Solve (1+1.5%)^12-1/15%

$$\frac { ( 1 + 1.5 \% ) ^ { 12 } - 1 } { 15 \% }$$

Evaluate

$$1.3041211430769016770752673193359375$$

Solution Steps

Expand \frac{1.5}{100} by multiplying both numerator and the denominator by 10.

$$\frac{\left(1+\frac{15}{1000}\right)^{12}-1}{\frac{15}{100}}$$

Reduce the fraction \frac{15}{1000} to lowest terms by extracting and canceling out 5.

$$\frac{\left(1+\frac{3}{200}\right)^{12}-1}{\frac{15}{100}}$$

Add 1 and \frac{3}{200} to get \frac{203}{200}.

$$\frac{\left(\frac{203}{200}\right)^{12}-1}{\frac{15}{100}}$$

Calculate \frac{203}{200} to the power of 12 and get \frac{4897252030306448390395044241}{4096000000000000000000000000}.

$$\frac{\frac{4897252030306448390395044241}{4096000000000000000000000000}-1}{\frac{15}{100}}$$

Subtract 1 from \frac{4897252030306448390395044241}{4096000000000000000000000000} to get \frac{801252030306448390395044241}{4096000000000000000000000000}.

$$\frac{\frac{801252030306448390395044241}{4096000000000000000000000000}}{\frac{15}{100}}$$

Reduce the fraction \frac{15}{100} to lowest terms by extracting and canceling out 5.

$$\frac{\frac{801252030306448390395044241}{4096000000000000000000000000}}{\frac{3}{20}}$$

Divide \frac{801252030306448390395044241}{4096000000000000000000000000} by \frac{3}{20} by multiplying \frac{801252030306448390395044241}{4096000000000000000000000000} by the reciprocal of \frac{3}{20}.

$$\frac{801252030306448390395044241}{4096000000000000000000000000}\times \frac{20}{3}$$

Multiply \frac{801252030306448390395044241}{4096000000000000000000000000} and \frac{20}{3} to get \frac{267084010102149463465014747}{204800000000000000000000000}.

$$\frac{267084010102149463465014747}{204800000000000000000000000}$$

Factor

$$\frac{3 \cdot 13 \cdot 19 \cdot 31 \cdot 73 \cdot 281 \cdot 2137 \cdot 40609 \cdot 22600297 \cdot 17 ^ {2}}{2 ^ {34} \cdot 5 ^ {23}} = 1\frac{6.228401010214945 \times 10^{25}}{2.0479999999999996 \times 10^{26}} = 1.3041211430769017$$