Biasing in this FM transmitter
You used the wrong equation for the base current. The correct one is:

\$ I_B = \frac{V_{CC} - V_{BE}}{(\beta +1)R_1 + R_2} \approx 160\mu A \$

But in your circuit, the situation is more complicated because the MIC will sink current (around of \$ I_{MIC} \approx 500 \mu A\$).

Therefore: 

$$I_B = \frac{(V_{CC} - V_{BE}) - I_{MIC}\cdot R_2}{(\beta +1)R_1 + R_2} \approx 114 \mu A $$ 

For \$\beta = 100\$ and \$V_{BE} = 0.7V\$

Because the base current is lower than the electret microphone current. 
We can neglect the base current and solve for the emitter current directly. 

$$I_E = \frac{V_{CC} -  I_{MIC}\cdot R_2 - V_{BE}}{R_1} \approx 12.7mA$$