# How do interest rates work?

My question is very simple. I am considering a CD for my money, but I don't know a whole lot of the financial math that goes into that kind of stuff. My question is about interests rates. Do CD's make more money with higher interest rates, or is it the other way around? Could someone please explain to me how interest rates work?

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Could someone please explain to me how interest rates work?

I like to think of interest rates as the price of money. It is specified as a percentage paid per unit of time (for example, 3%/year). To figure out how much interest money you get (or have to pay) for a given amount and time, multiply the amount with the interest rate and then divide by the time divided by the interest rate's specified time. That sounds awfully complicated, so let's look at a simple example instead.

You deposit $1,000 at a fixed interest rate of 2% per year, for two and a half years, where the interest is paid at the end of the term. This means that you earn$1,000 * 2% = $20 per year in interest. Multiply this by [2.5 years] / [year] = 2.5, and you will have received$20 * 2.5 = $50 in interest over 2.5 years. If the interest is paid yearly, this gets slightly more complicated, but the principle is the same. Now imagine that you deposit$5,000 at a fixed 3% per year, for half a year. Again, the interest is paid at the end of the term. You now earn $5,000 * 3% [per year] * [[0.5 years] / [year]] =$75 in interest over six months.

Variable interest rates makes this a little more complicated, but it is exactly the same thing in principle: calculate the interest paid for each period (taking any compounding into account), then add up all periods to get the total amount of interest paid over time.

It also works the same way if you take out a loan rather than depositing money.

Tax effects (capitals gains taxes or interest expense deductions) may make the actual amount paid or received different, but that does not change the fundamental aspect of how to calculate interest.

Do CD's make more money with higher interest rates, or is it the other way around?

Usually fixed interest rate instruments such as certificates of deposit, or loans with fixed rates, pay a higher interest rate for longer terms. This is because it is harder to judge credit risk in a longer term, so whoever gives the loan usually wants a premium for the additional risk. So a 6-month CD will normally pay a smaller percentage interest per year than a five-year CD. Note that this is not always the case; the technical term for when this does not hold is inverted yield curve.

Interest rates are almost always formally specified in terms of percent per year, which makes it easy to compare rates. If you buy a $100 6-month CD paying 1% (I told you these were only examples :)) and then reinvest the money at the end of the term in another 6-month CD also paying 1%, the total amount paid will be ($100 * 1 + (1% * 6/12)) = $100.50 for the first term, then ($100.50 * 1 + (1% * 6/12)) = $101.0025 at the end of the second term. As you can see, the compounding of the interest makes this return slightly more than a single$100 12-month CD ($100 * 1 + 1% =$101), but unless you are dealing with large amounts of money, the difference is small enough to be negligible.

If you were to put $100 in a 2% one-year CD, you'd get back$102 at the end of the year. Put the same amount in a 5% one-year CD, and you get back \$105. So yes, higher interest rates means more interest money paid, for loans as well as deposits. Keep in mind that loans and deposits really are essentially the same thing, and interest calculations work the same way for both.

The interest rate of a normal certificate of deposit does not change if the variable interest rates change, but rather is locked in when the money is deposited (or the CD is bought, whichever way you prefer to look at it).

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+1 a beautiful lecture on something many of us take granted. –  JoeTaxpayer Feb 1 '13 at 15:47
Thank you @JoeTaxpayer –  Michael Kjörling Feb 1 '13 at 22:31
The 6-month versus 12-month CD example is not quite correct in that the interest rates do not specify the frequency of compounding. I seem to remember that the IRS insists (or maybe used to insist) that for CDs with duration longer than three months, the interest must be compounded quarterly or at least reported as being "paid" quarterly so that with a one-year CD issued before October 1, at least one quarter's interest was taxable income for that year. If the 1% interest is compounded quarterly (or semi-annually), there is no difference between two successive 6-month CDs and the 1-year CD. –  Dilip Sarwate Feb 13 '14 at 16:43
@DilipSarwate You are correct in that interest compounding complicates the issue, but I explicitly mentioned that even before today's edit. And what a US government agency might or might not say about interest payments reporting does not change what interest is or how it is calculated, which is more along the lines of what the question is about. (The question does not specify a locale, and the OP's profile gives nothing else to go on and currently little hope of clarification.) –  Michael Kjörling Feb 13 '14 at 20:43