Modulation Index of Conventional AM Signal
Modulation index for linear (continuous wave) amplitude modulation may be defined in different ways. But the one I found relevant to your definition is:

$$ \mu = \frac{ | \min \{ m(t) \} | } {A_c} $$

where $A_c$ is the carrier amplitude, $m(t)$ is the message signal and $\mu$ is the modulation index.

For simple demodulation of a conventional AM modulated signal $s(t)$ we look for $\mu &lt; 1$ so that the envelope of $s(t)$ never becomes less than zero.

$$s(t) = [ A_c + m(t) ] \cos(2 \pi f_0 t) $$

Your signal is:
$$ s(t) = [ 100 + 100 \left( ~~\sin(2000 \pi t)+5\cos(4000 \pi t)~~ \right) ] \cos(2 \pi f_c t) $$

Your message signal is:
$$ m(t) = 100 \left( ~~\sin(2000 \pi t)+5\cos(4000 \pi t)~~ \right) $$

whose min value is $-600$ and from which you deduce the modulation index as:

$$ \mu = \frac{ | \min \{ m(t) \} | } {A_c} = \frac{ | -600 | } {100}  = 6 $$

I'm sorry to say but this is severely overmodulated...