Solve 10000/1.05^5+685/0.05left(1-1/1.05^5right)

$$\frac{ 10000 }{ { 1.05 }^{ 5 } } + \frac{ 685 }{ 0.05 } \left( 1- \frac{ 1 }{ { 1.05 }^{ 5 } } \right)$$

Evaluate

$$\frac{44112183700}{4084101}\approx 10800.953184067$$

Solution Steps

Calculate 1.05 to the power of 5 and get 1.2762815625.

$$\frac{10000}{1.2762815625}+\frac{685}{0.05}\left(1-\frac{1}{1.05^{5}}\right)$$

Expand \frac{10000}{1.2762815625} by multiplying both numerator and the denominator by 10000000000.

$$\frac{100000000000000}{12762815625}+\frac{685}{0.05}\left(1-\frac{1}{1.05^{5}}\right)$$

Reduce the fraction \frac{100000000000000}{12762815625} to lowest terms by extracting and canceling out 3125.

$$\frac{32000000000}{4084101}+\frac{685}{0.05}\left(1-\frac{1}{1.05^{5}}\right)$$

Expand \frac{685}{0.05} by multiplying both numerator and the denominator by 100.

$$\frac{32000000000}{4084101}+\frac{68500}{5}\left(1-\frac{1}{1.05^{5}}\right)$$

Divide 68500 by 5 to get 13700.

$$\frac{32000000000}{4084101}+13700\left(1-\frac{1}{1.05^{5}}\right)$$

Calculate 1.05 to the power of 5 and get 1.2762815625.

$$\frac{32000000000}{4084101}+13700\left(1-\frac{1}{1.2762815625}\right)$$

Expand \frac{1}{1.2762815625} by multiplying both numerator and the denominator by 10000000000.

$$\frac{32000000000}{4084101}+13700\left(1-\frac{10000000000}{12762815625}\right)$$

Reduce the fraction \frac{10000000000}{12762815625} to lowest terms by extracting and canceling out 3125.

$$\frac{32000000000}{4084101}+13700\left(1-\frac{3200000}{4084101}\right)$$

Convert 1 to fraction \frac{4084101}{4084101}.

$$\frac{32000000000}{4084101}+13700\left(\frac{4084101}{4084101}-\frac{3200000}{4084101}\right)$$

Since \frac{4084101}{4084101} and \frac{3200000}{4084101} have the same denominator, subtract them by subtracting their numerators.

$$\frac{32000000000}{4084101}+13700\times \frac{4084101-3200000}{4084101}$$

Subtract 3200000 from 4084101 to get 884101.

$$\frac{32000000000}{4084101}+13700\times \frac{884101}{4084101}$$

Express 13700\times \frac{884101}{4084101} as a single fraction.

$$\frac{32000000000}{4084101}+\frac{13700\times 884101}{4084101}$$

Multiply 13700 and 884101 to get 12112183700.

$$\frac{32000000000}{4084101}+\frac{12112183700}{4084101}$$

Since \frac{32000000000}{4084101} and \frac{12112183700}{4084101} have the same denominator, add them by adding their numerators.

$$\frac{32000000000+12112183700}{4084101}$$

Add 32000000000 and 12112183700 to get 44112183700.

$$\frac{44112183700}{4084101}$$

Factor

$$\frac{13 \cdot 15361 \cdot 2 ^ {2} \cdot 5 ^ {2} \cdot 47 ^ {2}}{3 ^ {5} \cdot 7 ^ {5}} = 10800\frac{3892900}{4084101} = 10800.953184066702$$