Compounding

Can anyone tell me the meaning of the term "compounding" other than what Reg DD states? I have always thought that it basically meant paying interest on the interest.

You're right. According to Baron's compound interest is "interest added to interest previously earned on a principal balance." Interest can be compounded based on any time increment - annually, quarterly, monthly, daily, continuously.

I hope this helps...

So, Robert, what is your opinion on this: a 10 month CD with interest "compounded" at maturity......the interest is really not paid until maturity......would the APY be the same as the rate or a higher APY?

The disclosure should not mention compounding since it is not done. However, the APY must be calculated using the APY formula, which will assume that interest is credited and rolled into principal at maturity. If one earns $291.51 on a $10,000 3.50% interest rate CD in 10 months (from today, ten months equals 304 days), the APY is

100*[(1+Int/Prin)^(365/304)-1] or 3.51%

And, you should include a statement that the APY assumes that principal and interest remain on deposit for one year.

BWest -

It looks like I didn't correctly answer the question in your first post. I gave the definition for "compound interest" (a noun). The term "compound" (a verb) also includes the definition of compute. Interchanging the word "compute" for "compound" in your last post results in "a 10 month CD with interest computed at maturity." Sorry for the missunderstanding.

I hate math, formulas, etc! Can you take the formula you listed here and tell me in plain english step-by-step just what figures to multiple, divide, add or whatever ? I know.......I am really dumb or maybe just plain brain-dead.

Sure.

1. Calculate the interest to be earned on the account for its entire term. If it's a savings or NOW account (no term), assume one year. This will have to be done with whatever interest payment and compounding routines are applied to the account. Use an arbitary principal amount, but make sure it's larger than $100. Let's assume we use $10,000 for our illustration.
   
2. Divide the amount of interest in step 1 by the principal amount, and add 1. You will have a decimal number greater than 1. If our interest amount was $205.51 and the principal was $10,000, you should now have 1.020551. Don't drop places or round at this stage.
   
3. Count the number of days in the term of the account. If your term is less than one year, you should have fewer than 365 days. If it's more than one year, you should have more than 365 days. I know that's obvious, but some people miss this check. Let's say we're working with ten months, or 304 days from 6/12/2002.
   
4. Divide 365 by the number of days from step 3. If the term was longer than a year, you'll get a decimal that's less than 1. If it's less than a year, you'll get a decimal that's greater than 1. Call this result your "exponent." For our examples, it's 365/304, or 1.2006578.
   
5. This is where you need more than your fingers, toes and long division! Using a financial calculator or a spreadsheet program, take your Step 2 result, and raise it to the power of the exponent from step 4. Your result should still be a decimal, greater than 1, but less than 2. You should at this point have 1.024725.
   
6. OK, now subtract 1. Now you have a decimal that's less than 1. Multiply by 100 and round to two decimal places.
   
7. Voilá! Your answer for this set of numbers is 2.47%.

Easier yet, if you have Excel:

1. Calculate the total interest to be earned as above. Put it in cell A1.
2. Put the principal amount in cell A2.
3. Put the beginning date of the term in cell A3 and the ending date of the term in cell A4.
4. Put in cell A5 the equation =A4-A3.
5. In cell A6, type =ROUND(100*((1+A1/B1)^(365/A5)-1),2)
6. Voilá again!

Well, I have finally answered my own question. I am just plain DUMB. I am no closer in figuring this out than before. There is no plain english to the formula and I don't know how to work Excel. Thanks anyway John!

Ask your bank to send you to an Excel class--it is cheap and easy to learn. In the mean time, you could ask John to email you his Excel spreadsheet. If you do not have Excel, then get out a pencil Pythagorus.

I see from your profile that you are an attorney. No wonder your mom " may not necessarily agree with your opinion"! Just kidding you zaibatsu.......got to laugh to keep from going crazy!

bwest, just bluff.

If anyone persists in defining compounding, go into a Cliff Claven routine from Cheers. "Back in ancient Egypy they had more sand than dirt so they'd trade dirt and use it as barter. The more dirt you had, the more you had to compound it into buckets to carry. So you had dirt on dirt and had more than when you started." Or maybe not.

Is it Friday yet?

Since I am not working tomorrow, today is my Friday and I will share my favorite Clavenism:

Well you see, Norm, it's like this...A herd of buffalo can only move as fast as the slowest buffalo. And when the herd is hunted, it is the slowest and weakest ones at the back that are killed first. This natural selection is good for the herd as a whole, because the general speed and health of the whole group keeps improving by the regular killing of the weakest members. In much the same way, the human brain can only operate as fast as the slowest brain cells. Now, as we know, excessive intake of alcohol kills brain cells. But naturally, it attacks the slowest and weakest brain cells first. In this way, regular consumption of beer eliminates the weaker brain cells, making the brain a faster and more efficient machine. And that, Norm, is why you always feel smarter after a few beers.

Enjoy your weekend--sit back and kill a slow, weak brain cell. But do so responsibly. You will be smarter for it on Monday.

HAHAHAHAHAHA!!!!!!

That really cute everyone! We WILL survive.
John, I found someone to help me with the Excel but something is wrong with the formula....it shows an error with the 2 you have at the end. Will you please take a look at it?

I think the problem is in step 5. The reference to Cell E1 should be A5.

That didn't work either. Still shows an error.

bwest- Excel is a survival skill for C/Os, so use this as an opportunity to learn as much as you can about this powerful tool. You can easily transfer John's formula & run it by doing the following:
1. go back to his post with the equation, drag across the formula and hit Ctrl C to copy it.
2. open a blank Excel spreadsheet & put your cursor anywhere in the middle of the page.
3. hit the "=" key and then Ctrl V (to paste the formula into the cell you picked.)
4. Excel won't recognize John's square braces, so you need to replace them with parens.
5. somewhere else on the sheet type in (or copy and paste) the principal amount and the interest amount.
6. click the cell where you pasted the formula, drag & highlight just the characters "Int" in the formula and then click the cell where you just typed the interest amount; ditto for "Prin".
7. when done editing the formula, hit Enter & there's your answer!

I think John just got ahead of himself in writing out the Excel formula - it looks like he's referring to cells in columns but the variables are assigned to rows. Try this in A6:

=ROUND(100*((1+A1/A2)^(365/A5)-1),2)

The logic is right on - it's just a matter of writing it out the right way.

Or, just do what Richard says.

Well, yes, I did screw up in using "E1" instead of "A5." I went back and edited it to hide the evidence!

But seriously, do get at least a beginning and intermediate understanding of Excel. Or Lotus 1-2-3 if your shop uses that old standby. They both can handle this APY formula easily.

One of the problems in doing APYs, though, is that you have to remember to start by calculating the interest to be earned in the period. You can't just dump in an interest rate and have the APY come out the other end.