Solve 25*1/0.035*(1-1/1.035^10)+1000/1.035^10

$$25 \times \frac{ 1 }{ 0.035 } \times (1- \frac{ 1 }{ { 1.035 }^{ 10 } } )+ \frac{ 1000 }{ { 1.035 }^{ 10 } }$$

Evaluate

$$\frac{132432366491144936778035000}{144445313087602911489249}\approx 916.833946774$$

Solution Steps

Expand \frac{1}{0.035} by multiplying both numerator and the denominator by 1000.

$$25\times \frac{1000}{35}\left(1-\frac{1}{1.035^{10}}\right)+\frac{1000}{1.035^{10}}$$

Reduce the fraction \frac{1000}{35} to lowest terms by extracting and canceling out 5.

$$25\times \frac{200}{7}\left(1-\frac{1}{1.035^{10}}\right)+\frac{1000}{1.035^{10}}$$

Express 25\times \frac{200}{7} as a single fraction.

$$\frac{25\times 200}{7}\left(1-\frac{1}{1.035^{10}}\right)+\frac{1000}{1.035^{10}}$$

Multiply 25 and 200 to get 5000.

$$\frac{5000}{7}\left(1-\frac{1}{1.035^{10}}\right)+\frac{1000}{1.035^{10}}$$

Calculate 1.035 to the power of 10 and get 1.410598760621122182512197265625.

$$\frac{5000}{7}\left(1-\frac{1}{1.410598760621122182512197265625}\right)+\frac{1000}{1.035^{10}}$$

Expand \frac{1}{1.410598760621122182512197265625} by multiplying both numerator and the denominator by 1000000000000000000000000000000.

$$\frac{5000}{7}\left(1-\frac{1000000000000000000000000000000}{1410598760621122182512197265625}\right)+\frac{1000}{1.035^{10}}$$

Reduce the fraction \frac{1000000000000000000000000000000}{1410598760621122182512197265625} to lowest terms by extracting and canceling out 9765625.

$$\frac{5000}{7}\left(1-\frac{102400000000000000000000}{144445313087602911489249}\right)+\frac{1000}{1.035^{10}}$$

Convert 1 to fraction \frac{144445313087602911489249}{144445313087602911489249}.

$$\frac{5000}{7}\left(\frac{144445313087602911489249}{144445313087602911489249}-\frac{102400000000000000000000}{144445313087602911489249}\right)+\frac{1000}{1.035^{10}}$$

Since \frac{144445313087602911489249}{144445313087602911489249} and \frac{102400000000000000000000}{144445313087602911489249} have the same denominator, subtract them by subtracting their numerators.

$$\frac{5000}{7}\times \frac{144445313087602911489249-102400000000000000000000}{144445313087602911489249}+\frac{1000}{1.035^{10}}$$

Subtract 102400000000000000000000 from 144445313087602911489249 to get 42045313087602911489249.

$$\frac{5000}{7}\times \frac{42045313087602911489249}{144445313087602911489249}+\frac{1000}{1.035^{10}}$$

Multiply \frac{5000}{7} times \frac{42045313087602911489249}{144445313087602911489249} by multiplying numerator times numerator and denominator times denominator.

$$\frac{5000\times 42045313087602911489249}{7\times 144445313087602911489249}+\frac{1000}{1.035^{10}}$$

Do the multiplications in the fraction \frac{5000\times 42045313087602911489249}{7\times 144445313087602911489249}.

$$\frac{210226565438014557446245000}{1011117191613220380424743}+\frac{1000}{1.035^{10}}$$

Reduce the fraction \frac{210226565438014557446245000}{1011117191613220380424743} to lowest terms by extracting and canceling out 7.

$$\frac{30032366491144936778035000}{144445313087602911489249}+\frac{1000}{1.035^{10}}$$

Calculate 1.035 to the power of 10 and get 1.410598760621122182512197265625.

$$\frac{30032366491144936778035000}{144445313087602911489249}+\frac{1000}{1.410598760621122182512197265625}$$

Expand \frac{1000}{1.410598760621122182512197265625} by multiplying both numerator and the denominator by 1000000000000000000000000000000.

$$\frac{30032366491144936778035000}{144445313087602911489249}+\frac{1000000000000000000000000000000000}{1410598760621122182512197265625}$$

Reduce the fraction \frac{1000000000000000000000000000000000}{1410598760621122182512197265625} to lowest terms by extracting and canceling out 9765625.

$$\frac{30032366491144936778035000}{144445313087602911489249}+\frac{102400000000000000000000000}{144445313087602911489249}$$

Since \frac{30032366491144936778035000}{144445313087602911489249} and \frac{102400000000000000000000000}{144445313087602911489249} have the same denominator, add them by adding their numerators.

$$\frac{30032366491144936778035000+102400000000000000000000000}{144445313087602911489249}$$

Add 30032366491144936778035000 and 102400000000000000000000000 to get 132432366491144936778035000.

$$\frac{132432366491144936778035000}{144445313087602911489249}$$

Factor

$$\frac{26486473298228987355607 \cdot 2 ^ {3} \cdot 5 ^ {4}}{3 ^ {20} \cdot 23 ^ {10}} = 916\frac{1.2045970290067 \times 10^{23}}{1.4444531308760291 \times 10^{23}} = 916.8339467742204$$