What the relationship between age of gold with gold’s price?

There is absolutely no relation. That is why the gold is precious metal, it does not change over time, it does not rust. Whoever tell you something about “aged” gold bars or gold bullion, they don’t know what they speak about.

Sometimes, non authoritative gold bullion will be re-smelted, refined and hallmarked with new brand, but that does change the price of gold. Most of refineries I know will pay for such gold 99% of the actual gold price.