# Rewards Checking Account Math

Back in July, I debated whether or not to use my credit union’s rewards checking account. I’ve been using it for a few months now for my emergency fund and some other small savings accounts.

So how exactly do these accounts work? Mine works as follows:

• I earn Q% on the first \$M in the account.
• I earn H% on any funds above \$M in the account.
• I need at least one ACH transaction in the qualifying period and D debit card transactions to get the qualify Q% and H% rates. In my calculations, I will assume that this happens.

At first I thought it only made sense to keep \$M of savings in this account, but then I started looking at the math.

These calculations assume that the alternative to placing your savings in the rewards checking account is in an online savings account earning 1.00% or S%.

The base formula for calculating how much you should keep in the rewards checking account beyond \$M is:

(i) \$M x Q% + \$X x H% = (\$M + \$X) x S%

If we solve for \$X, we get:

(ii) \$X = \$M x (Q% – S%) / (S% – H%)

So to maximize the interest on your savings, you should keep \$M + \$X of savings in your rewards checking account.

I was surprised when I ran the numbers on my account – \$X actually turned out to be more than double \$M. But I did the math for both sides of (i) and it was correct.