Solve 5000^left(1+frac{0.06^4right)}^20

$${ 5000 }^{ } { \left(1+ \frac{ { 0.06 }^{ } }{ 4 } \right) }^{ 20 }$$

Evaluate

$$6734.275032750280188002965088812050574688459587574005126953125$$

Solution Steps

Calculate 5000 to the power of 1 and get 5000.

$$5000\left(1+\frac{0.06^{1}}{4}\right)^{20}$$

Calculate 0.06 to the power of 1 and get 0.06.

$$5000\left(1+\frac{0.06}{4}\right)^{20}$$

Expand \frac{0.06}{4} by multiplying both numerator and the denominator by 100.

$$5000\left(1+\frac{6}{400}\right)^{20}$$

Reduce the fraction \frac{6}{400} to lowest terms by extracting and canceling out 2.

$$5000\left(1+\frac{3}{200}\right)^{20}$$

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

$$5000\times \left(\frac{203}{200}\right)^{20}$$

Calculate \frac{203}{200} to the power of 20 and get \frac{14122798353482315596830794241932369486809052401}{10485760000000000000000000000000000000000000000}.

$$5000\times \frac{14122798353482315596830794241932369486809052401}{10485760000000000000000000000000000000000000000}$$

Multiply 5000 and \frac{14122798353482315596830794241932369486809052401}{10485760000000000000000000000000000000000000000} to get \frac{14122798353482315596830794241932369486809052401}{2097152000000000000000000000000000000000000}.

$$\frac{14122798353482315596830794241932369486809052401}{2097152000000000000000000000000000000000000}$$

Factor

$$\frac{7 ^ {20} \cdot 29 ^ {20}}{2 ^ {57} \cdot 5 ^ {36}} = 6734\frac{5.767854823143072 \times 10^{41}}{2.097152 \times 10^{42}} = 6734.27503275028$$