Solve 20.000/(1+0,14)^2+50000/(1+0,14)^2+50.000/(1+0,14)^3+25,000/(1+0,14)^4

$$\frac { 20.000 } { ( 1 + 0,14 ) ^ { 2 } } + \frac { 50000 } { ( 1 + 0,14 ) ^ { 2 } } + \frac { 50.000 } { ( 1 + 0,14 ) ^ { 3 } } + \frac { 25,000 } { ( 1 + 0,14 ) ^ { 4 } }$$

Evaluate

$$\frac{7134100000}{185193}\approx 38522.514349894$$

Solution Steps

Add 1 and 0.14 to get 1.14.

$$\frac{20}{1.14^{2}}+\frac{50000}{\left(1+0.14\right)^{2}}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Calculate 1.14 to the power of 2 and get 1.2996.

$$\frac{20}{1.2996}+\frac{50000}{\left(1+0.14\right)^{2}}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Expand \frac{20}{1.2996} by multiplying both numerator and the denominator by 10000.

$$\frac{200000}{12996}+\frac{50000}{\left(1+0.14\right)^{2}}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Reduce the fraction \frac{200000}{12996} to lowest terms by extracting and canceling out 4.

$$\frac{50000}{3249}+\frac{50000}{\left(1+0.14\right)^{2}}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Add 1 and 0.14 to get 1.14.

$$\frac{50000}{3249}+\frac{50000}{1.14^{2}}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Calculate 1.14 to the power of 2 and get 1.2996.

$$\frac{50000}{3249}+\frac{50000}{1.2996}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

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

$$\frac{50000}{3249}+\frac{500000000}{12996}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

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

$$\frac{50000}{3249}+\frac{125000000}{3249}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Add \frac{50000}{3249} and \frac{125000000}{3249} to get \frac{125050000}{3249}.

$$\frac{125050000}{3249}+\frac{50}{\left(1+0.14\right)^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Add 1 and 0.14 to get 1.14.

$$\frac{125050000}{3249}+\frac{50}{1.14^{3}}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Calculate 1.14 to the power of 3 and get 1.481544.

$$\frac{125050000}{3249}+\frac{50}{1.481544}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Expand \frac{50}{1.481544} by multiplying both numerator and the denominator by 1000000.

$$\frac{125050000}{3249}+\frac{50000000}{1481544}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Reduce the fraction \frac{50000000}{1481544} to lowest terms by extracting and canceling out 8.

$$\frac{125050000}{3249}+\frac{6250000}{185193}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Add \frac{125050000}{3249} and \frac{6250000}{185193} to get \frac{7134100000}{185193}.

$$\frac{7134100000}{185193}+\frac{25\times 0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Multiply 25 and 0 to get 0.

$$\frac{7134100000}{185193}+\frac{0\times 0\times 0}{\left(1+0.14\right)^{4}}$$

Multiply 0 and 0 to get 0.

$$\frac{7134100000}{185193}+\frac{0\times 0}{\left(1+0.14\right)^{4}}$$

Multiply 0 and 0 to get 0.

$$\frac{7134100000}{185193}+\frac{0}{\left(1+0.14\right)^{4}}$$

Add 1 and 0.14 to get 1.14.

$$\frac{7134100000}{185193}+\frac{0}{1.14^{4}}$$

Calculate 1.14 to the power of 4 and get 1.68896016.

$$\frac{7134100000}{185193}+\frac{0}{1.68896016}$$

Zero divided by any non-zero number gives zero.

$$\frac{7134100000}{185193}+0$$

Add \frac{7134100000}{185193} and 0 to get \frac{7134100000}{185193}.

$$\frac{7134100000}{185193}$$

Factor

$$\frac{71341 \cdot 2 ^ {5} \cdot 5 ^ {5}}{3 ^ {3} \cdot 19 ^ {3}} = 38522\frac{95254}{185193} = 38522.51434989444$$