Solve P_{A}=80/1.1+80/1.1^2+80/1.1^3+80/1.14+frac{80}{1.15}+frac{1000}{1.1^5}

$$P _ { A } = \frac { 80 } { 1.1 } + \frac { 80 } { 1.1 ^ { 2 } } + \frac { 80 } { 1.1 ^ { 3 } } + \frac { 80 } { 1.14 } + \frac { 80 } { 1.15 } + \frac { 1000 } { 1.1 ^ { 5 } }$$

Solve for P_A

$$P_{A} = \frac{202610032000}{211137861} = 959\frac{128823301}{211137861} \approx 959.610138326$$

Steps for Solving Linear Equation

Expand \frac{80}{1.1} by multiplying both numerator and the denominator by 10.

$$P_{A}=\frac{800}{11}+\frac{80}{1.1^{2}}+\frac{80}{1.1^{3}}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Calculate 1.1 to the power of 2 and get 1.21.

$$P_{A}=\frac{800}{11}+\frac{80}{1.21}+\frac{80}{1.1^{3}}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Expand \frac{80}{1.21} by multiplying both numerator and the denominator by 100.

$$P_{A}=\frac{800}{11}+\frac{8000}{121}+\frac{80}{1.1^{3}}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Least common multiple of 11 and 121 is 121. Convert \frac{800}{11} and \frac{8000}{121} to fractions with denominator 121.

$$P_{A}=\frac{8800}{121}+\frac{8000}{121}+\frac{80}{1.1^{3}}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Since \frac{8800}{121} and \frac{8000}{121} have the same denominator, add them by adding their numerators.

$$P_{A}=\frac{8800+8000}{121}+\frac{80}{1.1^{3}}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Add 8800 and 8000 to get 16800.

$$P_{A}=\frac{16800}{121}+\frac{80}{1.1^{3}}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Calculate 1.1 to the power of 3 and get 1.331.

$$P_{A}=\frac{16800}{121}+\frac{80}{1.331}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Expand \frac{80}{1.331} by multiplying both numerator and the denominator by 1000.

$$P_{A}=\frac{16800}{121}+\frac{80000}{1331}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Least common multiple of 121 and 1331 is 1331. Convert \frac{16800}{121} and \frac{80000}{1331} to fractions with denominator 1331.

$$P_{A}=\frac{184800}{1331}+\frac{80000}{1331}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Since \frac{184800}{1331} and \frac{80000}{1331} have the same denominator, add them by adding their numerators.

$$P_{A}=\frac{184800+80000}{1331}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Add 184800 and 80000 to get 264800.

$$P_{A}=\frac{264800}{1331}+\frac{80}{1.14}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Expand \frac{80}{1.14} by multiplying both numerator and the denominator by 100.

$$P_{A}=\frac{264800}{1331}+\frac{8000}{114}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Reduce the fraction \frac{8000}{114} to lowest terms by extracting and canceling out 2.

$$P_{A}=\frac{264800}{1331}+\frac{4000}{57}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Least common multiple of 1331 and 57 is 75867. Convert \frac{264800}{1331} and \frac{4000}{57} to fractions with denominator 75867.

$$P_{A}=\frac{15093600}{75867}+\frac{5324000}{75867}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Since \frac{15093600}{75867} and \frac{5324000}{75867} have the same denominator, add them by adding their numerators.

$$P_{A}=\frac{15093600+5324000}{75867}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Add 15093600 and 5324000 to get 20417600.

$$P_{A}=\frac{20417600}{75867}+\frac{80}{1.15}+\frac{1000}{1.1^{5}}$$

Expand \frac{80}{1.15} by multiplying both numerator and the denominator by 100.

$$P_{A}=\frac{20417600}{75867}+\frac{8000}{115}+\frac{1000}{1.1^{5}}$$

Reduce the fraction \frac{8000}{115} to lowest terms by extracting and canceling out 5.

$$P_{A}=\frac{20417600}{75867}+\frac{1600}{23}+\frac{1000}{1.1^{5}}$$

Least common multiple of 75867 and 23 is 1744941. Convert \frac{20417600}{75867} and \frac{1600}{23} to fractions with denominator 1744941.

$$P_{A}=\frac{469604800}{1744941}+\frac{121387200}{1744941}+\frac{1000}{1.1^{5}}$$

Since \frac{469604800}{1744941} and \frac{121387200}{1744941} have the same denominator, add them by adding their numerators.

$$P_{A}=\frac{469604800+121387200}{1744941}+\frac{1000}{1.1^{5}}$$

Add 469604800 and 121387200 to get 590992000.

$$P_{A}=\frac{590992000}{1744941}+\frac{1000}{1.1^{5}}$$

Calculate 1.1 to the power of 5 and get 1.61051.

$$P_{A}=\frac{590992000}{1744941}+\frac{1000}{1.61051}$$

Expand \frac{1000}{1.61051} by multiplying both numerator and the denominator by 100000.

$$P_{A}=\frac{590992000}{1744941}+\frac{100000000}{161051}$$

Least common multiple of 1744941 and 161051 is 211137861. Convert \frac{590992000}{1744941} and \frac{100000000}{161051} to fractions with denominator 211137861.

$$P_{A}=\frac{71510032000}{211137861}+\frac{131100000000}{211137861}$$

Since \frac{71510032000}{211137861} and \frac{131100000000}{211137861} have the same denominator, add them by adding their numerators.

$$P_{A}=\frac{71510032000+131100000000}{211137861}$$

Add 71510032000 and 131100000000 to get 202610032000.

$$P_{A}=\frac{202610032000}{211137861}$$

Assign P_A

$$P_{A}≔\frac{202610032000}{211137861}$$