# Getting compound interest calculation wrong but don't know why

Investopedia says that the formula for compound interest is

Ic = P[(1 + rN) − 1]

Which due to the Order of Operations can be heavily simplified to

Ic = PrN

(and I checked via Wolfram Alpha just to make sure I wasn't forgetting something basic here. Lol.)

Now, the thing Investopedia above just stated right after this is,

"Borrowing \$1,000 at a 6% annual interest rate for 8 months means that you would owe \$40.70."

However, I handwrote it out, calculated it with the basic Win7 `calc.exe`, and calculated it via Wolfram Alpha, but I cannot see what I'm misunderstanding here. No matter what I do, it always comes out as `\$0.000 000 2`, i.e. `0.000 02¢`. Well, considering this is far less than \$40.00, I figured there must be something I'm doing wrong, but I just can't figure it out.

Could you help me out here?

• The exponent N should be outside the brackets, thus invalidating your Order of Operations simplification...Your source is incorrect... – DJohnM Aug 13 '15 at 0:53
• How do you figure that? I mean, look here: the exponent N is very clearly a superscript... :/ – SarahofGaia Aug 13 '15 at 17:27
• @SarahofGaia: It is a superscript, but it should be (1+r)^N, not (1+r^N). It looks like it's just a typo on that page (they're missing a parenthesis). – BrenBarn Aug 13 '15 at 17:38
• I don't understand. How? The parentheses around "interest rate" and "months" merely are annotative parentheses, not mathematical parentheses, and the parentheses that are part of the equation itself show the N being inside the `1 + 4` expression, not outside it. – SarahofGaia Aug 13 '15 at 19:21
• Please see the answer and correct equation below. I'll be kind to Investopedia, and just say "typos happen." – JTP - Apologise to Monica Aug 13 '15 at 19:22

The problem is that your source equation is wrong, and poorly written as well. Let's dissect how bad it is (here's a snip from the web-site)

.

First, the sloppiness. Algebraic symbols should not have explanatory notes added to them by including plain language phrases in brackets. The normal method is to give the algebra, followed by "where P = ..., I = ..., and N = ..."

Secondly, if you insist on this technique, the word "(months)" should be written in superscript font along with N, the variable to which it refers.

Next, the three descriptive phrases used are inconsistent. The first two give the quantity, while the third gives the units for the quantity. Thus, if the interest rate is anything but monthly, the formula is wrong!

Finally, the typo: Because of the stray open and close brackets floating around, the author of the equation placed the exponent N in the wrong position. It should be immediately to the right of the only instance of "))" in the formula.

This is the way to write the equation and explain it -

• DJ - I added a quick image. If the edit was not welcome you can roll it back, but I think it does well to clarify how awful the original equation looked to us. – JTP - Apologise to Monica Aug 13 '15 at 18:59
• @JoeTaxpayer I was dragging the same image back to add it when your edit appeared! – DJohnM Aug 13 '15 at 19:00
• Wait, what is A? – SarahofGaia Aug 13 '15 at 19:25
• The Accumulated Amount, the total of original amount and the interest earned... That's why the "-1" is not found in the proper formula... – DJohnM Aug 13 '15 at 22:14