Solve V=-1000+372.5/(1+10%)+372.5/(1+10%)^2+372.5/(1.110%)^3+372.5/(11+10%)^4+frac{612.5}{(1+10%)^5}

$$V = - 1000 + \frac { 372.5 } { ( 1 + 10 \% ) } + \frac { 372.5 } { ( 1 + 10 \% ) ^ { 2 } } + \frac { 372.5 } { ( 1.110 \% ) ^ { 3 } } + \frac { 372.5 } { ( 11 + 10 \% ) ^ { 4 } } + \frac { 612.5 } { ( 1 + 10 \% ) ^ { 5 } }$$

Solve for V

$$V = \frac{6659056878371212275475}{24448675760091} = 272368816\frac{8827326639472}{24448675760091} \approx 272368816.361055406$$

Steps for Solving Linear Equation

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$V=-1000+\frac{372.5}{1+\frac{1}{10}}+\frac{372.5}{\left(1+\frac{10}{100}\right)^{2}}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Add 1 and \frac{1}{10} to get \frac{11}{10}.

$$V=-1000+\frac{372.5}{\frac{11}{10}}+\frac{372.5}{\left(1+\frac{10}{100}\right)^{2}}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Divide 372.5 by \frac{11}{10} by multiplying 372.5 by the reciprocal of \frac{11}{10}.

$$V=-1000+372.5\times \frac{10}{11}+\frac{372.5}{\left(1+\frac{10}{100}\right)^{2}}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Multiply 372.5 and \frac{10}{11} to get \frac{3725}{11}.

$$V=-1000+\frac{3725}{11}+\frac{372.5}{\left(1+\frac{10}{100}\right)^{2}}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Add -1000 and \frac{3725}{11} to get -\frac{7275}{11}.

$$V=-\frac{7275}{11}+\frac{372.5}{\left(1+\frac{10}{100}\right)^{2}}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$V=-\frac{7275}{11}+\frac{372.5}{\left(1+\frac{1}{10}\right)^{2}}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Add 1 and \frac{1}{10} to get \frac{11}{10}.

$$V=-\frac{7275}{11}+\frac{372.5}{\left(\frac{11}{10}\right)^{2}}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Calculate \frac{11}{10} to the power of 2 and get \frac{121}{100}.

$$V=-\frac{7275}{11}+\frac{372.5}{\frac{121}{100}}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Divide 372.5 by \frac{121}{100} by multiplying 372.5 by the reciprocal of \frac{121}{100}.

$$V=-\frac{7275}{11}+372.5\times \frac{100}{121}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Multiply 372.5 and \frac{100}{121} to get \frac{37250}{121}.

$$V=-\frac{7275}{11}+\frac{37250}{121}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Add -\frac{7275}{11} and \frac{37250}{121} to get -\frac{42775}{121}.

$$V=-\frac{42775}{121}+\frac{372.5}{\left(\frac{1.11}{100}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Expand \frac{1.11}{100} by multiplying both numerator and the denominator by 100.

$$V=-\frac{42775}{121}+\frac{372.5}{\left(\frac{111}{10000}\right)^{3}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Calculate \frac{111}{10000} to the power of 3 and get \frac{1367631}{1000000000000}.

$$V=-\frac{42775}{121}+\frac{372.5}{\frac{1367631}{1000000000000}}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Divide 372.5 by \frac{1367631}{1000000000000} by multiplying 372.5 by the reciprocal of \frac{1367631}{1000000000000}.

$$V=-\frac{42775}{121}+372.5\times \frac{1000000000000}{1367631}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Multiply 372.5 and \frac{1000000000000}{1367631} to get \frac{372500000000000}{1367631}.

$$V=-\frac{42775}{121}+\frac{372500000000000}{1367631}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Add -\frac{42775}{121} and \frac{372500000000000}{1367631} to get \frac{45072441499583975}{165483351}.

$$V=\frac{45072441499583975}{165483351}+\frac{372.5}{\left(11+\frac{10}{100}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$V=\frac{45072441499583975}{165483351}+\frac{372.5}{\left(11+\frac{1}{10}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Add 11 and \frac{1}{10} to get \frac{111}{10}.

$$V=\frac{45072441499583975}{165483351}+\frac{372.5}{\left(\frac{111}{10}\right)^{4}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Calculate \frac{111}{10} to the power of 4 and get \frac{151807041}{10000}.

$$V=\frac{45072441499583975}{165483351}+\frac{372.5}{\frac{151807041}{10000}}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Divide 372.5 by \frac{151807041}{10000} by multiplying 372.5 by the reciprocal of \frac{151807041}{10000}.

$$V=\frac{45072441499583975}{165483351}+372.5\times \frac{10000}{151807041}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Multiply 372.5 and \frac{10000}{151807041} to get \frac{3725000}{151807041}.

$$V=\frac{45072441499583975}{165483351}+\frac{3725000}{151807041}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Add \frac{45072441499583975}{165483351} and \frac{3725000}{151807041} to get \frac{5003041006904546225}{18368651961}.

$$V=\frac{5003041006904546225}{18368651961}+\frac{612.5}{\left(1+\frac{10}{100}\right)^{5}}$$

Reduce the fraction \frac{10}{100} to lowest terms by extracting and canceling out 10.

$$V=\frac{5003041006904546225}{18368651961}+\frac{612.5}{\left(1+\frac{1}{10}\right)^{5}}$$

Add 1 and \frac{1}{10} to get \frac{11}{10}.

$$V=\frac{5003041006904546225}{18368651961}+\frac{612.5}{\left(\frac{11}{10}\right)^{5}}$$

Calculate \frac{11}{10} to the power of 5 and get \frac{161051}{100000}.

$$V=\frac{5003041006904546225}{18368651961}+\frac{612.5}{\frac{161051}{100000}}$$

Divide 612.5 by \frac{161051}{100000} by multiplying 612.5 by the reciprocal of \frac{161051}{100000}.

$$V=\frac{5003041006904546225}{18368651961}+612.5\times \frac{100000}{161051}$$

Multiply 612.5 and \frac{100000}{161051} to get \frac{61250000}{161051}.

$$V=\frac{5003041006904546225}{18368651961}+\frac{61250000}{161051}$$

Add \frac{5003041006904546225}{18368651961} and \frac{61250000}{161051} to get \frac{6659056878371212275475}{24448675760091}.

$$V=\frac{6659056878371212275475}{24448675760091}$$

Assign V

$$V≔\frac{6659056878371212275475}{24448675760091}$$