An audio signal given by $15\mathrm{}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{}2\mathrm{\pi }\mathrm{}\left(2000\mathrm{}\mathrm{t}\right)$ amplitude modulates a sinusoidal carrier wave $60\mathrm{}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{}2\mathrm{\pi }\mathrm{}\left(100000\mathrm{}\mathrm{t}\right).$ Determine
(i) percent modulation
(ii) frequencies of modulating signal and carrier and
(iii) frequency spectrum of the modulated wave.