Simple annualized yield for a short-term instrument based on purchase price, holding-period income, and an Actual/360 convention.
Money market yield is a simple annualized yield for a short-term instrument, commonly calculated from the return relative to purchase price and scaled using the actual days held over a 360-day year. The label must be verified because Treasury bill discount rates, Treasury investment rates, money-market instrument yields, and money market fund seven-day yields use different formulas.
For a discount instrument purchased for (P), paying face or maturity value (F) after (N) actual days, the holding-period yield is:
A simple Actual/360 money market yield is:
This annualization assumes simple scaling and no reinvestment. It does not mean the investor earns that annualized percentage during the actual short holding period.
If the same instrument is quoted using a bank discount rate (d), its price is (P=F(1-dN/360)). Substitution gives the conversion to a purchase-price money market yield:
Enter the rate as a decimal, so 4.8% is 0.048. The conversion assumes the same maturity value, remaining days, and 360-day basis, with no separate costs. It changes the quotation convention, not the cash proceeds.
Assume a short-term instrument pays USD 100 at maturity, costs USD 98.80, and has 90 days remaining. Ignore taxes, transaction costs, default, and settlement differences.
The discount is:
The holding-period yield is:
The simple Actual/360 money market yield is:
The bank discount yield instead divides by face value:
A 365-day purchase-price annualization is:
All three annualized numbers describe the same USD 1.20 discount. The formulas, not the instrument’s economics, create the immediate quotation differences.
| Measure | Return denominator | Annual basis | Compounding |
|---|---|---|---|
| Holding-period yield | Purchase price | None | Actual period only |
| Money market yield | Purchase price | 360 | Simple annualization |
| Bank discount yield | Face value | 360 | Simple discount quote |
| Treasury investment rate | Purchase price | 365 or 366 | Treasury coupon-equivalent convention |
| Effective annual yield | Purchase price | Usually 365 | Includes assumed reinvestment or compounding |
| Money market fund seven-day yield | Initial value of a hypothetical fund account | 365 annualization | Standardized fund calculation; effective version compounds the base-period return |
Names vary across markets and systems. Always inspect the published formula or instrument documentation rather than relying only on a screen label.
U.S. Treasury bills are sold at par or at a discount and pay face value at maturity. Treasury auction materials distinguish the discount rate, which is based on par and a 360-day basis, from the investment rate, which is based on purchase price and a 365- or 366-day basis.
For Treasury floating-rate notes, index and index rate have distinct regulatory meanings. The index is the highest accepted discount rate at a 13-week bill auction. The index rate converts that discount quote into a simple-interest money market yield on an Actual/360 basis. The conversion is expressly defined in 31 CFR 356.2, rather than being just a switch in terminology.
The FRN’s spread is then added to its applicable index rate under the note’s terms. Use the prescribed rounding, reset, and lockout rules for an actual FRN calculation. Do not substitute either the unconverted auction discount rate or the bill’s published investment rate.
A money market instrument is a short-term debt claim such as a Treasury bill, commercial paper instrument, or certificate of deposit. A money market fund is a pooled investment vehicle holding short-term assets.
The SEC reports seven-day gross and net yields for money market funds. Those fund yields annualize recent income under standardized fund calculations and can change as portfolio income and expenses change. They are not the same as applying the instrument-level MMY formula to one security.
Under SEC Form N-1A, Item 26(a), the seven-day yield starts with the income-related change in a hypothetical fund account after the prescribed deductions, excluding capital changes. It divides by the account’s starting value and annualizes the result by 365/7. Income is therefore part of the numerator, not the denominator. The effective seven-day yield uses a separate compounding calculation.
This page provides general financial education, not legal, lending, deposit, accounting, tax, investment, or personalized financial advice. Verify the quote convention and offering documents before comparing instruments.