Solve 32500/1.13+32500/1.13^2+32500/1.13^3+32500/1.13^4+frac{32500}{1.13^5}-110000

$$\frac{ 32500 }{ 1.13 } + \frac{ 32500 }{ { 1.13 }^{ 2 } } + \frac{ 32500 }{ { 1.13 }^{ 3 } } + \frac{ 32500 }{ { 1.13 }^{ 4 } } + \frac{ 32500 }{ { 1.13 }^{ 5 } } -110000$$

Evaluate

$$\frac{79409251020000}{18424351793}\approx 4310.016000138$$

Solution Steps

Expand \frac{32500}{1.13} by multiplying both numerator and the denominator by 100.

$$\frac{3250000}{113}+\frac{32500}{1.13^{2}}+\frac{32500}{1.13^{3}}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Calculate 1.13 to the power of 2 and get 1.2769.

$$\frac{3250000}{113}+\frac{32500}{1.2769}+\frac{32500}{1.13^{3}}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Expand \frac{32500}{1.2769} by multiplying both numerator and the denominator by 10000.

$$\frac{3250000}{113}+\frac{325000000}{12769}+\frac{32500}{1.13^{3}}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Least common multiple of 113 and 12769 is 12769. Convert \frac{3250000}{113} and \frac{325000000}{12769} to fractions with denominator 12769.

$$\frac{367250000}{12769}+\frac{325000000}{12769}+\frac{32500}{1.13^{3}}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Since \frac{367250000}{12769} and \frac{325000000}{12769} have the same denominator, add them by adding their numerators.

$$\frac{367250000+325000000}{12769}+\frac{32500}{1.13^{3}}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Add 367250000 and 325000000 to get 692250000.

$$\frac{692250000}{12769}+\frac{32500}{1.13^{3}}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Calculate 1.13 to the power of 3 and get 1.442897.

$$\frac{692250000}{12769}+\frac{32500}{1.442897}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Expand \frac{32500}{1.442897} by multiplying both numerator and the denominator by 1000000.

$$\frac{692250000}{12769}+\frac{32500000000}{1442897}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Least common multiple of 12769 and 1442897 is 1442897. Convert \frac{692250000}{12769} and \frac{32500000000}{1442897} to fractions with denominator 1442897.

$$\frac{78224250000}{1442897}+\frac{32500000000}{1442897}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Since \frac{78224250000}{1442897} and \frac{32500000000}{1442897} have the same denominator, add them by adding their numerators.

$$\frac{78224250000+32500000000}{1442897}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Add 78224250000 and 32500000000 to get 110724250000.

$$\frac{110724250000}{1442897}+\frac{32500}{1.13^{4}}+\frac{32500}{1.13^{5}}-110000$$

Calculate 1.13 to the power of 4 and get 1.63047361.

$$\frac{110724250000}{1442897}+\frac{32500}{1.63047361}+\frac{32500}{1.13^{5}}-110000$$

Expand \frac{32500}{1.63047361} by multiplying both numerator and the denominator by 100000000.

$$\frac{110724250000}{1442897}+\frac{3250000000000}{163047361}+\frac{32500}{1.13^{5}}-110000$$

Least common multiple of 1442897 and 163047361 is 163047361. Convert \frac{110724250000}{1442897} and \frac{3250000000000}{163047361} to fractions with denominator 163047361.

$$\frac{12511840250000}{163047361}+\frac{3250000000000}{163047361}+\frac{32500}{1.13^{5}}-110000$$

Since \frac{12511840250000}{163047361} and \frac{3250000000000}{163047361} have the same denominator, add them by adding their numerators.

$$\frac{12511840250000+3250000000000}{163047361}+\frac{32500}{1.13^{5}}-110000$$

Add 12511840250000 and 3250000000000 to get 15761840250000.

$$\frac{15761840250000}{163047361}+\frac{32500}{1.13^{5}}-110000$$

Calculate 1.13 to the power of 5 and get 1.8424351793.

$$\frac{15761840250000}{163047361}+\frac{32500}{1.8424351793}-110000$$

Expand \frac{32500}{1.8424351793} by multiplying both numerator and the denominator by 10000000000.

$$\frac{15761840250000}{163047361}+\frac{325000000000000}{18424351793}-110000$$

Least common multiple of 163047361 and 18424351793 is 18424351793. Convert \frac{15761840250000}{163047361} and \frac{325000000000000}{18424351793} to fractions with denominator 18424351793.

$$\frac{1781087948250000}{18424351793}+\frac{325000000000000}{18424351793}-110000$$

Since \frac{1781087948250000}{18424351793} and \frac{325000000000000}{18424351793} have the same denominator, add them by adding their numerators.

$$\frac{1781087948250000+325000000000000}{18424351793}-110000$$

Add 1781087948250000 and 325000000000000 to get 2106087948250000.

$$\frac{2106087948250000}{18424351793}-110000$$

Convert 110000 to fraction \frac{2026678697230000}{18424351793}.

$$\frac{2106087948250000}{18424351793}-\frac{2026678697230000}{18424351793}$$

Since \frac{2106087948250000}{18424351793} and \frac{2026678697230000}{18424351793} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2106087948250000-2026678697230000}{18424351793}$$

Subtract 2026678697230000 from 2106087948250000 to get 79409251020000.

$$\frac{79409251020000}{18424351793}$$

Factor

$$\frac{3 \cdot 11 \cdot 2399 \cdot 50153 \cdot 2 ^ {5} \cdot 5 ^ {4}}{113 ^ {5}} = 4310\frac{294792170}{18424351793} = 4310.016000137933$$