Solve 5000{left(1+.05/12right)}^12*3

$$5000 { \left(1+ \frac{ .05 }{ 12 } \right) }^{ 12 \times 3 }$$

Evaluate

$$\frac{56573563162838304036154442586729060773998588220667529705458026430810720836542285256641}{9741698791694239883101319830790025940713189094195200000000000000000000000000000000}\approx 5807.361156667$$

Solution Steps

Expand \frac{0.05}{12} by multiplying both numerator and the denominator by 100.

$$5000\left(1+\frac{5}{1200}\right)^{12\times 3}$$

Reduce the fraction \frac{5}{1200} to lowest terms by extracting and canceling out 5.

$$5000\left(1+\frac{1}{240}\right)^{12\times 3}$$

Add 1 and \frac{1}{240} to get \frac{241}{240}.

$$5000\times \left(\frac{241}{240}\right)^{12\times 3}$$

Multiply 12 and 3 to get 36.

$$5000\times \left(\frac{241}{240}\right)^{36}$$

Calculate \frac{241}{240} to the power of 36 and get \frac{56573563162838304036154442586729060773998588220667529705458026430810720836542285256641}{48708493958471199415506599153950129703565945470976000000000000000000000000000000000000}.

$$5000\times \frac{56573563162838304036154442586729060773998588220667529705458026430810720836542285256641}{48708493958471199415506599153950129703565945470976000000000000000000000000000000000000}$$

Multiply 5000 and \frac{56573563162838304036154442586729060773998588220667529705458026430810720836542285256641}{48708493958471199415506599153950129703565945470976000000000000000000000000000000000000} to get \frac{56573563162838304036154442586729060773998588220667529705458026430810720836542285256641}{9741698791694239883101319830790025940713189094195200000000000000000000000000000000}.

$$\frac{56573563162838304036154442586729060773998588220667529705458026430810720836542285256641}{9741698791694239883101319830790025940713189094195200000000000000000000000000000000}$$

Factor

$$\frac{241 ^ {36}}{2 ^ {141} \cdot 3 ^ {36} \cdot 5 ^ {32}} = 5807\frac{3.5182794698432063 \times 10^{81}}{9.741698791694242 \times 10^{81}} = 5807.361156667341$$