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CFA Level I Exam · Yield and Yield Spread Measures for Floating-Rate Instruments

Money Market Yield Measures: Discount Rate vs Add-On Yield

Updated 7 October 2026 · Fact-checked

Money market instruments are quoted either on a discount basis (bank discount yield, based on face value and a 360-day year) or an add-on basis (money market yield, based on price). To compare them, convert price first: Price = FV × (1 − Days/360 × DR). Then compute the holding period yield and annualize it.

Understand Money Market Yield Measures and Instruments

Money market instruments are short-term debt securities with maturities of one year or less. Examples are Treasury bills, commercial paper, certificates of deposit and repos. Some are quoted on a discount basis and others on an add-on basis.

A discount-basis instrument, such as a T-bill or commercial paper, is quoted with a discount rate (DR). The discount is taken off the face value (FV) and the rate is applied to the face value, not to the price you pay. Price = FV − (FV × Days/360 × DR). Because the base is the larger face value, the discount rate understates the true return. It is called the bank discount yield.

An add-on instrument, such as a bank CD or Libor-style deposit, is quoted with a rate applied to the amount invested. You pay the principal and receive principal plus interest at maturity: FV = PV × (1 + Days/360 × AOR). The add-on rate (AOR) is based on the investment amount, so it is a true return measure. Many add-on instruments use a 360-day year, but some currencies, such as GBP, use 365 days. Read the question for the day-count.

The key idea is that a quote is not comparable until it has the same basis. The way to compare is to convert everything to a price, find the holding period yield (HPY) = (FV − Price) ÷ Price, and then annualize it. Annualizing on 360 days gives the money market yield (MMY). Annualizing on 365 days gives the bond equivalent yield (BEY), which lets you compare with bonds paying semiannual coupons on a 365-day basis.

Key formulas to remember

Price from discount rate
PV = FV × (1 − (Days/360) × DR)
Use for T-bills and commercial paper quoted on a discount basis. Days is the actual days to maturity.
Bank discount yield
DR = (360/Days) × (FV − PV) ÷ FV
Based on face value and a 360-day year. It understates the return.
Price from add-on rate
PV = FV ÷ (1 + (Days/Year) × AOR)
Year is 360 for most instruments but 365 for some currencies such as GBP.
Holding period yield
HPY = (FV − PV) ÷ PV
Unannualized return over the life of the instrument.
Money market yield
MMY = HPY × (360/Days)
Equals the add-on rate on a 360-day basis. Also MMY = (360 × DR) ÷ (360 − Days × DR).
Bond equivalent yield
BEY = HPY × (365/Days)
Simple annualization on 365 days. Also BEY = MMY × (365/360).
Effective annual yield
EAY = (1 + HPY)^(365/Days) − 1
Compounded version. Do not confuse with BEY, which is not compounded.

How to solve Money Market Yield Measures and Instruments questions

Use the same route for any money market question. Always go through price and HPY, and the conversion between yield measures becomes mechanical.

  1. 1Identify the basis of the quote: discount rate (DR) or add-on rate (AOR). Note the actual days to maturity and the day-count (360 or 365).
  2. 2If quoted as a discount rate, compute price: PV = FV × (1 − Days/360 × DR). If quoted as an add-on rate, compute PV = FV ÷ (1 + Days/Year × AOR), or work forward from a known PV.
  3. 3Compute the holding period yield: HPY = (FV − PV) ÷ PV.
  4. 4Annualize to the measure asked. Money market yield: HPY × 360/Days. Bond equivalent yield: HPY × 365/Days. Effective annual yield: (1 + HPY)^(365/Days) − 1.
  5. 5If comparing instruments, put them all on the same measure before ranking. The highest yield on the same basis is the best.
  6. 6Check direction: for the same instrument, DR < MMY < BEY < EAY (for periods under a year). If your answer breaks this order, recheck.

Quickest way: Rate-to-rate shortcut through the 360 and 365 factors

When to use it: Use when the exam gives a discount rate and asks for MMY or BEY directly, and you want to save time.

  1. Compute the price as a decimal of face value: 1 − Days/360 × DR. Treat FV as 1.
  2. HPY = (1 − price) ÷ price.
  3. MMY = HPY × 360/Days.
  4. BEY = MMY × 365/360, or HPY × 365/Days.
  5. Eliminate options: MMY must be above DR, and BEY must be above MMY. This often removes two choices before you finish.
  6. Calculator: on the BA II Plus, store the price with STO 1, then compute (1 − RCL 1) ÷ RCL 1 × 360 ÷ Days. On the HP 12C, use the same chain with the STO and RCL keys.

