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The more often the interest compounds in an account, the more interest you'll ultimately receive. Daily compounding means you get "paid" your interest every day — 365 days a year. Quarterly compounding means you get paid just four times a year, every three months. That might seem like a big difference, but in practice, it is often almost negligible.
"Compound interest" refers to interest that gets added to the principal balance of an account, so that the interest itself begins to earns interest. Say you had $1,000 in an account that earns 2 percent interest a year, and interest was paid just once a year. After a year, you'd have earned $20 in interest. If it's compound interest, that $20 goes into your account. Your new balance is $1,020. In the next year, you earn 2 percent of that, or $20.40. Your new balance is $1,040.40, and now you earn 2 percent of that amount, and so on. Compounding is the act of adding the earned interest into the account. The alternative to compound interest is simple interest, in which you receive interest but that money doesn't get added into the principal. In the example above, the balance would stay at $1,000, and you'd get a check for $20 every year.
When discussing compound interest accounts, it's critical to understand the difference between accrual and compounding. Accrual is the schedule by which accounts actually earn interest. Compounding is the schedule by which the earned interest gets added into an account. U.S. bank accounts typically accrue interest on a daily basis, but they may differ in their compounding schedules. Imagine two accounts that pay 2 percent interest a year. Both accrue daily, but one compounds daily while the other compounds semiannually. With a 2 percent annual rate, each pays a daily interest rate of about 0.00548 percent. Now say you have $1,000 in each account. After one day, each account has earned about 5 cents in interest. The daily compounding account adds the interest to the principal immediately, so that the balance is $1,000.05. In the quarterly compounding account, though, the balance remains $1,000; the 5 cents is essentially "set aside" until the next compounding date, when three months' worth of earned interest will be dropped into the account all at once.
Because daily interest accruals are so small — in the example above, less than one-hundredth of one percentage point — the practical difference between interest that compounds daily and interest that compounds quarterly is actually quite slim. Over the course of a year, $1,000 in an account that pays 2 percent interest, accrued and compounded daily, will grow to $1,020.20. In the account that compounds quarterly, it will grow to $1,020.15. The difference: a nickel.
The more often an account compounds interest, the better, since it gets your interest earning its own interest as quickly as possible. Even a nickel is still money, after all. But unless you have large amounts of money involved, like six or seven figures, the difference may amount to pocket change.