Solve 25000/0.08left(1-1/1.08^10right)+500000/1.08^10

$$\frac{ 25000 }{ 0.08 } \left( 1- \frac{ 1 }{ { 1.08 }^{ 10 } } \right) + \frac{ 500000 }{ { 1.08 }^{ 10 } }$$

Evaluate

$$\frac{27407457404065000000}{68630377364883}\approx 399348.779015878$$

Solution Steps

Expand \frac{25000}{0.08} by multiplying both numerator and the denominator by 100.

$$\frac{2500000}{8}\left(1-\frac{1}{1.08^{10}}\right)+\frac{500000}{1.08^{10}}$$

Divide 2500000 by 8 to get 312500.

$$312500\left(1-\frac{1}{1.08^{10}}\right)+\frac{500000}{1.08^{10}}$$

Calculate 1.08 to the power of 10 and get 2.15892499727278669824.

$$312500\left(1-\frac{1}{2.15892499727278669824}\right)+\frac{500000}{1.08^{10}}$$

Expand \frac{1}{2.15892499727278669824} by multiplying both numerator and the denominator by 100000000000000000000.

$$312500\left(1-\frac{100000000000000000000}{215892499727278669824}\right)+\frac{500000}{1.08^{10}}$$

Reduce the fraction \frac{100000000000000000000}{215892499727278669824} to lowest terms by extracting and canceling out 1048576.

$$312500\left(1-\frac{95367431640625}{205891132094649}\right)+\frac{500000}{1.08^{10}}$$

Convert 1 to fraction \frac{205891132094649}{205891132094649}.

$$312500\left(\frac{205891132094649}{205891132094649}-\frac{95367431640625}{205891132094649}\right)+\frac{500000}{1.08^{10}}$$

Since \frac{205891132094649}{205891132094649} and \frac{95367431640625}{205891132094649} have the same denominator, subtract them by subtracting their numerators.

$$312500\times \frac{205891132094649-95367431640625}{205891132094649}+\frac{500000}{1.08^{10}}$$

Subtract 95367431640625 from 205891132094649 to get 110523700454024.

$$312500\times \frac{110523700454024}{205891132094649}+\frac{500000}{1.08^{10}}$$

Express 312500\times \frac{110523700454024}{205891132094649} as a single fraction.

$$\frac{312500\times 110523700454024}{205891132094649}+\frac{500000}{1.08^{10}}$$

Multiply 312500 and 110523700454024 to get 34538656391882500000.

$$\frac{34538656391882500000}{205891132094649}+\frac{500000}{1.08^{10}}$$

Calculate 1.08 to the power of 10 and get 2.15892499727278669824.

$$\frac{34538656391882500000}{205891132094649}+\frac{500000}{2.15892499727278669824}$$

Expand \frac{500000}{2.15892499727278669824} by multiplying both numerator and the denominator by 100000000000000000000.

$$\frac{34538656391882500000}{205891132094649}+\frac{50000000000000000000000000}{215892499727278669824}$$

Reduce the fraction \frac{50000000000000000000000000}{215892499727278669824} to lowest terms by extracting and canceling out 1048576.

$$\frac{34538656391882500000}{205891132094649}+\frac{47683715820312500000}{205891132094649}$$

Since \frac{34538656391882500000}{205891132094649} and \frac{47683715820312500000}{205891132094649} have the same denominator, add them by adding their numerators.

$$\frac{34538656391882500000+47683715820312500000}{205891132094649}$$

Add 34538656391882500000 and 47683715820312500000 to get 82222372212195000000.

$$\frac{82222372212195000000}{205891132094649}$$

Reduce the fraction \frac{82222372212195000000}{205891132094649} to lowest terms by extracting and canceling out 3.

$$\frac{27407457404065000000}{68630377364883}$$

Factor

$$\frac{331 \cdot 1741 \cdot 9512003 \cdot 2 ^ {6} \cdot 5 ^ {7}}{3 ^ {29}} = 399348\frac{53464153705188}{68630377364883} = 399348.7790158784$$