Bond Dirty Price Calculator
This tool calculates the **Dirty Price** (also known as the **Full Price**) of a bond. The dirty price is the actual price paid for a bond, which includes the quoted price (Clean Price) plus any interest that has accumulated since the last coupon payment (Accrued Interest).
Enter the **Clean Price** and the **Accrued Interest** of the bond. Ensure both are in the same currency unit.
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Understanding Bond Prices: Clean vs. Dirty
What is Clean Price?
The **Clean Price** is the price of a bond quoted in the market. It *excludes* any interest that has accrued since the last coupon payment. It's often the price you see listed on financial websites or trading platforms. It reflects the bond's value based purely on market factors like interest rates, credit risk, and supply/demand, without accounting for the timing of the next interest payment.
What is Accrued Interest?
**Accrued Interest** is the interest that has accumulated on a bond since the last time a coupon payment was made up to the settlement date of the trade. If a bond pays interest semi-annually, and you buy it two months after the last payment, there are two months' worth of interest that the seller has "earned" but hasn't received yet. The buyer compensates the seller for this accrued interest.
What is Dirty Price?
The **Dirty Price** (or **Full Price**) is the actual total amount of money paid by the buyer to the seller for the bond. It is the sum of the Clean Price and the Accrued Interest.
The relationship is simple:
Dirty Price = Clean Price + Accrued Interest
This is the price that is debited from the buyer's account and credited to the seller's account on the settlement date.
Why the Distinction?
Separating the price into Clean Price and Accrued Interest provides a clearer picture of the bond's market value fluctuations (reflected in the clean price) independently of the mechanical accumulation of interest over time.
Bond Dirty Price Examples
Here are some examples of calculating the dirty price:
Example 1: Standard Bond Purchase
Scenario: You are buying a bond in the secondary market.
Known Values: Clean Price = $980.50, Accrued Interest = $12.35.
Calculation: Dirty Price = Clean Price + Accrued Interest = $980.50 + $12.35
Result: Dirty Price = $992.85.
Conclusion: The total amount paid for the bond is $992.85.
Example 2: Bond Trading At a Premium
Scenario: A bond is trading above its par value.
Known Values: Clean Price = $1025.75, Accrued Interest = $8.10.
Calculation: Dirty Price = Clean Price + Accrued Interest = $1025.75 + $8.10
Result: Dirty Price = $1033.85.
Conclusion: The buyer pays $1033.85 in total.
Example 3: Bond Trading At a Discount
Scenario: A bond is trading below its par value.
Known Values: Clean Price = $955.00, Accrued Interest = $20.50.
Calculation: Dirty Price = Clean Price + Accrued Interest = $955.00 + $20.50
Result: Dirty Price = $975.50.
Conclusion: The total price paid is $975.50.
Example 4: Purchase Immediately After Coupon Payment
Scenario: You buy a bond very shortly after the last coupon payment date.
Known Values: Clean Price = $1005.30, Accrued Interest = $0.00.
Calculation: Dirty Price = Clean Price + Accrued Interest = $1005.30 + $0.00
Result: Dirty Price = $1005.30.
Conclusion: When there is no accrued interest, the dirty price equals the clean price.
Example 5: Purchase Just Before Coupon Payment
Scenario: You buy a bond when significant interest has accrued.
Known Values: Clean Price = $995.15, Accrued Interest = $28.90.
Calculation: Dirty Price = Clean Price + Accrued Interest = $995.15 + $28.90
Result: Dirty Price = $1024.05.
Conclusion: The accrued interest is added to the clean price.
Example 6: High Accrued Interest
Scenario: A bond with a long period since the last coupon or a high coupon rate.
Known Values: Clean Price = $960.00, Accrued Interest = $45.50.
Calculation: Dirty Price = Clean Price + Accrued Interest = $960.00 + $45.50
Result: Dirty Price = $1005.50.
Conclusion: High accrued interest increases the dirty price.
Example 7: Zero-Coupon Bond Scenario (Approx)
Scenario: Zero-coupon bonds don't pay periodic interest, so accrued interest is typically zero by definition.
