Question: I am a retiree with a lot of money in certificates of deposit. Since a bank that offers the highest interest rate at one time often doesn’t offer the best rate later, I now have CDs at eight different banks, which is very inconvenient. A little bank in my neighborhood currently offers 5.3 percent while one of the large area banks pays just 4.8 percent. Why is there so much difference?

Answer: The variation does seem baffling sometimes.

In fact, I can top your story. A couple of weeks ago I opened a custodial savings account for my 12-year-old son, Dash, who had accumulated $600 after years of hoarding his allowance and birthday and Christmas gifts.

We drove over to the local branch of my bank, did all the paperwork and handed over his wad of cash.

Only then did I think to ask about the interest rate. We were told the account would pay a whopping 0.25 percent.

I’d expected the rate on such a small account would be inconsequential, and the main reason for opening the account was to keep my son’s money safe. But a quarter of a percentage point? The account would earn just $1.50 over the next year.

Meanwhile, the bank is charging more than 6 percent on a traditional 30-year, fixed-rate mortgage.

When we got home, we poked around on the Internet and found that Ing Bank, which operates only on the Web, pays 4.5 percent on savings accounts and has no minimum deposit.

You can guess what we decided to do.

In an age of lightning-fast communication and global competition, you’d expect interest rates on similar accounts to settle into a very narrow range. How can my bank compete for savings accounts if it won’t match the competition?

It’s not trying to. It’s just not interested in my son’s $600 – or in any account this small.

Imagine that the bank lent Dash’s $600 to a homebuyer taking out a 6 percent mortgage. The bank would collect $36 a year. It would spend about $5 a year mailing Dash his monthly statements. The statements would cost something to produce.

The bank must pay the tellers who will handle Dash’s deposits and withdrawals. The branch office has to be maintained, the lawn mowed and sidewalks shoveled. …

It just doesn’t pay for the bank to have such dinky accounts. It offers them anyway because some customers who want small savings accounts also have, or may someday have, other accounts that are more profitable for the bank.

Ing and other pure online banks are able to offer higher rates because they don’t have all those branch buildings to maintain.

By offering a near-zero interest rate on savings accounts, my bank encourages us to open some other type of account, such as a CD. At this bank, those require a $1,000 minimum.

For the bank, the CDs are preferable because the money is tied up for a known period of months or years. That way the bank can lend it out without worrying the depositor will demand it back at a moment’s notice.

But to your question: Why do CD rates vary so much from one institution to another?

Because sometimes they want your money and sometimes they don’t.

If the bank is approving mortgages or car loans like hotcakes, it may be willing to pay higher savings rates to bring in the cash to lend. But if the lending business is slow, the bank doesn’t want to sign up new savers. The new cash could sit around earning nothing, and the bank would have to pay interest on it.

At other times, the bank may offer attractive savings rates because it’s going to try to push the new customers to other, profitable lines of business. It could try to sell them mortgages, or urge them to open brokerage accounts or invest in the bank’s mutual funds.

It’s all more complicated than I’ve described, but you get the idea.

Unfortunately, that doesn’t ease your headaches. To get the highest rates, there’s no alternative to shopping around. And that may well leave you with accounts at numerous institutions.

If you can, shop on the Internet. You can compare rates on all sorts of bank products at www.bankrate.com.