Solve 20000/left(1+0.14right)^1+50000/left(1+0.14right)^2+50000^/left(1+0.14right)^3+25000/{left(1+0.14right)^4}-100000

$$\frac{ 20000 }{ { \left(1+0.14 \right) }^{ 1 } } + \frac{ 50000 }{ { \left(1+0.14 \right) }^{ 2 } } + \frac{ { 50000 }^{ } }{ { \left(1+0.14 \right) }^{ 3 } } + \frac{ 25000 }{ { \left(1+0.14 \right) }^{ 4 } } -100000$$

Evaluate

$$\frac{48217900000}{10556001}\approx 4567.818816993$$

Solution Steps

Add 1 and 0.14 to get 1.14.

$$\frac{20000}{1.14^{1}}+\frac{50000}{\left(1+0.14\right)^{2}}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Calculate 1.14 to the power of 1 and get 1.14.

$$\frac{20000}{1.14}+\frac{50000}{\left(1+0.14\right)^{2}}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Expand \frac{20000}{1.14} by multiplying both numerator and the denominator by 100.

$$\frac{2000000}{114}+\frac{50000}{\left(1+0.14\right)^{2}}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Reduce the fraction \frac{2000000}{114} to lowest terms by extracting and canceling out 2.

$$\frac{1000000}{57}+\frac{50000}{\left(1+0.14\right)^{2}}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Add 1 and 0.14 to get 1.14.

$$\frac{1000000}{57}+\frac{50000}{1.14^{2}}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Calculate 1.14 to the power of 2 and get 1.2996.

$$\frac{1000000}{57}+\frac{50000}{1.2996}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Expand \frac{50000}{1.2996} by multiplying both numerator and the denominator by 10000.

$$\frac{1000000}{57}+\frac{500000000}{12996}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Reduce the fraction \frac{500000000}{12996} to lowest terms by extracting and canceling out 4.

$$\frac{1000000}{57}+\frac{125000000}{3249}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Add \frac{1000000}{57} and \frac{125000000}{3249} to get \frac{182000000}{3249}.

$$\frac{182000000}{3249}+\frac{50000^{1}}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Calculate 50000 to the power of 1 and get 50000.

$$\frac{182000000}{3249}+\frac{50000}{\left(1+0.14\right)^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Add 1 and 0.14 to get 1.14.

$$\frac{182000000}{3249}+\frac{50000}{1.14^{3}}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Calculate 1.14 to the power of 3 and get 1.481544.

$$\frac{182000000}{3249}+\frac{50000}{1.481544}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Expand \frac{50000}{1.481544} by multiplying both numerator and the denominator by 1000000.

$$\frac{182000000}{3249}+\frac{50000000000}{1481544}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Reduce the fraction \frac{50000000000}{1481544} to lowest terms by extracting and canceling out 8.

$$\frac{182000000}{3249}+\frac{6250000000}{185193}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Add \frac{182000000}{3249} and \frac{6250000000}{185193} to get \frac{16624000000}{185193}.

$$\frac{16624000000}{185193}+\frac{25000}{\left(1+0.14\right)^{4}}-100000$$

Add 1 and 0.14 to get 1.14.

$$\frac{16624000000}{185193}+\frac{25000}{1.14^{4}}-100000$$

Calculate 1.14 to the power of 4 and get 1.68896016.

$$\frac{16624000000}{185193}+\frac{25000}{1.68896016}-100000$$

Expand \frac{25000}{1.68896016} by multiplying both numerator and the denominator by 100000000.

$$\frac{16624000000}{185193}+\frac{2500000000000}{168896016}-100000$$

Reduce the fraction \frac{2500000000000}{168896016} to lowest terms by extracting and canceling out 16.

$$\frac{16624000000}{185193}+\frac{156250000000}{10556001}-100000$$

Add \frac{16624000000}{185193} and \frac{156250000000}{10556001} to get \frac{1103818000000}{10556001}.

$$\frac{1103818000000}{10556001}-100000$$

Subtract 100000 from \frac{1103818000000}{10556001} to get \frac{48217900000}{10556001}.

$$\frac{48217900000}{10556001}$$

Factor

$$\frac{482179 \cdot 2 ^ {5} \cdot 5 ^ {5}}{3 ^ {4} \cdot 19 ^ {4}} = 4567\frac{8643433}{10556001} = 4567.818816993291$$