Solve 5000*1/8%*(1-1/1.08^30)

$$5000 \times \frac { 1 } { 8 \% } \times ( 1 - \frac { 1 } { 1.08 ^ { 30 } } )$$

Evaluate

$$\frac{491287614381206804917839702423798373181301500000}{8727963568087712425891397479476727340041449}\approx 56288.916715637$$

Solution Steps

Divide 1 by \frac{8}{100} by multiplying 1 by the reciprocal of \frac{8}{100}.

$$5000\times \frac{100}{8}\left(1-\frac{1}{1.08^{30}}\right)$$

Reduce the fraction \frac{100}{8} to lowest terms by extracting and canceling out 4.

$$5000\times \frac{25}{2}\left(1-\frac{1}{1.08^{30}}\right)$$

Express 5000\times \frac{25}{2} as a single fraction.

$$\frac{5000\times 25}{2}\left(1-\frac{1}{1.08^{30}}\right)$$

Multiply 5000 and 25 to get 125000.

$$\frac{125000}{2}\left(1-\frac{1}{1.08^{30}}\right)$$

Divide 125000 by 2 to get 62500.

$$62500\left(1-\frac{1}{1.08^{30}}\right)$$

Calculate 1.08 to the power of 30 and get 10.062656889073430111910396911109936282712980852099973040308224.

$$62500\left(1-\frac{1}{10.062656889073430111910396911109936282712980852099973040308224}\right)$$

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

$$62500\left(1-\frac{1000000000000000000000000000000000000000000000000000000000000}{10062656889073430111910396911109936282712980852099973040308224}\right)$$

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

$$62500\left(1-\frac{867361737988403547205962240695953369140625}{8727963568087712425891397479476727340041449}\right)$$

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

$$62500\left(\frac{8727963568087712425891397479476727340041449}{8727963568087712425891397479476727340041449}-\frac{867361737988403547205962240695953369140625}{8727963568087712425891397479476727340041449}\right)$$

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

$$62500\times \frac{8727963568087712425891397479476727340041449-867361737988403547205962240695953369140625}{8727963568087712425891397479476727340041449}$$

Subtract 867361737988403547205962240695953369140625 from 8727963568087712425891397479476727340041449 to get 7860601830099308878685435238780773970900824.

$$62500\times \frac{7860601830099308878685435238780773970900824}{8727963568087712425891397479476727340041449}$$

Express 62500\times \frac{7860601830099308878685435238780773970900824}{8727963568087712425891397479476727340041449} as a single fraction.

$$\frac{62500\times 7860601830099308878685435238780773970900824}{8727963568087712425891397479476727340041449}$$

Multiply 62500 and 7860601830099308878685435238780773970900824 to get 491287614381206804917839702423798373181301500000.

$$\frac{491287614381206804917839702423798373181301500000}{8727963568087712425891397479476727340041449}$$

Factor

$$\frac{7 \cdot 11 \cdot 13 \cdot 31 \cdot 61 \cdot 97 \cdot 181 \cdot 1151 \cdot 1201 \cdot 2029 \cdot 104491 \cdot 463741 \cdot 217538003281 \cdot 2 ^ {5} \cdot 5 ^ {6}}{3 ^ {90}} = 56288\frac{8.001060685630728 \times 10^{42}}{8.727963568087711 \times 10^{42}} = 56288.91671563741$$