I don't get the question. This probably varies wildly based on bank, etc...
Generally, for most banks, no. It's a seperate thing. They approve for 18k means you can max get 18k. However you can buy a car valued (usually NADA Retail or equivalent) at 16,400 and finance upto 18k. Usually people would buy the car for 16.4k (valued at 16.4k) and roll-in taxes and tags, dealer extras like warranty/gap (gap is usually a ripoff at the dealer, try your insr company) into the loan...typically why lenders allow 110% LTV.
But as I said you can't do the reverse with most banks. That is buy a car valued at 20k, finance 1.1*18k (your approval) of it.
Best to probably call your bank, but what bank is this?
