Solve 5/left(1+0.05right)^1+5/left(1+0.05right)^2+5/left(1+0.05right)^3+5/left(1+0.05right)^4+frac{100}{{left(1+0.05right)}^4}

$$\frac{ 5 }{ { \left(1+0.05 \right) }^{ 1 } } + \frac{ 5 }{ { \left(1+0.05 \right) }^{ 2 } } + \frac{ 5 }{ { \left(1+0.05 \right) }^{ 3 } } + \frac{ 5 }{ { \left(1+0.05 \right) }^{ 4 } } + \frac{ 100 }{ { \left(1+0.05 \right) }^{ 4 } }$$

Evaluate

$$100$$

Solution Steps

Add 1 and 0.05 to get 1.05.

$$\frac{5}{1.05^{1}}+\frac{5}{\left(1+0.05\right)^{2}}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Calculate 1.05 to the power of 1 and get 1.05.

$$\frac{5}{1.05}+\frac{5}{\left(1+0.05\right)^{2}}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Expand \frac{5}{1.05} by multiplying both numerator and the denominator by 100.

$$\frac{500}{105}+\frac{5}{\left(1+0.05\right)^{2}}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Reduce the fraction \frac{500}{105} to lowest terms by extracting and canceling out 5.

$$\frac{100}{21}+\frac{5}{\left(1+0.05\right)^{2}}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Add 1 and 0.05 to get 1.05.

$$\frac{100}{21}+\frac{5}{1.05^{2}}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Calculate 1.05 to the power of 2 and get 1.1025.

$$\frac{100}{21}+\frac{5}{1.1025}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Expand \frac{5}{1.1025} by multiplying both numerator and the denominator by 10000.

$$\frac{100}{21}+\frac{50000}{11025}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Reduce the fraction \frac{50000}{11025} to lowest terms by extracting and canceling out 25.

$$\frac{100}{21}+\frac{2000}{441}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Add \frac{100}{21} and \frac{2000}{441} to get \frac{4100}{441}.

$$\frac{4100}{441}+\frac{5}{\left(1+0.05\right)^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Add 1 and 0.05 to get 1.05.

$$\frac{4100}{441}+\frac{5}{1.05^{3}}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Calculate 1.05 to the power of 3 and get 1.157625.

$$\frac{4100}{441}+\frac{5}{1.157625}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Expand \frac{5}{1.157625} by multiplying both numerator and the denominator by 1000000.

$$\frac{4100}{441}+\frac{5000000}{1157625}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Reduce the fraction \frac{5000000}{1157625} to lowest terms by extracting and canceling out 125.

$$\frac{4100}{441}+\frac{40000}{9261}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Add \frac{4100}{441} and \frac{40000}{9261} to get \frac{126100}{9261}.

$$\frac{126100}{9261}+\frac{5}{\left(1+0.05\right)^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Add 1 and 0.05 to get 1.05.

$$\frac{126100}{9261}+\frac{5}{1.05^{4}}+\frac{100}{\left(1+0.05\right)^{4}}$$

Calculate 1.05 to the power of 4 and get 1.21550625.

$$\frac{126100}{9261}+\frac{5}{1.21550625}+\frac{100}{\left(1+0.05\right)^{4}}$$

Expand \frac{5}{1.21550625} by multiplying both numerator and the denominator by 100000000.

$$\frac{126100}{9261}+\frac{500000000}{121550625}+\frac{100}{\left(1+0.05\right)^{4}}$$

Reduce the fraction \frac{500000000}{121550625} to lowest terms by extracting and canceling out 625.

$$\frac{126100}{9261}+\frac{800000}{194481}+\frac{100}{\left(1+0.05\right)^{4}}$$

Add \frac{126100}{9261} and \frac{800000}{194481} to get \frac{3448100}{194481}.

$$\frac{3448100}{194481}+\frac{100}{\left(1+0.05\right)^{4}}$$

Add 1 and 0.05 to get 1.05.

$$\frac{3448100}{194481}+\frac{100}{1.05^{4}}$$

Calculate 1.05 to the power of 4 and get 1.21550625.

$$\frac{3448100}{194481}+\frac{100}{1.21550625}$$

Expand \frac{100}{1.21550625} by multiplying both numerator and the denominator by 100000000.

$$\frac{3448100}{194481}+\frac{10000000000}{121550625}$$

Reduce the fraction \frac{10000000000}{121550625} to lowest terms by extracting and canceling out 625.

$$\frac{3448100}{194481}+\frac{16000000}{194481}$$

Add \frac{3448100}{194481} and \frac{16000000}{194481} to get 100.

$$100$$

Factor

$$2^{2}\times 5^{2}$$