Declan has a PAF that includes up to $$5,000$ in coverage for musical instruments. On January $1,$ he bought a brand new oboe for $$4,000.$ Since he was so busy with rehearsals, he never got around to reporting the new instrument to his insurer before the instrument was destroyed in a fire on February $2.$ The oboe had only depreciated $$100$ at the time of the fire. How much will Declan's PAF pay for his destroyed oboe?