How much will Litecoin be worth?

Nobody can actually say for sure.

Litecoin increased by +500% since the start of the year, this was down to two things -

SegWit activation - faster transactions (BTC does not currently support)
CoinBase Integration - CoinBase is a regulated platform that is U.S based, they added LTC trading into the mix alongside the pre-existing BTC & ETH.
Litecoin has a ton of updates on their roadmap, a few to outline:

RootStock
Atomic Swaps
DriveChain
I believe that LTC will increase due to uncertainty around the BTC hard fork (1st Aug 2017).

If you’re looking to store your coins safely, I suggest using a hardware wallet, Ledgers are regarded to be the most secure and easy to use.