Common mistakes in Money Market Yield Measures and Instruments

  • Treating the discount rate as a return on the price paid

    The word 'rate' suggests interest on the amount invested.

    Fix: Remember that DR is applied to face value. Convert to price first, then compute the yield on price.

  • Using 365 instead of 360 for money market yield

    Bond problems usually use 365 days or half-year periods.

    Fix: MMY always uses 360. Use 365 only for BEY, or when a question says the add-on rate uses 365 days.

  • Calling BEY the compounded yield

    Both BEY and EAY use 365 in the formula.

    Fix: BEY = HPY × 365/Days is simple annualization. EAY compounds using the exponent 365/Days.

  • Using 360 days instead of actual days to maturity

    The year basis and the days to maturity get mixed up.

    Fix: Days is the actual number of days left. The 360 is only the year convention.

  • Ranking instruments quoted on different bases

    A 4.8% discount rate looks lower than a 4.9% add-on rate.

    Fix: Convert both to the same measure, such as MMY or BEY, before comparing. A DR understates the true yield, so the apparent gap may reverse.

  • Forgetting that the add-on rate equals MMY only on a 360-day basis

    Students memorize 'add-on = MMY' without the condition.

    Fix: If the add-on instrument uses a 365-day year, the quoted rate is already on a 365-day basis and it is not the 360-day MMY.

Worked examples

Example 1

A 120-day Treasury bill with face value $1,000,000 is quoted at a bank discount rate of 3.60%. Which of the following is closest to its money market yield? A) 3.59% B) 3.64% C) 3.70%

Show the solution
  1. Price = 1,000,000 × (1 − 120/360 × 0.036) = 1,000,000 × (1 − 0.012) = 988,000.
  2. HPY = (1,000,000 − 988,000) ÷ 988,000 = 12,000 ÷ 988,000 = 0.012146.
  3. MMY = 0.012146 × 360/120 = 0.012146 × 3 = 0.036437, or 3.64%.
  4. Check: MMY must exceed DR (3.60%). 3.59% fails. 3.70% is too high. 3.64% fits.

Answer: B) 3.64%

Example 2

For the same 120-day bill priced at $988,000 (face value $1,000,000), which is closest to the bond equivalent yield? A) 3.64% B) 3.69% C) 3.75%

Show the solution
  1. HPY = 12,000 ÷ 988,000 = 0.012146.
  2. BEY = HPY × 365/120 = 0.012146 × 3.041667 = 0.036944, or 3.69%.
  3. Cross-check: BEY = MMY × 365/360 = 3.6437% × 1.013889 = 3.694%.
  4. BEY must exceed MMY (3.64%), so A is out. 3.75% is too high.

Answer: B) 3.69%

Exam tips

  • Questions are three-option and the options are sorted from smallest to largest. Use the ordering DR < MMY < BEY < EAY to eliminate options fast.
  • Always read which yield the question asks for, and check the stated day-count before calculating.
  • Do the price step even when you want the yield directly. It keeps the HPY clean and reduces formula errors.
  • Keep at least five decimal places in HPY. Rounding early shifts the answer enough to land on the wrong option.
  • About 90 seconds per question: money market conversions take 60 seconds if you follow the same price, HPY, annualize route every time.

Practice questions from Yield and Yield Spread Measures for Floating-Rate Instruments

Money Market Yield Measures and Instruments in other exams

The same ground in other exams, if you are preparing for more than one or want another angle on it.

Money Market Yield Measures and Instruments: frequently asked questions

What is the difference between bank discount yield and money market yield?

Bank discount yield is based on face value and a 360-day year, so it understates the return. Money market yield is based on the price paid and also uses 360 days. For the same instrument, the money market yield is higher.

What is the difference between an add-on rate and a discount rate?

A discount rate is applied to the face value and the interest is deducted up front, so you pay less than face value. An add-on rate is applied to the amount invested and the interest is added at maturity. The add-on rate is a true return on money invested.

How do I calculate money market yield from the discount rate?

Compute the price as FV × (1 − Days/360 × DR). Then HPY = (FV − Price) ÷ Price, and MMY = HPY × 360/Days. A direct formula is MMY = 360 × DR ÷ (360 − Days × DR).

How is bond equivalent yield different for money market instruments?

Bond equivalent yield annualizes the holding period yield on a 365-day year: BEY = HPY × 365/Days. It makes a money market yield comparable with a bond yield stated on a 365-day basis. It is simple, not compounded.