Nominal, Current, YTM & YTC

What yield is

• We first discussed the concept of yield in the preferred stock chapter. The idea is the same for bonds: yield measures the overall return of an investment.
• With bonds, several factors affect yield:

The coupon is part of the yield, but the two will differ when a bond is purchased at a discount or a premium.

Nominal yield

The nominal yield is another name for the bond’s coupon rate. 📌 You typically won’t calculate nominal yield in practice, but you may be asked to identify the formula.

Worked example A $1,000 par, 4% bond

Nominal yield = Annual income ÷ Par Nominal yield = $40 ÷ $1,000 Nominal yield = 4%

As you can see, the calculation simply returns the 4% coupon that was given. Nominal yield depends on two values that don’t change over the life of the bond:

• No matter what happens to the bond’s market price, this bond pays $40 per year.
• The nominal yield is a fixed rate over the life of the bond.
• ⚠️ Unlike the other yields we’ll cover, market price is not part of the calculation.
• 📌 When you’re given bond information, the nominal yield is usually the first percentage you’ll see.

Current yield

Discount bond example

Let’s add one detail to the previous example: A $1,000 par, 4% bond bought for $800.

If this bond is bought at $800 (discount), the investor’s overall return will be higher than the 4% coupon. That’s because the investor earns return from two sources:

The investor receives 4% of par ($1,000) each year, and also benefits from the bond moving from the purchase price ($800) back to par ($1,000) at maturity. That extra $200 increases the overall return, so the yield will be above 4%.

In the preferred stock chapter, we discussed current yield, which is also important for bonds. Current yield is annual income divided by the security’s current market price.

Worked example — discount bond A $1,000 par, 4% bond bought for $800. What’s the current yield?

Current yield = Annual income ÷ Market price Current yield = $40 ÷ $800 Current yield = 5%

The current yield (5%) is higher than the coupon (4%). This leads to a key relationship:

⚠️ Limitation of current yield

Although current yield is important for the exam, it has a major limitation as an investing tool: it doesn’t account for time.

• Yield is an annualized measure of overall return.
• For a discount bond, part of the return comes from the $200 discount. But that $200 is earned over the life of the bond.
• A one-year bond and a 30-year bond shouldn’t have the same annualized return from the discount — and current yield doesn’t capture that difference.

Premium bond example

Now let’s see how current yield works for premium bonds (bonds trading above par): A $1,000 par, 4% bond bought for $1,100.

• The investor still receives $40 per year in interest.
• However, because bonds mature at par, paying $1,100 for a bond that matures at $1,000 creates a $100 loss at maturity.
• That loss reduces the investor’s overall return, so yields on premium bonds are lower than the coupon.

Worked example — premium bond A $1,000 par, 4% bond bought for $1,100. What is the current yield?

Current yield = Annual income ÷ Market price Current yield = $40 ÷ $1,100 Current yield = 3.6%

The current yield (3.6%) is lower than the coupon (4%). Another key relationship follows:

Yield to maturity (YTM)

🔑 YTM formula — discount bond

YTM = [ C + ( (F − P) ÷ n ) ] ÷ [ (F + P) ÷ 2 ]

where: C = coupon interest payment F = face value (par) P = price n = years to maturity

Worked example — discount bond A 10 year, $1,000 par, 4% bond is trading at $800. What is the yield to maturity (YTM)?

YTM = [ C + ( (F − P) ÷ n ) ] ÷ [ (F + P) ÷ 2 ] YTM = [ 40 + ( (1,000 − 800) ÷ 10 ) ] ÷ [ (1,000 + 800) ÷ 2 ] YTM = ( 40 + 20 ) ÷ 900 YTM = 6.7%

This formula is easier to understand if you separate it into parts:

Because the investor earns both coupon interest and the discount over time, the YTM (6.7%) is higher than the coupon (4%).

🔑 YTM formula — premium bond

YTM = [ C − ( (P − F) ÷ n ) ] ÷ [ (F + P) ÷ 2 ]

where: C = coupon rate F = face value (par) P = price n = years to maturity

Worked example — premium bond A 10 year, $1,000 par, 4% bond is trading at $1,100. What is the yield to maturity (YTM)?

YTM = [ C − ( (P − F) ÷ n ) ] ÷ [ (F + P) ÷ 2 ] YTM = [ 40 − ( (1,100 − 1,000) ÷ 10 ) ] ÷ [ (1,000 + 1,100) ÷ 2 ] YTM = ( 40 − 10 ) ÷ 1,050 YTM = 2.9%

Here’s what’s happening:

Since the investor loses the premium over time, the YTM (2.9%) is lower than the coupon (4%).

