Solve 80000*0,08/(1-frac{1{1.08^30})}

$$\frac { 80000 \times 0,08 } { ( 1 - \frac { 1 } { 1.08 ^ { 30 } } ) }$$

Evaluate

$$\frac{6982370854470169940713117983581381872033159200}{982575228762413609835679404847596746362603}\approx 7106.194670982$$

Solution Steps

Multiply 80000 and 0.08 to get 6400.

$$\frac{6400}{1-\frac{1}{1.08^{30}}}$$

Calculate 1.08 to the power of 30 and get 10.062656889073430111910396911109936282712980852099973040308224.

$$\frac{6400}{1-\frac{1}{10.062656889073430111910396911109936282712980852099973040308224}}$$

Expand \frac{1}{10.062656889073430111910396911109936282712980852099973040308224} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000000000000000.

$$\frac{6400}{1-\frac{1000000000000000000000000000000000000000000000000000000000000}{10062656889073430111910396911109936282712980852099973040308224}}$$

Reduce the fraction \frac{1000000000000000000000000000000000000000000000000000000000000}{10062656889073430111910396911109936282712980852099973040308224} to lowest terms by extracting and canceling out 1152921504606846976.

$$\frac{6400}{1-\frac{867361737988403547205962240695953369140625}{8727963568087712425891397479476727340041449}}$$

Convert 1 to fraction \frac{8727963568087712425891397479476727340041449}{8727963568087712425891397479476727340041449}.

$$\frac{6400}{\frac{8727963568087712425891397479476727340041449}{8727963568087712425891397479476727340041449}-\frac{867361737988403547205962240695953369140625}{8727963568087712425891397479476727340041449}}$$

Since \frac{8727963568087712425891397479476727340041449}{8727963568087712425891397479476727340041449} and \frac{867361737988403547205962240695953369140625}{8727963568087712425891397479476727340041449} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6400}{\frac{8727963568087712425891397479476727340041449-867361737988403547205962240695953369140625}{8727963568087712425891397479476727340041449}}$$

Subtract 867361737988403547205962240695953369140625 from 8727963568087712425891397479476727340041449 to get 7860601830099308878685435238780773970900824.

$$\frac{6400}{\frac{7860601830099308878685435238780773970900824}{8727963568087712425891397479476727340041449}}$$

Divide 6400 by \frac{7860601830099308878685435238780773970900824}{8727963568087712425891397479476727340041449} by multiplying 6400 by the reciprocal of \frac{7860601830099308878685435238780773970900824}{8727963568087712425891397479476727340041449}.

$$6400\times \frac{8727963568087712425891397479476727340041449}{7860601830099308878685435238780773970900824}$$

Express 6400\times \frac{8727963568087712425891397479476727340041449}{7860601830099308878685435238780773970900824} as a single fraction.

$$\frac{6400\times 8727963568087712425891397479476727340041449}{7860601830099308878685435238780773970900824}$$

Multiply 6400 and 8727963568087712425891397479476727340041449 to get 55858966835761359525704943868651054976265273600.

$$\frac{55858966835761359525704943868651054976265273600}{7860601830099308878685435238780773970900824}$$

Reduce the fraction \frac{55858966835761359525704943868651054976265273600}{7860601830099308878685435238780773970900824} to lowest terms by extracting and canceling out 8.

$$\frac{6982370854470169940713117983581381872033159200}{982575228762413609835679404847596746362603}$$

Factor

$$\frac{2 ^ {5} \cdot 3 ^ {90} \cdot 5 ^ {2}}{7 \cdot 11 \cdot 13 \cdot 31 \cdot 61 \cdot 97 \cdot 181 \cdot 1151 \cdot 1201 \cdot 2029 \cdot 104491 \cdot 463741 \cdot 217538003281} = 7106\frac{1.9127888445981596 \times 10^{41}}{9.825752287624134 \times 10^{41}} = 7106.194670981784$$