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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.

Paul Razvan Berg
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1 Answers1

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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.

Jay
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