In basic terms, each bitcoin is currently worth about $1050, so 16 million bitcoins are worth about $17 billion. If you add $10 billion to that, then each bitcoin would be worth about $1690.
The price of bitcoins would increase as you buy more and more, and as the price is increasing, there are other people that are going to buy bitcoins too so they can short trade. Not all of the 16 million bitcoins are on exchange sites or in circulation, there are early investors that are either dead or have already forgotten or lost their private keys.
I don't think there's a single formula to know what would be the price of bitcoin if someone invested x amount simply because at the process of you doing it, there would be people dumping their coins and there would be people buying more coins.