A certificate of deposit is like a vomited savings account. Imagine that set of financial institutions in an economy with a reasonably well developed financial industry, which offer their own customers a savings account. The rate the customer gets is partly by virtue of them having an ongoing relationship with that financial institution. It is also a function of the funding cost for that financial institution. They'll put in a profit margin on top of their own funding cost and call that the savings rate. This they then pay you.
Time deposits are the placing of your money with a financial institution for a fixed period of time. You're not supposed to withdraw your money before a certain agreed maturity, and if you do, you face financial penalties which will probably wipe out most of your anticipated returns. Again, your local friendly bank will be only too happy to take your money off you for a fixed period of time (and will reward you with a slightly higher rate of return for the discipline you show in not asking for it back before maturity).
This financial institution is probably signed up to some kind of deposit insurance scheme run by a central banking authority on behalf of the domestic government of the economic region, which means that some of the money it could have lent to you has to go to pay this government bill.
Also, the saver will get his money plus interest back at expiry, and not before (unless he presses a big red button and invokes a get-out clause which will probably cost him the majority of his accrued interest, up to 6 months worth for longer dated CDs). The issuer can also set up a regular CD which pays interest on a schedule. Now, a CD is just something quite like one of those bank savings accounts except you don't need to be a customer of that bank in the same way as you do with the savings account. If the bank savings account is a bit like a steady relationship, then a certificate of deposit is a one night stand. (Or one month, or three months, or half a year or a year, and on up to five years). Another simile is to consider a regular savings account as some food digesting in a human belly, and the CD as food vomited up into a sick bag. There's a degree of distance implied in having a CD with a financial institution. Whereas the internal bank savings account is a bit of a black box, CDs are on their way to being an external market. You can certainly shop around, but it is possible to make ready comparisons of various CD rates. Ceteris paribis, you will expect to get a better rate with smaller, riskier CD issuers, and when you lend larger sums, and when you are lending on a five year window over the shorter expiries. By the way, these days you don't often get a certificate, just a book entry change in your account.
By tradition, the CD rates tend to compensate you at approximately the current rate of inflation, approximately, meaning you are not actually growing your real wealth, merely allowing it to keep up with inflation. But this is only based on periods of healthy shaped yield curves. In general you're lending to a bank. These days, that's considered a lot more risky than it used to. So there ought to be a risk free and a credit component. In the days pre-crisis, the credit spread would have been quite minimal and so you had a risk free
As you might expect, the usual rules on calculating simple or compound interest apply. Part of what it means to compound is the implicit understanding that you re-invest your interest payments, as soon as you get them.
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