The demand of bitcoin will increase with time as more institutions decide to embrace ~(bitcoin) as a payment method. As the demand starts to increase then you can be rest assured that the value of bitcoin will also increase.
this part is correct, as demand increases the price goes up since the supply is capped. but your title is completely wrong. price and how it increases has nothing to do with when the whole 21 million will be mined. we may reach mass adoption in 2-3 years and price stops having major rises after that which is a long ways before the 21 million (just an example) or it can take 20 years or 50,...
a common misunderstanding these days is that people forget that it is called supply AND demand not just supply on its own.