Solve 40000/1.08+60000/1.08^2+70000/1.08^3+60000/1.08^4+frac{40000}{1.08^5}

$$\frac{ 40000 }{ 1.08 } + \frac{ 60000 }{ { 1.08 }^{ 2 } } + \frac{ 70000 }{ { 1.08 }^{ 3 } } + \frac{ 60000 }{ { 1.08 }^{ 4 } } + \frac{ 40000 }{ { 1.08 }^{ 5 } }$$

Evaluate

$$\frac{3090334750000}{14348907}\approx 215370.742175693$$

Solution Steps

Expand \frac{40000}{1.08} by multiplying both numerator and the denominator by 100.

$$\frac{4000000}{108}+\frac{60000}{1.08^{2}}+\frac{70000}{1.08^{3}}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Reduce the fraction \frac{4000000}{108} to lowest terms by extracting and canceling out 4.

$$\frac{1000000}{27}+\frac{60000}{1.08^{2}}+\frac{70000}{1.08^{3}}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Calculate 1.08 to the power of 2 and get 1.1664.

$$\frac{1000000}{27}+\frac{60000}{1.1664}+\frac{70000}{1.08^{3}}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Expand \frac{60000}{1.1664} by multiplying both numerator and the denominator by 10000.

$$\frac{1000000}{27}+\frac{600000000}{11664}+\frac{70000}{1.08^{3}}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Reduce the fraction \frac{600000000}{11664} to lowest terms by extracting and canceling out 48.

$$\frac{1000000}{27}+\frac{12500000}{243}+\frac{70000}{1.08^{3}}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Least common multiple of 27 and 243 is 243. Convert \frac{1000000}{27} and \frac{12500000}{243} to fractions with denominator 243.

$$\frac{9000000}{243}+\frac{12500000}{243}+\frac{70000}{1.08^{3}}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Since \frac{9000000}{243} and \frac{12500000}{243} have the same denominator, add them by adding their numerators.

$$\frac{9000000+12500000}{243}+\frac{70000}{1.08^{3}}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Add 9000000 and 12500000 to get 21500000.

$$\frac{21500000}{243}+\frac{70000}{1.08^{3}}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Calculate 1.08 to the power of 3 and get 1.259712.

$$\frac{21500000}{243}+\frac{70000}{1.259712}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Expand \frac{70000}{1.259712} by multiplying both numerator and the denominator by 1000000.

$$\frac{21500000}{243}+\frac{70000000000}{1259712}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Reduce the fraction \frac{70000000000}{1259712} to lowest terms by extracting and canceling out 64.

$$\frac{21500000}{243}+\frac{1093750000}{19683}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Least common multiple of 243 and 19683 is 19683. Convert \frac{21500000}{243} and \frac{1093750000}{19683} to fractions with denominator 19683.

$$\frac{1741500000}{19683}+\frac{1093750000}{19683}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Since \frac{1741500000}{19683} and \frac{1093750000}{19683} have the same denominator, add them by adding their numerators.

$$\frac{1741500000+1093750000}{19683}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Add 1741500000 and 1093750000 to get 2835250000.

$$\frac{2835250000}{19683}+\frac{60000}{1.08^{4}}+\frac{40000}{1.08^{5}}$$

Calculate 1.08 to the power of 4 and get 1.36048896.

$$\frac{2835250000}{19683}+\frac{60000}{1.36048896}+\frac{40000}{1.08^{5}}$$

Expand \frac{60000}{1.36048896} by multiplying both numerator and the denominator by 100000000.

$$\frac{2835250000}{19683}+\frac{6000000000000}{136048896}+\frac{40000}{1.08^{5}}$$

Reduce the fraction \frac{6000000000000}{136048896} to lowest terms by extracting and canceling out 768.

$$\frac{2835250000}{19683}+\frac{7812500000}{177147}+\frac{40000}{1.08^{5}}$$

Least common multiple of 19683 and 177147 is 177147. Convert \frac{2835250000}{19683} and \frac{7812500000}{177147} to fractions with denominator 177147.

$$\frac{25517250000}{177147}+\frac{7812500000}{177147}+\frac{40000}{1.08^{5}}$$

Since \frac{25517250000}{177147} and \frac{7812500000}{177147} have the same denominator, add them by adding their numerators.

$$\frac{25517250000+7812500000}{177147}+\frac{40000}{1.08^{5}}$$

Add 25517250000 and 7812500000 to get 33329750000.

$$\frac{33329750000}{177147}+\frac{40000}{1.08^{5}}$$

Calculate 1.08 to the power of 5 and get 1.4693280768.

$$\frac{33329750000}{177147}+\frac{40000}{1.4693280768}$$

Expand \frac{40000}{1.4693280768} by multiplying both numerator and the denominator by 10000000000.

$$\frac{33329750000}{177147}+\frac{400000000000000}{14693280768}$$

Reduce the fraction \frac{400000000000000}{14693280768} to lowest terms by extracting and canceling out 1024.

$$\frac{33329750000}{177147}+\frac{390625000000}{14348907}$$

Least common multiple of 177147 and 14348907 is 14348907. Convert \frac{33329750000}{177147} and \frac{390625000000}{14348907} to fractions with denominator 14348907.

$$\frac{2699709750000}{14348907}+\frac{390625000000}{14348907}$$

Since \frac{2699709750000}{14348907} and \frac{390625000000}{14348907} have the same denominator, add them by adding their numerators.

$$\frac{2699709750000+390625000000}{14348907}$$

Add 2699709750000 and 390625000000 to get 3090334750000.

$$\frac{3090334750000}{14348907}$$

Factor

$$\frac{43 \cdot 103 \cdot 2791 \cdot 2 ^ {4} \cdot 5 ^ {6}}{3 ^ {15}} = 215370\frac{10649410}{14348907} = 215370.74217569325$$