Determining Voltage gain in a BJT amplifier
The only thing you seem to be forgetting is that the BJT gain is not the system gain. System gain is Vout / Vsig. But the BJT gain must be applied to the base voltage, not to Vsig.

You yourself computed the BJT gain as around 99 V/V. I am not double-checking that. Hopefully it is correct. But the base voltage can be computed using the votlage divider rule. First, we need Rpi, the resistance looking into the base. That is given by re * beta. Beta is given as 100, and re can be computed using Vt/Ic = 52. So Rpi is 5200.

The way I was taught to solve these problems is to view them as a series of gains which are multiplied together. The gain of the voltage divider formed by Rsig and Rpi is Rpi / (Rsig + Rpi). That is 2500 / (2500 + 5200) = 0.67. The gain from base to collector is -99.2 (per your calculation).

So the system gain is Vout/Vsig = 0.67 * -99 = -67 V/V.

Hope that helps. Let me know if I am wrong about anything.