Hello
I´m little confused of the problem. An amplifier with gain 100 is no match, but what is output waveform of frequency 1 kHz? An amplifier has allways a range of frequencies, i.e. from 50 Hz to 50 kHz.
You can do a 2-stage amplifier with bjt and do a feedback from output to the first transistor emitter. A two stage amplifier has an open loop amplifing of around 1000 (no emitter capacitor at first stage). The feedback resistor should bee 100 times the first transistor emitter resistor. I.e. if the emitter resistor is 1 kohm, the feedback should bee 100 kohm.