Emitter dynamic-resistance (dV/dI) is just 1/transconductance, at least at lower frequencies. At 0.8mA, that is 30 ohms looking into the emitter.

30 ohms and 10uF are 300uS tau, or 33Krad/second / 6.28, or 5KHz. Your midband Freq should be a few octaves above that, e.g. 20KHz, for accurate gain of the bipolar.

Ignoring Vearly effects, bipolar gain is Rc * gm or Rc / reac, 6,800 / 30 = 220.

The opamp, at 20,000Hz, has only 1MHz/20,000Hz = 50x openloop gain. The opamp topology promises 47/1 = 47X but with loop-gain-margin of 50/47 = 1.06 that gain is not really being controlled by the opamp.

Note the computed bipolar gain, times opamp gain, 220 * 50, is 11,000x, only 2dB higher than the "answer".

Emitter dynamic-resistance (dV/dI) is just 1/transconductance, at least at lower frequencies. At 0.8mA, that is 30 ohms looking into the emitter.

30 ohms and 10uF are 300uS tau, or 3.3Krad/second / 6.28, or 500 Hz. Your midband Freq should be a few octaves above that, e.g. 2KHz, for accurate gain of the bipolar.
[ my original answer used 5,000Hz and 20KHz; the ultimate gain only increases 1dB]

Ignoring Vearly effects, bipolar gain is Rc * gm or Rc / reac, 6,800 / 30 = 220.

The opamp, at 2,000Hz, has only 1MHz/2,000Hz = 500x openloop gain. The opamp topology promises 47/1 = 47X but with loop-gain-margin of 500/47 = 10.6 that gain is not being controlled by the opamp; expect gain to 1dB shy of 47.

Note the computed bipolar gain, times opamp gain, 220 * 47, is 10,400x, only 1dB higher than the "answer".