Solve 966.64(1/0.005)(1-1/(1.005)^24)

$$966.64 ( \frac { 1 } { 0.005 } ) ( 1 - \frac { 1 } { ( 1.005 ) ^ { 24 } } )$$

Evaluate

$$\frac{412443448105003220371682965999750665547305943109667045287728}{18910603031909517609304823750309063692518962297803044801}\approx 21810.169004608$$

Solution Steps

Expand \frac{1}{0.005} by multiplying both numerator and the denominator by 1000.

$$966.64\times \frac{1000}{5}\left(1-\frac{1}{1.005^{24}}\right)$$

Divide 1000 by 5 to get 200.

$$966.64\times 200\left(1-\frac{1}{1.005^{24}}\right)$$

Multiply 966.64 and 200 to get 193328.

$$193328\left(1-\frac{1}{1.005^{24}}\right)$$

Calculate 1.005 to the power of 24 and get 1.127159776205391741353560909647289734632907050717058467924594879150390625.

$$193328\left(1-\frac{1}{1.127159776205391741353560909647289734632907050717058467924594879150390625}\right)$$

Expand \frac{1}{1.127159776205391741353560909647289734632907050717058467924594879150390625} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000000000000000000000000000.

$$193328\left(1-\frac{1000000000000000000000000000000000000000000000000000000000000000000000000}{1127159776205391741353560909647289734632907050717058467924594879150390625}\right)$$

Reduce the fraction \frac{1000000000000000000000000000000000000000000000000000000000000000000000000}{1127159776205391741353560909647289734632907050717058467924594879150390625} to lowest terms by extracting and canceling out 59604644775390625.

$$193328\left(1-\frac{16777216000000000000000000000000000000000000000000000000}{18910603031909517609304823750309063692518962297803044801}\right)$$

Convert 1 to fraction \frac{18910603031909517609304823750309063692518962297803044801}{18910603031909517609304823750309063692518962297803044801}.

$$193328\left(\frac{18910603031909517609304823750309063692518962297803044801}{18910603031909517609304823750309063692518962297803044801}-\frac{16777216000000000000000000000000000000000000000000000000}{18910603031909517609304823750309063692518962297803044801}\right)$$

Since \frac{18910603031909517609304823750309063692518962297803044801}{18910603031909517609304823750309063692518962297803044801} and \frac{16777216000000000000000000000000000000000000000000000000}{18910603031909517609304823750309063692518962297803044801} have the same denominator, subtract them by subtracting their numerators.

$$193328\times \frac{18910603031909517609304823750309063692518962297803044801-16777216000000000000000000000000000000000000000000000000}{18910603031909517609304823750309063692518962297803044801}$$

Subtract 16777216000000000000000000000000000000000000000000000000 from 18910603031909517609304823750309063692518962297803044801 to get 2133387031909517609304823750309063692518962297803044801.

$$193328\times \frac{2133387031909517609304823750309063692518962297803044801}{18910603031909517609304823750309063692518962297803044801}$$

Express 193328\times \frac{2133387031909517609304823750309063692518962297803044801}{18910603031909517609304823750309063692518962297803044801} as a single fraction.

$$\frac{193328\times 2133387031909517609304823750309063692518962297803044801}{18910603031909517609304823750309063692518962297803044801}$$

Multiply 193328 and 2133387031909517609304823750309063692518962297803044801 to get 412443448105003220371682965999750665547305943109667045287728.

$$\frac{412443448105003220371682965999750665547305943109667045287728}{18910603031909517609304823750309063692518962297803044801}$$