Coupon Bonds
By Ethan Yan | May 24, 2026
Coupon Rate
The Coupon Rate is the nominal yield paid by a fixed-income security. The coupon is also referred to the annual interest paid on the security until it matures. The coupon rate is also known as the nominal yield.
Coupon Bonds
So how do we apply the Coupon Rate to a Coupon Bond? The coupon rate of a bond simply means that when you purchase a fixed-income security, such as a bond, the yield would be a fixed amount based on the face value (par value) of the bond, not the price you purchased it at.
For example, if you purchased a 5-Year Bond with a 5% coupon rate at a face value of $100, it’ll pay $5 for all 5 years until it matures. Even if you purchased the bond at a discount for $90, the coupon rate will still yield $5. Conversely, purchasing it at a premium, like $110, will still result in a $5 yield.
The takeaway is that the coupon rate remains constant to the bond’s face value, even if the market price is fluctuating. It’s very similar to ETFs having their NAV and Market Price. One of the biggest scares of coupon rates in bonds is that they’re greatly influenced by interest rate changes by the government. If they decide to increase or decrease the minimum interest rate, any pre-existing bonds with coupon rates will either lose or gain value based on these actions.
Coupon Rate Versus
Bond Yield
The bond yield is the real yield paid by a fixed-income security. If we go back to the example in Coupon Bonds, when you purchase a bond at a discount, so the $90, with a yield of $5, it’s actually a yield of 5.5%. Conversely, purchasing it at a premium will result in the real bond yield to be at 4.5%. Technically the bond yield is a loose term for Yield-to-Maturity, which we’ll discuss later.
Interest Rate
Coupon rates are influenced by interest rates, but only during the creation of the coupon rate, but once it’s created it cannot be changed. If you purchased a bond at a 5% coupon rate and the government increases the minimum interest rate to 7%, your coupon bond’s overall yield will be less than any of the newer coupon bonds. Meaning if you should sell it at a discount.
Yield-to-Maturity (YTM)
Unlike the bond yield, the YTM is a fairly accurate number that interpolates the expected return of a security. In this case of the coupon bond, it incorporates the face value, purchased price, time to maturity, coupon rate, and compound interest. The main purpose of the YTM is for investors who want to maximize profits by holding onto the bond to maturity.
YTM is also called the Bond Equivalent Yield (BEY). From my understanding, it mostly applies to U.S. bonds that equate these two terminologies the same. However, in theory they’re not strictly the same.
History of YTM Formula
Before financial calculators became more prominent, investors would have to approximate the YTM of a bond by finding the range in which the median YTM can be in. To know the ranges, they compare the YTM results to the Bond’s Current Yield, so if it’s less than the Current Yield, it’s the minimum; greater than is the maximum. This technique is mostly known for bonds that have multiple payments within a year. Regardless, the important formulas are as follows:
YTM = [C +(FV-PV)/n] / [(FV+PV)/2]
C = (Coupon Rate x FV)
Current Yield = Annual Cash Flow / PV
C = Coupon Payments, FV = Face Value, PV = Purchased Value, n = Periods.
Example 1:
Let’s look at an example without needing to find ranges. Let’s say I purchased a 2 year annual coupon bond at $95, with a coupon rate of 5% and a face value of $100.
Step 1: solving the coupon payments
Coupon Payments = ( Coupon Rate x FV )
Coupon Payments = ( 5% x $100 )
Coupon Payments = $5
Step 2: Calculating the Current Yield
Current Yield = Annual Cash Flow / PV
Current Yield = $5 / $95
Current Yield = ~5.26%
Step 3: Calculating YTM
YTM = [ C + ( FV - PV ) / n ] / [ ( FV + PV ) / 2 ]
YTM = [ $5 + ( $100 - $95 ) / 2 ] / [ ( $100 + $95 ) / 2 ]
YTM = [ $5 + ( $5 ) / 2 ] / [ ( $195 ) / 2 ]
YTM = [ $5 + $2.5 ] / [ $97.5 ]
YTM = [ $7.5 ] / [ $97.5 ]
YTM = ~7.69%
Example 2:
Now let’s dive into a bond that would require a range. For example, let’s say I purchased a 5 year semi-annual coupon bond at $95, with a coupon rate of 5% and a face value of $100. Let’s go step by step in calculating the range.
Step 1: solving the coupon payments
We will divide the coupon payments by the number of payments. So since it’s semi-annual, it'll be 2.
Coupon Payments = ( Coupon Rate x FV )
Coupon Payments = ( 5% x $100 )
Coupon Payments = $5 / 2
Coupon Payments = $2.5
Step 2: Finding PV(face) Value
Since our coupon rate is 5%, we can just go 1% higher to see if it’s above or below our purchased price of $95. But keep in mind, we must adjust for the bond being semi-annual, so we’ll divide the new rate by 2.
r = 6% / 2
r = 3%
We know that the bond must return the FV of $100, plus $2.5 for all 10 periods. So in total it’s $2.5 for 9 periods and $102.5 for period 10. So let’s use the formula below to find PV(face)
PV(face) = Total Yield / ( 1 + r )^n
PV(face) = $102.5 / ( 1 + 3% ) ^10
PV(face) = $76.18
Step 3: Finding PV(Coupons)
We have to discount the $2.5 for the 10 periods using the formula of PV(Coupons) below.
