Mistake in Investopedia's article on APY?

Question

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.

Jay · Accepted Answer

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.

Mistake in Investopedia's article on APY?

One Answer

Add your own answers!

Ask a Question