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.

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    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) – D Stanley Feb 12 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%. – Paul Razvan Berg Feb 12 at 16:26
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    @PaulRazvanBerg Exactly. – Jay Feb 12 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. – Tanner Swett Feb 12 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 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. – Tanner Swett Feb 13 at 22:12

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