Known Values: Clean Price = $850.00, Accrued Interest = $0.00.
Calculation: Dirty Price = Clean Price + Accrued Interest = $850.00 + $0.00
Result: Dirty Price = $850.00.
Conclusion: For a zero-coupon bond, the dirty price is generally equal to the clean price as there are no periodic interest payments to accrue.
Example 8: Municipal Bond Example
Scenario: Calculating the dirty price for a municipal bond with a par value of $5,000.
Known Values: Clean Price = $5100.00, Accrued Interest = $75.20.
Calculation: Dirty Price = Clean Price + Accrued Interest = $5100.00 + $75.20
Result: Dirty Price = $5175.20.
Conclusion: The same calculation applies regardless of the par value, provided inputs are the actual dollar amounts.
Example 9: Small Transaction
Scenario: Calculating dirty price for a small bond holding or a fractional amount.
Known Values: Clean Price = $50.75, Accrued Interest = $1.20.
Calculation: Dirty Price = Clean Price + Accrued Interest = $50.75 + $1.20
Result: Dirty Price = $51.95.
Conclusion: The calculation method remains the same.
Example 10: When Clean Price is Zero (Hypothetical/Distressed)
Scenario: A highly distressed bond trading with a near-zero clean price, but still with accrued interest.
Known Values: Clean Price = $0.50, Accrued Interest = $10.00.
Calculation: Dirty Price = Clean Price + Accrued Interest = $0.50 + $10.00
Result: Dirty Price = $10.50.
Conclusion: Even if the clean price is very low, the accrued interest is still added to get the dirty price.
Importance in Trading
When bonds are traded, the transaction is settled at the dirty price. While bond prices are typically quoted as the clean price, the actual cash exchanged includes the accrued interest. This ensures the seller receives the interest earned up to the sale date, and the buyer is entitled to the full next coupon payment.
Frequently Asked Questions about Bond Dirty Price
1. What is the formula for Bond Dirty Price?
The formula is simple: **Dirty Price = Clean Price + Accrued Interest**.
2. Why isn't the quoted price the actual price I pay?
The quoted price is the Clean Price, which excludes accrued interest. You pay the Dirty Price, which includes the Clean Price plus any interest the bond has earned since the last coupon payment.
3. How is Accrued Interest calculated?
Accrued interest calculation depends on the bond's coupon rate, par value, payment frequency (e.g., semi-annual), and the number of days since the last coupon payment relative to the total number of days in the coupon period. Different day count conventions (like 30/360 or actual/actual) are used depending on the bond type and market.
4. Does a Zero-Coupon Bond have accrued interest?
Zero-coupon bonds do not pay periodic interest, so there is typically no accrued interest component in the conventional sense. Their price simply accretes towards face value over time. The dirty price and clean price are generally the same for zero-coupon bonds.
5. What is another name for Dirty Price?
Dirty Price is also commonly referred to as the **Full Price**.
6. When is the Accrued Interest typically highest?
Accrued interest is highest just before a coupon payment is due and drops to zero immediately after the coupon is paid.
7. Can Accrued Interest be negative?
No, accrued interest represents interest earned over time, so it is always zero or positive.
8. What happens to Accrued Interest on the coupon payment date?
On the coupon payment date, the bondholder receives the full coupon payment, and the accrued interest drops back to zero for the next period.
9. Why is it important for investors to understand Dirty Price?
Understanding the dirty price is crucial because it's the actual cash amount exchanged in a bond transaction. It helps investors calculate the true cost of their investment and understand how much of the purchase price is attributable to the bond's market value (clean price) versus earned interest (accrued interest).
10. Does this calculator determine the Accrued Interest for me?
No, this calculator assumes you already know the Accrued Interest. Calculating accrued interest requires knowing the bond's features (coupon rate, par value, payment dates) and the trade's settlement date, often using specific day count conventions. This tool focuses solely on the final step of adding the known clean price and accrued interest.
