<p><strong>Edit</strong> this answer was written for the original question, before user completely edited whole question to something completely different and unrelated to original question for some reason:</p>
<blockquote>
<p><strong>How is it that the coupon rate is higher than the interest rate?</strong></p>
<p>How can the coupon rate be higher than the interest rate?
Doesn't that mean that after one year, you're beating the interest rate. For example, if the coupon rate was 8% and the interest rate was 4%. On a $100 priced bond, I would get 8 dollars in the first year, which is 8% returns, as opposed to 5% returns on the interest rate. Am I missing something? If I'm not missing something, then is this scenario not possible?</p>
</blockquote>
<p>I believe that at the heart of this question is confusion between the price of the bond and face value of the bond.</p>
<p>A general bond pricing formula (see <a href="https://courses.lumenlearning.com/boundless-finance/chapter/valuing-bonds/" rel="nofollow noreferrer">here</a> an example) can be expressed as as a discounted stream of future cash flows from the coupon and the value of the bond itself. Hence we have:</p>
<p><span class="math-container">$$ P = \sum^T_{t=1} \frac{C_t}{(1+i)^t}+\frac{M}{(1+i)^T}$$</span></p>
<p>where <span class="math-container">$P$</span> is the price of the bond, <span class="math-container">$C$</span> is the coupon, <span class="math-container">$i$</span> is the interest rate, and <span class="math-container">$M$</span> is the value at maturity (i.e. the face value — the value printed out on the bond).</p>
<p>Based on the above formula if the coupon was <span class="math-container">$8\%$</span> of the <span class="math-container">$\\\$100$</span> face value (i.e. <span class="math-container">$\\\$8$</span>), the interest rate <span class="math-container">$4\%$</span>, and we assume <span class="math-container">$T=2$</span> the actual price of the bond simply cannot be <span class="math-container">$\\\$100$</span>.</p>
<p>The correct price would be:</p>
<p><span class="math-container">$$ P = \sum^2_{t=1} \frac{\\\$8}{(1+0.04)^t}+\frac{\\\$100}{(1+0.04)^2} \approx \\\$107.54$$</span></p>
<p>If the price would  be lower than <span class="math-container">$\\\$107.54$</span> people would increase their demand for the bond until it would reach its equilibrium at that price and vice versa if the original price would be above.</p>
<p>It is simply not viable for the price to stay at <span class="math-container">$\\\$100$</span> in free bond market. In real life there might be some mispricing occurring at some times (although to discuss why is outside the scope of this answer) that can create arbitrage opportunity but as people start taking advantage of it, it will eventually disappear unless the mispricing is deliberately encouraged by some policy.</p>

CC BY-SA 4.0
2020-07-31T17:44:03.407Z
2020-07-31T18:22:33.640Z
2020-07-31T18:22:33.640Z
1muflon1
<p>How do coupons get priced in together?</p>

CC BY-SA 4.0
2020-07-31T16:42:03.157Z
The yield is less than the coupon rate if the price of the bond is over $100. Any bond pricing primer should cover this.
Brian Romanchuk
CC BY-SA 4.0
2020-07-31T16:44:47.157Z
@BrianRomanchuk What do you mean exactly? Am I beating the interest rate with this higher coupon rate?
Allan
CC BY-SA 4.0
2020-07-31T17:17:20.310Z
[Pricing Money](http://www.jdawiseman.com/books/pricing-money/Pricing_Money_JDAWiseman.html)
Rodrigo de Azevedo
CC BY-SA 4.0
2020-07-31T17:25:45.733Z
@Allan you are confusing the price of the bond with its face value. The 100$ might be printed out on the bond but that does not mean that will be its market price
1muflon1
CC BY-SA 4.0
2020-07-31T17:53:46.057Z
The question title and text do not match each other. This needs to be cleared up. It appears that you need to read basic primers about how bonds are priced. They should be easy to find with a web search.
Brian Romanchuk
<interest-rate><bonds>
Are coupons all semi-annual?
Allan
# Are coupons all semi-annual?

(Asked by: username_0 on 2020-07-31)

How do coupons get priced in together?

**Tags:** interest-rate, bonds
> **Comments:**
> **username_1**: The yield is less than the coupon rate if the price of the bond is over $100. Any bond pricing primer should cover this.  
> **username_0**: @BrianRomanchuk What do you mean exactly? Am I beating the interest rate with this higher coupon rate?  
> **username_2**: [Pricing Money](http://www.jdawiseman.com/books/pricing-money/Pricing_Money_JDAWiseman.html)  
> **username_3**: @Allan you are confusing the price of the bond with its face value. The 100$ might be printed out on the bond but that does not mean that will be its market price  
> **username_1**: The question title and text do not match each other. This needs to be cleared up. It appears that you need to read basic primers about how bonds are priced. They should be easy to find with a web search.  

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## 1 answers

### Answer by username_3 on 2020-07-31. Score: 2

**Edit** this answer was written for the original question, before user completely edited whole question to something completely different and unrelated to original question for some reason:

> **How is it that the coupon rate is higher than the interest rate?**
>
> How can the coupon rate be higher than the interest rate?
> Doesn't that mean that after one year, you're beating the interest rate. For example, if the coupon rate was 8% and the interest rate was 4%. On a $100 priced bond, I would get 8 dollars in the first year, which is 8% returns, as opposed to 5% returns on the interest rate. Am I missing something? If I'm not missing something, then is this scenario not possible?

I believe that at the heart of this question is confusion between the price of the bond and face value of the bond.

A general bond pricing formula (see [here](https://courses.lumenlearning.com/boundless-finance/chapter/valuing-bonds/) an example) can be expressed as as a discounted stream of future cash flows from the coupon and the value of the bond itself. Hence we have:

$$ P = \sum^T\_{t=1} \frac{C\_t}{(1+i)^t}+\frac{M}{(1+i)^T}$$

where $P$ is the price of the bond, $C$ is the coupon, $i$ is the interest rate, and $M$ is the value at maturity (i.e. the face value — the value printed out on the bond).

Based on the above formula if the coupon was $8\%$ of the $\\\$100$ face value (i.e. $\\\$8$), the interest rate $4\%$, and we assume $T=2$ the actual price of the bond simply cannot be $\\\$100$.

The correct price would be:

$$ P = \sum^2\_{t=1} \frac{\\\$8}{(1+0.04)^t}+\frac{\\\$100}{(1+0.04)^2} \approx \\\$107.54$$

If the price would be lower than $\\\$107.54$ people would increase their demand for the bond until it would reach its equilibrium at that price and vice versa if the original price would be above.

It is simply not viable for the price to stay at $\\\$100$ in free bond market. In real life there might be some mispricing occurring at some times (although to discuss why is outside the scope of this answer) that can create arbitrage opportunity but as people start taking advantage of it, it will eventually disappear unless the mispricing is deliberately encouraged by some policy.


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