Solve 5700(1+.052/12)^(12)(3)

$$5700 ( 1 + \frac { .052 } { 12 } ) ^ { ( 12 ) ( 3 ) }$$

Evaluate

$$\frac{3332133103739854463733016283011562187986311408157796148712509906113662489591237676263899411298251639610893979776799517998366179}{500315450989997070000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}\approx 6660.064359688$$

Solution Steps

Expand \frac{0.052}{12} by multiplying both numerator and the denominator by 1000.

$$5700\left(1+\frac{52}{12000}\right)^{12\times 3}$$

Reduce the fraction \frac{52}{12000} to lowest terms by extracting and canceling out 4.

$$5700\left(1+\frac{13}{3000}\right)^{12\times 3}$$

Add 1 and \frac{13}{3000} to get \frac{3013}{3000}.

$$5700\times \left(\frac{3013}{3000}\right)^{12\times 3}$$

Multiply 12 and 3 to get 36.

$$5700\times \left(\frac{3013}{3000}\right)^{36}$$

Calculate \frac{3013}{3000} to the power of 36 and get \frac{175375426512623919143842962263766430946647968850410323616447889795455920504801982961257863752539559979520735777726290420966641}{150094635296999121000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$5700\times \frac{175375426512623919143842962263766430946647968850410323616447889795455920504801982961257863752539559979520735777726290420966641}{150094635296999121000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Multiply 5700 and \frac{175375426512623919143842962263766430946647968850410323616447889795455920504801982961257863752539559979520735777726290420966641}{150094635296999121000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000} to get \frac{3332133103739854463733016283011562187986311408157796148712509906113662489591237676263899411298251639610893979776799517998366179}{500315450989997070000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}.

$$\frac{3332133103739854463733016283011562187986311408157796148712509906113662489591237676263899411298251639610893979776799517998366179}{500315450989997070000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000}$$

Factor

$$\frac{19 \cdot 23 ^ {36} \cdot 131 ^ {36}}{2 ^ {106} \cdot 3 ^ {35} \cdot 5 ^ {106}} = 6660\frac{3.2200146474505624 \times 10^{121}}{5.003154509899971 \times 10^{122}} = 6660.064359688295$$