A lender offers you a mortgage interest rate based upon a number of factors, but by far the most important is the secondary market for mortgages. Banks typically sell their mortgages to aggregators like Fannie Mae and Freddie Mac, which are government-sponsored enterprises that buy and repackage mortgages. Aggregators issue mortgage-backed bonds to investors in the secondary market. The daily fluctuations of supply and demand affect the interest rates investors require to buy these bonds. As the economy strengthens, investors require a higher interest rate on bonds because of growing competition for their investment dollars. Banks peg their mortgage interest rates to the daily interest rate on mortgage-backed bonds in the secondary market.
Typically your lender will want to see a couple of months of mortgage payments in reserves. A lender does not want to give a mortgage loan to someone who is depleting all of their savings to qualify. The more reserves you have the better. Having a large amount of savings can sometimes make it a little easier to qualify for a mortgage. A large amount of reserves is seen as a compensating factor, it could help make up for having flawed credit.