PV(Coupons) = Coupon Payments x [ ( 1 - ( 1 + r )^-n ) / ( r ) ]
PV(Coupons) = $2.5 x [ ( 1 - ( 1 + 3% )^-10 / ( 3% )
PV(Coupons) = $2.5 x [ ( 1 - 0.7441) / ( 3% )
PV(Coupons) = $2.5 x 8.53
PV(Coupons) = $21.33
Step 4: Sum of All Present Values(PV)
Now we simply combine Step 2 and 3 to get the total price.
Total Price = $76.18 + $21.33
Total Price = $97.74
What this means is that the price at a 6% rate is above the price in which we bought it at, therefore it’s too high and the yield must be higher.
Step 5: Repeating Steps
Since it’s too high 6%, we’ll try the next rate at 8%. Now we want to do Steps 3 & 4 again, but instead using 8%. Our final outcome in Total Price would be $91.97, which is too low. Our range will be 6% < YTM < 8%.
Step 6: Interpolation
We know that Y1 = 6%, the price (P1) is $97.74 and Y2 = 8%, the price (P2) is $91.97. Our target price (P) is $95, so to find the YTM, we must use the interpolation formula:
YTM = Y1 + [ [ ( P1 - P) / ( P1 - P2 ) ] x [ Y2 - Y1 ] ]
YTM = 6% + [ [ ( $97.74 - $95 ) / ( $97.74 - $91.97 ) ] x [ 8% - 6% ] ]
YTM = 6% + [ ($2.74) / ($5.77) ] x (2%)
YTM = 6% + [ ($0.475) x (2%) ]
YTM = 6% + 0.95%
YTM = 6.95% (annually)
In reality, we wouldn’t stick with the 6% and 8%. We’d marginally increase or decrease the percentage ranges by 0.1% to get an extremely accurate number. This process requires trial and error.
Main Takeaway
What we can gather from these examples is that investors would do a lot of work to ensure their bond purchases were worth it. It’s not necessarily difficult, but it’s more time consuming than what we can do today. The reality is that we can use financial calculators or online calculators to get faster and more accurate YTMs without needing to do the math. It’s still interpolating, so it’s great to know the moving parts, but we can just bypass the time it takes with technology. To show you how simple it has become, I quickly made a YTM calculator for Annual and Semi-Annual Coupon Bonds on Google Sheets.
Effective Yield
Both the YTM and the Coupon Rate don’t factor in compounding or reinvestment in the bond. On the other hand, the Effective Yield, or Effective Annual Yield (EAY), does account for compounding interest and reinvestment. This technique is more effective if the bond pays semi-annually, quarterly, etc., as compounding interest can add up a lot over time. Some downsides of the Effective Yield is that it assumes your bond is selling at par value and reinvestments are done at the same rate. The formula for Effective Yield is:
Effective Yield = [ 1 + ( r / n ) ]^n - 1
EAY = ( 1 + ( YTM / n )^n - 1)
r = nominal rate, n = number of payments per year
It’s important to notice that the nominal rate is not the nominal yield. We can’t use the 5% in this formula, but rather we need to use the YTM. So if we take Example 2’s bond information, it’ll be:
Effective Yield = [ 1 + ( 6.95% / 2 ) ]^2 - 1
Effective Yield = 7.95%
It’s supported that investors should use EAY over YTM if the bond’s payments happen more than once a year. To know you got your EAY correct, it should be greater than your YTM.
The Bottom Line
Just use financial calculators. Calculating it by hand is extremely rough and one mistake makes it even worse. Physical Coupon Bonds aren’t as popular anymore, but the digital version of it still exists. You’re not required to physically rip the coupons to receive interest payments, but digital versions still have a coupon rate. There is also another terminology that I didn’t get to cover (mostly because my brain has melted researching and figuring it out), which is the IRR YTM. I may discuss more about it, but it’s a more accurate version of the YTM.
SOURCes
Bloomenthal, A. (November 19, 2024). Current Yield vs. Yield to Maturity: What’s the Difference?. Investopedia. https://www.investopedia.com/ask/answers/072915/what-relationship-between-current-yield-and-yield-maturity-ytm.asp
Boyte-White, C. (October 13, 2025). Understanding Bond Yield Rate and Coupon Rate Differences. Investopedia. https://www.investopedia.com/ask/answers/051215/what-difference-between-bonds-yield-rate-and-its-coupon-rate.asp
CFI Team. (September 6, 2020). Effective Yield. Corporate Finance Institute. https://corporatefinanceinstitute.com/resources/fixed-income/effective-yield/
Chen, J. (August 5, 2025). What Is a Bond Coupon, and How Is It Calculated? Investopedia. https://www.investopedia.com/terms/c/coupon.asp
Chen, J. (May 25, 2025). What Is the Coupon Rate on a Bond and How Do You Calculate It. Investopedia. https://www.investopedia.com/terms/c/coupon-rate.asp
Chen, J. (May 14, 2026). Effective Yield Explained: Calculate and Enhance Your Bond Returns. Investopedia. https://www.investopedia.com/terms/e/effectiveyield.asp