# Issue with demonstrating amplitude modulation of sinusoid using MatLab

I am trying to demonstrate Conventional and DSB-SC modulation of a signal $$\sin(2\pi1000t)$$ using MatLab. My carrier signal is $$\sin(2\pi f_ct)$$ where $$f_c = 100\text{ MHz}$$. Now according to theory, after modulation, the modulated signal should have a spectrum same as that of message signal shifted to the frequency of carrier on both sides. But I am getting the plot as that of the carrier signal in the frequency domain. This is the code that I am using for DSB-SC modulation

% CODE FOR PLOTTING MESSAGE SIGNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%

Fs = 20*100*10^6/3;
Fm = 1000; %Hz
t = 0:1/Fs:0.005-1/Fs;

Am = 1;

m = Am*sin(2*pi*Fm*t);

temp = size(m);
N = temp(2);

f = -Fs/2:Fs/(N-1):Fs/2;

M = fftshift(fft(m));
figure(1)
plot(f,abs(M))
grid('on')
title('Message signal')
xlabel('Frequency in Hertz')
ylabel('|M(F)|')

% CODE FOR PLOTTING CARRIER SIGNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Fc=100*10^6;%100 MHz

Fs = 20*Fc/3;
Ac = 1;%amplitude
c = Ac*sin(2*pi*Fc*t);

temp = size(c);
N = temp(2);

f = -Fs/2:Fs/(N-1):Fs/2;

C = fftshift(fft(c));
figure(2)
plot(f,abs(C))
grid('on')
title('Carrier signal')
xlabel('Frequency in Hertz')
ylabel('|C(F)|')

% CODE FOR PLOTTING DSB-SC MODUALTED SIGNAL %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

s = Ac*m.*sin(2*pi*Fc*t);

temp = size(s);
N = temp(2);

f = -Fs/2:Fs/(N-1):Fs/2;

S = fftshift(fft(s));
figure(3)
plot(f,abs(S))
grid('on')
title('DSB-SB Modulated signal')
xlabel('Frequency in Hertz')
ylabel('|S(F)|')


And this is the spectrum of $$S(f)$$ in code. As you can see. there are only two peaks, one at $$+f_c$$ and one at $$-f_c$$(not shown in figure). But in reality, it should have been 2 peaks at $$f_c+f_m , f_c-f_m$$ and two peaks at $$-f_c-f_m,-f_c+f_m$$. So what is going wrong here? How can I fix this?