It's very easy to overlook the interest rate for the savings account linked to your checking/debt account. These rates can vary greatly between banks.
A local credit union, which I have an account with for access to cash, has an Annual Percent Yield (APY) of 0.01%. That means for every $100 you have in that account, you'll earn $0.01 in interest for the year.
Online only banks tend to offer much higher rates than their brick and mortar counterparts. Discover Bank is currently offering an APY of 3.70%. That's $3.70 for every $100, or $37 for every $1,000.
Shop around. It's well worth your time!