Solve 200*1.06*1.06^10-1/1.06^10/0.06

$$\frac { 200 \times 1.06 \times \frac { 1.06 ^ { 10 } - 1 } { 1.06 ^ { 10 } } } { 0.06 }$$

Evaluate

$$\frac{5148748024367536600}{3299763591802133}\approx 1560.3384549$$

Solution Steps

Multiply 200 and 1.06 to get 212.

$$\frac{212\times \frac{1.06^{10}-1}{1.06^{10}}}{0.06}$$

Calculate 1.06 to the power of 10 and get 1.79084769654285362176.

$$\frac{212\times \frac{1.79084769654285362176-1}{1.06^{10}}}{0.06}$$

Subtract 1 from 1.79084769654285362176 to get 0.79084769654285362176.

$$\frac{212\times \frac{0.79084769654285362176}{1.06^{10}}}{0.06}$$

Calculate 1.06 to the power of 10 and get 1.79084769654285362176.

$$\frac{212\times \frac{0.79084769654285362176}{1.79084769654285362176}}{0.06}$$

Expand \frac{0.79084769654285362176}{1.79084769654285362176} by multiplying both numerator and the denominator by 100000000000000000000.

$$\frac{212\times \frac{79084769654285362176}{179084769654285362176}}{0.06}$$

Reduce the fraction \frac{79084769654285362176}{179084769654285362176} to lowest terms by extracting and canceling out 1024.

$$\frac{212\times \frac{77231220365513049}{174887470365513049}}{0.06}$$

Express 212\times \frac{77231220365513049}{174887470365513049} as a single fraction.

$$\frac{\frac{212\times 77231220365513049}{174887470365513049}}{0.06}$$

Multiply 212 and 77231220365513049 to get 16373018717488766388.

$$\frac{\frac{16373018717488766388}{174887470365513049}}{0.06}$$

Reduce the fraction \frac{16373018717488766388}{174887470365513049} to lowest terms by extracting and canceling out 53.

$$\frac{\frac{308924881462052196}{3299763591802133}}{0.06}$$

Express \frac{\frac{308924881462052196}{3299763591802133}}{0.06} as a single fraction.

$$\frac{308924881462052196}{3299763591802133\times 0.06}$$

Multiply 3299763591802133 and 0.06 to get 197985815508127.98.

$$\frac{308924881462052196}{197985815508127.98}$$

Expand \frac{308924881462052196}{197985815508127.98} by multiplying both numerator and the denominator by 100.

$$\frac{30892488146205219600}{19798581550812798}$$

Reduce the fraction \frac{30892488146205219600}{19798581550812798} to lowest terms by extracting and canceling out 6.

$$\frac{5148748024367536600}{3299763591802133}$$

Factor

$$\frac{11 \cdot 61 \cdot 103 \cdot 151 \cdot 181 \cdot 3191 \cdot 4271 \cdot 2 ^ {3} \cdot 5 ^ {2}}{53 ^ {9}} = 1560\frac{1116821156209672}{3299763591802133} = 1560.3384548999159$$