Solve 5000*left(1+0.023right)^200.023/left(1+0.023right)^20-1

$$5000 \times \frac{ { \left( 1+0.023 \right) }^{ 20 } 0.023 }{ { \left( 1+0.023 \right) }^{ 20 } -1 }$$

Evaluate

$$\frac{7879210053475856694256321196399307683387250214035356018176005}{25036609160659623428315836490428762464236958382916139288487}\approx 314.707554961$$

Solution Steps

Add 1 and 0.023 to get 1.023.

$$5000\times \frac{1.023^{20}\times 0.023}{\left(1+0.023\right)^{20}-1}$$

Calculate 1.023 to the power of 20 and get 1.575842010695171338851264239279861536677450042807071203635201.

$$5000\times \frac{1.575842010695171338851264239279861536677450042807071203635201\times 0.023}{\left(1+0.023\right)^{20}-1}$$

Multiply 1.575842010695171338851264239279861536677450042807071203635201 and 0.023 to get 0.036244366245988940793579077503436815343581350984562637683609623.

$$5000\times \frac{0.036244366245988940793579077503436815343581350984562637683609623}{\left(1+0.023\right)^{20}-1}$$

Add 1 and 0.023 to get 1.023.

$$5000\times \frac{0.036244366245988940793579077503436815343581350984562637683609623}{1.023^{20}-1}$$

Calculate 1.023 to the power of 20 and get 1.575842010695171338851264239279861536677450042807071203635201.

$$5000\times \frac{0.036244366245988940793579077503436815343581350984562637683609623}{1.575842010695171338851264239279861536677450042807071203635201-1}$$

Subtract 1 from 1.575842010695171338851264239279861536677450042807071203635201 to get 0.575842010695171338851264239279861536677450042807071203635201.

$$5000\times \frac{0.036244366245988940793579077503436815343581350984562637683609623}{0.575842010695171338851264239279861536677450042807071203635201}$$

Expand \frac{0.036244366245988940793579077503436815343581350984562637683609623}{0.575842010695171338851264239279861536677450042807071203635201} by multiplying both numerator and the denominator by 1000000000000000000000000000000000000000000000000000000000000000.

$$5000\times \frac{36244366245988940793579077503436815343581350984562637683609623}{575842010695171338851264239279861536677450042807071203635201000}$$

Reduce the fraction \frac{36244366245988940793579077503436815343581350984562637683609623}{575842010695171338851264239279861536677450042807071203635201000} to lowest terms by extracting and canceling out 23.

$$5000\times \frac{1575842010695171338851264239279861536677450042807071203635201}{25036609160659623428315836490428762464236958382916139288487000}$$

Multiply 5000 and \frac{1575842010695171338851264239279861536677450042807071203635201}{25036609160659623428315836490428762464236958382916139288487000} to get \frac{7879210053475856694256321196399307683387250214035356018176005}{25036609160659623428315836490428762464236958382916139288487}.

$$\frac{7879210053475856694256321196399307683387250214035356018176005}{25036609160659623428315836490428762464236958382916139288487}$$