Solve 100(1-1/1.01^5)+100/1.01

$$100 ( 1 - \frac { 1 } { 1.01 ^ { 5 } } ) + \frac { 100 } { 1.01 }$$

Evaluate

$$\frac{1091614060100}{10510100501}\approx 103.863332229$$

Solution Steps

Calculate 1.01 to the power of 5 and get 1.0510100501.

$$100\left(1-\frac{1}{1.0510100501}\right)+\frac{100}{1.01}$$

Expand \frac{1}{1.0510100501} by multiplying both numerator and the denominator by 10000000000.

$$100\left(1-\frac{10000000000}{10510100501}\right)+\frac{100}{1.01}$$

Convert 1 to fraction \frac{10510100501}{10510100501}.

$$100\left(\frac{10510100501}{10510100501}-\frac{10000000000}{10510100501}\right)+\frac{100}{1.01}$$

Since \frac{10510100501}{10510100501} and \frac{10000000000}{10510100501} have the same denominator, subtract them by subtracting their numerators.

$$100\times \frac{10510100501-10000000000}{10510100501}+\frac{100}{1.01}$$

Subtract 10000000000 from 10510100501 to get 510100501.

$$100\times \frac{510100501}{10510100501}+\frac{100}{1.01}$$

Express 100\times \frac{510100501}{10510100501} as a single fraction.

$$\frac{100\times 510100501}{10510100501}+\frac{100}{1.01}$$

Multiply 100 and 510100501 to get 51010050100.

$$\frac{51010050100}{10510100501}+\frac{100}{1.01}$$

Expand \frac{100}{1.01} by multiplying both numerator and the denominator by 100.

$$\frac{51010050100}{10510100501}+\frac{10000}{101}$$

Least common multiple of 10510100501 and 101 is 10510100501. Convert \frac{51010050100}{10510100501} and \frac{10000}{101} to fractions with denominator 10510100501.

$$\frac{51010050100}{10510100501}+\frac{1040604010000}{10510100501}$$

Since \frac{51010050100}{10510100501} and \frac{1040604010000}{10510100501} have the same denominator, add them by adding their numerators.

$$\frac{51010050100+1040604010000}{10510100501}$$

Add 51010050100 and 1040604010000 to get 1091614060100.

$$\frac{1091614060100}{10510100501}$$

Factor

$$\frac{53 \cdot 127 \cdot 1621771 \cdot 2 ^ {2} \cdot 5 ^ {2}}{101 ^ {5}} = 103\frac{9073708497}{10510100501} = 103.86333222942413$$