APY - annual percentage yield - the percentage increase in an investment value including reinvestments after holding one year.
This is a standard figure that is supposed to make comparing products easy.
It is simple enough for bank accounts. They calculate it for you based on the rate (APR) and frequency of compounding (daily, monthly). But it is not so simple for MMFs or T-bills. Rather than calculate compounded yield over a year as a bank does, the figures you see with MMFs and T-bills use simple interest to annualize.
The MMF 7 day SEC yield is just a daily yield multiplied by 36
5 (or 366), i.e. simple interest.
For a MMF, to get the effective annual yield (APY), the formula is:
APY = (1 + 7 day SEC yield/36
5) ^ 36
5 - 1 (use 366 as needed)
Fidelity shows the effective yields for its MMFs on the funds' "performance and risk" page.
The annualized yield quoted for a T-bill is just the total return of the T-bill to maturity multiplied out to a year (simple interest). For example, with an 8 week T-bill (
56 days), the total return of the T-bill is multiplied out by 36
5/
56.
To compound interest, we reinvest the T-bill (including interest) at maturity, repeating until we've covered a whole year. That might result in a fractional number of reinvestments. For example, an 8 week (
56 day) T-bill would get invested a total of 36
5/
56 times, or roughly 6.
5 times. No matter, the formula handles this.
T-bill total return = ($100 - purchase price)/ purchase price
APY = ((1 + T-bill total return)/T-bill days) ^ (36
5/T-bill days) - 1
Consider
this 8 week (56 day) T-bill. Purchase price was $99.216.
T-bill rate = ($100 - $99.216)/ $99.216 = 0.79019
51%
APY = (1 + 0.79019
51) ^ (36
5/
56) - 1 =
5.264%
The stated annualized yield (using simple interest) is
5.1
50378%.
A bank account with an APY of
5.0% looks better than SPAXX (current 7 day yield 4.94%), but SPAXX returns more (
5.06%) with compounding. Similarly, between a T-bill and a bank account with the same rate, the T-bill is better. Its quoted rate doesn't include the effect of compounding.