📌 Sidenote: “Basis”

⚠️ You may encounter a test question that refers to YTM as “basis.” This is just another way to say yield to maturity. For example:

A 5% bond trades on a 7% basis

This means a bond with a 5% coupon (nominal yield) is trading at a price that produces a 7% yield to maturity. A higher YTM than coupon implies the bond is trading at a discount.

Yield to call (YTC)

• ⚠️ Yield to call (YTC) applies only to callable bonds. If a bond isn’t callable, YTC doesn’t exist.
• YTC is the bond’s overall rate of return assuming the bond is called on the first call date (as soon as it’s eligible).

🔑 The YTC formula is similar to the YTM formula, but it uses:

🔑 YTC formula — discount bond

YTC = [ C + ( (CP − MP) ÷ t ) ] ÷ [ (CP + MP) ÷ 2 ]

where: C = coupon rate CP = call price MP = market price t = years to call

Worked example — discount bond, callable A 10 year, $1,000 par, 4% bond is trading at $800. The bond is callable at par after 5 years. What is the yield to call (YTC)?

YTC = [ C + ( (CP − MP) ÷ t ) ] ÷ [ (CP + MP) ÷ 2 ] YTC = [ 40 + ( (1,000 − 800) ÷ 5 ) ] ÷ [ (1,000 + 800) ÷ 2 ] YTC = ( 40 + 40 ) ÷ 900 YTC = 8.9%

The YTC (8.9%) is higher than the coupon (4%), and it’s also higher than the YTM (6.7%). 🔑 The reason is timing:

• The investor earns a $200 discount.
• If the bond is held to maturity, that $200 is earned over 10 years.
• If the bond is called in 5 years, the investor earns that same $200 in half the time, which increases the annualized return.

🔑 YTC formula — premium bond

YTC = [ C − ( (MP − CP) ÷ t ) ] ÷ [ (CP + MP) ÷ 2 ]

where: C = coupon rate CP = call price MP = market price t = years to call

Worked example — premium bond, callable A 10 year, $1,000 par, 4% bond is trading at $1,100. The bond is callable at par after 5 years. What is the yield to call (YTC)?

YTC = [ C − ( (MP − CP) ÷ t ) ] ÷ [ (CP + MP) ÷ 2 ] YTC = [ 40 − ( (1,100 − 1,000) ÷ 5 ) ] ÷ [ (1,000 + 1,100) ÷ 2 ] YTC = ( 40 − 20 ) ÷ 1,050 YTC = 1.9%

The YTC (1.9%) is lower than the coupon (4%), and it’s also lower than the YTM (2.9%). 🔑 Again, timing explains why:

• The investor will lose a $100 premium.
• If the bond is held to maturity, that $100 loss is spread over 10 years.
• If the bond is called in 5 years, the investor loses the $100 sooner, which lowers the annualized return.

🔑 Summary of the chapter’s worked examples ($1,000 par, 4% coupon, 10 years, callable at par in 5 years)

Key points

Nominal yield

• 🔑 NY = Annual income ÷ Par
• Measures the interest paid annually to investor
• Never changes over the life of the bond
• Also known as:
  • Coupon
  • Interest rate
  • Stated rate

Current yield

• 🔑 CY = Annual income ÷ Market price
• Measures overall rate of return based on the current market price
• Discount bonds CY > coupon
• Premium bonds CY < coupon

Yield to maturity (YTM)

• Measures overall rate of return if the bond is held to maturity
• Discount bonds YTM > coupon
• Premium bonds YTM < coupon

Yield to call (YTC)

• Measures overall rate of return if the bond is held until called
• Discount bonds YTC > coupon
• Premium bonds YTC < coupon

Practice questions

Q1. What is the difference between a bond’s coupon (interest rate) and its yield?

Q2. Calculate the nominal yield of a $1,000 par, 4% bond.

Q3. A $1,000 par, 4% bond is purchased at $800. What is the current yield?

Q4. The same 4% bond is purchased at $1,100. What is the current yield?

Q5. ⚠️ What is the major limitation of current yield as an investing tool?

Q6. A 10-year $1,000 par, 4% bond trades at $800. What is the yield to maturity (YTM)?

Q7. The same bond trades at $1,100. What is the YTM?

Q8. ⚠️ A 5% bond “trades on a 7% basis.” What does that mean, and is the bond at a discount or premium?

Q9. A 10-year $1,000 par, 4% bond at $800 is callable at par after 5 years. What is the YTC?

Q10. The same bond at $1,100 callable at par in 5 years. What is the YTC?

Sources

Primary/official references for the material on this page. Every link was fetched and returned HTTP 200 on 2026-08-15.