Solve 10,000/105^5+685/0.05*(1-1/1.05^5)

$$\frac { 10,000 } { 105 ^ { 5 } } + \frac { 685 } { 0.05 } \cdot ( 1 - \frac { 1 } { 1.05 ^ { 5 } } )$$

Evaluate

$$\frac{12112183700}{4084101}\approx 2965.691519382$$

Solution Steps

Multiply 10 and 0 to get 0.

$$\frac{0\times 0\times 0}{105^{5}}+\frac{685}{0.05}\left(1-\frac{1}{1.05^{5}}\right)$$

Multiply 0 and 0 to get 0.

$$\frac{0\times 0}{105^{5}}+\frac{685}{0.05}\left(1-\frac{1}{1.05^{5}}\right)$$

Multiply 0 and 0 to get 0.

$$\frac{0}{105^{5}}+\frac{685}{0.05}\left(1-\frac{1}{1.05^{5}}\right)$$

Calculate 105 to the power of 5 and get 12762815625.

$$\frac{0}{12762815625}+\frac{685}{0.05}\left(1-\frac{1}{1.05^{5}}\right)$$

Zero divided by any non-zero number gives zero.

$$0+\frac{685}{0.05}\left(1-\frac{1}{1.05^{5}}\right)$$

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

$$0+\frac{68500}{5}\left(1-\frac{1}{1.05^{5}}\right)$$

Divide 68500 by 5 to get 13700.

$$0+13700\left(1-\frac{1}{1.05^{5}}\right)$$

Calculate 1.05 to the power of 5 and get 1.2762815625.

$$0+13700\left(1-\frac{1}{1.2762815625}\right)$$

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

$$0+13700\left(1-\frac{10000000000}{12762815625}\right)$$

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

$$0+13700\left(1-\frac{3200000}{4084101}\right)$$

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

$$0+13700\left(\frac{4084101}{4084101}-\frac{3200000}{4084101}\right)$$

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

$$0+13700\times \frac{4084101-3200000}{4084101}$$

Subtract 3200000 from 4084101 to get 884101.

$$0+13700\times \frac{884101}{4084101}$$

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

$$0+\frac{13700\times 884101}{4084101}$$

Multiply 13700 and 884101 to get 12112183700.

$$0+\frac{12112183700}{4084101}$$

Add 0 and \frac{12112183700}{4084101} to get \frac{12112183700}{4084101}.

$$\frac{12112183700}{4084101}$$

Factor

$$\frac{137 \cdot 331 \cdot 2671 \cdot 2 ^ {2} \cdot 5 ^ {2}}{3 ^ {5} \cdot 7 ^ {5}} = 2965\frac{2824235}{4084101} = 2965.6915193821114$$