10222433339282000000}{352074461122017}.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{\left(1+0.1011\right)^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Add 1 and 0.1011 to get 1.1011.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{1.1011^{5}-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Calculate 1.1011 to the power of 5 and get 1.61857867121315416051.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{1.61857867121315416051-0.011^{4}\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Calculate 0.011 to the power of 4 and get 0.000000014641.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{1.61857867121315416051-0.000000014641\times 5-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Multiply 0.000000014641 and 5 to get 0.000000073205.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{1.61857867121315416051-0.000000073205-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Subtract 0.000000073205 from 1.61857867121315416051 to get 1.61857859800815416051.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{1.61857859800815416051-1}{0.01^{2}\left(1+0.011\right)^{5}}$$

Subtract 1 from 1.61857859800815416051 to get 0.61857859800815416051.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{0.61857859800815416051}{0.01^{2}\left(1+0.011\right)^{5}}$$

Calculate 0.01 to the power of 2 and get 0.0001.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{0.61857859800815416051}{0.0001\left(1+0.011\right)^{5}}$$

Add 1 and 0.011 to get 1.011.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{0.61857859800815416051}{0.0001\times 1.011^{5}}$$

Calculate 1.011 to the power of 5 and get 1.056223383366051.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{0.61857859800815416051}{0.0001\times 1.056223383366051}$$

Multiply 0.0001 and 1.056223383366051 to get 0.0001056223383366051.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{0.61857859800815416051}{0.0001056223383366051}$$

Expand \frac{0.61857859800815416051}{0.0001056223383366051} by multiplying both numerator and the denominator by 100000000000000000000.

$$\frac{10222433339282000000}{352074461122017}+1100\times \frac{61857859800815416051}{10562233833660510}$$

Multiply 1100 and \frac{61857859800815416051}{10562233833660510} to get \frac{6804364578089695765610}{1056223383366051}.

$$\frac{10222433339282000000}{352074461122017}+\frac{6804364578089695765610}{1056223383366051}$$

Add \frac{10222433339282000000}{352074461122017} and \frac{6804364578089695765610}{1056223383366051} to get \frac{6835031878107541765610}{1056223383366051}.

$$\frac{6835031878107541765610}{1056223383366051}$$

Factor

$$\frac{2 \cdot 5 \cdot 47 \cdot 14542621017250088863}{3 ^ {5} \cdot 337 ^ {5}} = 6471199\frac{175892535933763}{1056223383366051} = 6471199.166529674$$