How can I find the amplitude of the 20 Hz frequency component of a signal faster?
As pichenettes already pointed out in a comment above, one approach is to use the Goertzel algorithm. However, it is a somewhat common misconception that in order to deduce the amplitude of various frequency bands in a signal, one must use Fourier-transform-based techniques. There are other methods that may be more appropriate to your application.

In your case, for example, you would do equally well by just creating any bandpass filter centered at 20 Hz and watching the amplitude of its output over time. The DFT (and by extension the Goertzel algorithm) can be viewed as just a bank of equally-spaced, critically-sampled bandpass filters. If you only need one output, then a DFT is overkill, and the Goertzel algorithm can be limiting, as you don't have much control over its frequency response about 20 Hz.