Solve 50(1-1/1.02^5)+100/1.02^5

$$50 ( 1 - \frac { 1 } { 1.02 ^ { 5 } } ) + \frac { 100 } { 1.02 ^ { 5 } }$$

Evaluate

$$\frac{32876262550}{345025251}\approx 95.286540491$$

Solution Steps

Calculate 1.02 to the power of 5 and get 1.1040808032.

$$50\left(1-\frac{1}{1.1040808032}\right)+\frac{100}{1.02^{5}}$$

Expand \frac{1}{1.1040808032} by multiplying both numerator and the denominator by 10000000000.

$$50\left(1-\frac{10000000000}{11040808032}\right)+\frac{100}{1.02^{5}}$$

Reduce the fraction \frac{10000000000}{11040808032} to lowest terms by extracting and canceling out 32.

$$50\left(1-\frac{312500000}{345025251}\right)+\frac{100}{1.02^{5}}$$

Convert 1 to fraction \frac{345025251}{345025251}.

$$50\left(\frac{345025251}{345025251}-\frac{312500000}{345025251}\right)+\frac{100}{1.02^{5}}$$

Since \frac{345025251}{345025251} and \frac{312500000}{345025251} have the same denominator, subtract them by subtracting their numerators.

$$50\times \frac{345025251-312500000}{345025251}+\frac{100}{1.02^{5}}$$

Subtract 312500000 from 345025251 to get 32525251.

$$50\times \frac{32525251}{345025251}+\frac{100}{1.02^{5}}$$

Express 50\times \frac{32525251}{345025251} as a single fraction.

$$\frac{50\times 32525251}{345025251}+\frac{100}{1.02^{5}}$$

Multiply 50 and 32525251 to get 1626262550.

$$\frac{1626262550}{345025251}+\frac{100}{1.02^{5}}$$

Calculate 1.02 to the power of 5 and get 1.1040808032.

$$\frac{1626262550}{345025251}+\frac{100}{1.1040808032}$$

Expand \frac{100}{1.1040808032} by multiplying both numerator and the denominator by 10000000000.

$$\frac{1626262550}{345025251}+\frac{1000000000000}{11040808032}$$

Reduce the fraction \frac{1000000000000}{11040808032} to lowest terms by extracting and canceling out 32.

$$\frac{1626262550}{345025251}+\frac{31250000000}{345025251}$$

Since \frac{1626262550}{345025251} and \frac{31250000000}{345025251} have the same denominator, add them by adding their numerators.

$$\frac{1626262550+31250000000}{345025251}$$

Add 1626262550 and 31250000000 to get 32876262550.

$$\frac{32876262550}{345025251}$$

Factor

$$\frac{2 \cdot 101 \cdot 6510151 \cdot 5 ^ {2}}{3 ^ {5} \cdot 17 ^ {5}} = 95\frac{98863705}{345025251} = 95.2865404914958$$