# Mistake in Investopedia's article on APY?

My question is about James Chen's article on Investopedia, Annual Percentage Yield (APY), last updated on October 17, 2020.

It begins by correctly stating the formula for APY:

``````APY = (1 + r / n)^n - 1
``````

Where "r" is the per-period interest rate (normalised from 0 to 1) and "n" is the number of periods.

Later in the article, James says this (emphasis mine):

Suppose you are considering whether to invest in a one-year zero-coupon bond that pays 6% upon maturity or a high-yield money market account that pays 0.5% per month with monthly compounding.

At first glance, the yields appear equal because 12 months multiplied by 0.5% equals 6%. However, when the effects of compounding are included by calculating the APY, the money market investment actually yields 6.17%, as (1 + .005)^12 - 1 = 0.0617.

The last part doesn't seem to be correct. Shouldn't it have been like this?

``````(1 + .005 / 12)^12 - 1 = 0.00501
``````

That is, the 0.5% interest should be divided by 12, which makes the APY lower.

• Nitpick on the article: a "one-year zero-coupon bond that pays 6% upon maturity" is confusing. Either the bond is bought at par and pays a 6% coupon or was bought at a 6% discount (e.g. a \$100 bond bought for 100/1.06 = 94.34) Feb 12, 2021 at 16:35

No, he's correct. The interest rate is not 0.5% per YEAR, it's 0.5% per MONTH.

His point is that he's comparing getting 6% paid at one time at the end of the year, versus 6% nominal annual rate paid monthly. So he takes 6% / 12 = 0.5%. That's where the 0.5% comes from.

If it was 0.5% nominal annual rate, then your formula would be correct. But it's not 0.5% annual, it's 6% annual, and 6/12=0.5.

• Riiight, so 6% is the APR, which compounded monthly makes for an APY of 6.17%. Feb 12, 2021 at 16:26
• @PaulRazvanBerg Exactly.
– Jay
Feb 12, 2021 at 16:29
• @PaulRazvanBerg I don't think that's right. 6% is the annual interest rate (usually just called the "interest rate," and the fact that it's annual is implicit). I think the APR is the same as the APY, at least in this case. Feb 12, 2021 at 22:05
• @TannerSwett, APR is only the same as APY if the arrangement in question compounds annually, not monthly or daily or whatever-ly. APR (annual rate) doesn't consider compounding while APY (annual yield) does. This answer is absolutely 100% correct.
– quid
Feb 13, 2021 at 19:36
• @quid I'm not disputing anything in the answer. In any case, I did a quick web search and it looks like there are at least two meanings of APR: there's nominal APR, which doesn't take compounding into account, and effective APR, which does. Feb 13, 2021 at 22:12