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Par Rate Formula:
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The par rate is the coupon rate at which a bond's price equals its face value. When a bond is issued at par, its coupon rate equals the market interest rate for that bond's risk level and maturity.
The calculator determines the par rate using the relationship between coupon rate, bond price, and face value:
Where:
Explanation: When the bond price equals the face value, the coupon rate is by definition the par rate for that bond.
Details: The par rate is important for bond issuers and investors as it represents the fair coupon rate where the bond trades at its face value, reflecting current market conditions.
Tips: Enter the coupon rate as a decimal (e.g., 0.05 for 5%), bond price and face value in currency units. All values must be positive numbers.
Q1: What does it mean when a bond is priced at par?
A: When a bond is priced at par, its market price equals its face value, and its yield to maturity equals its coupon rate.
Q2: How is par rate different from yield to maturity?
A: Par rate is specifically the coupon rate when price equals face value, while YTM considers both coupon payments and any capital gain/loss if purchased at a different price.
Q3: Why would a bond trade at par?
A: Bonds trade at par when market interest rates equal the bond's coupon rate, making the bond fairly priced at its face value.
Q4: Can the par rate change over time?
A: The par rate for new bonds changes with market interest rates, but an existing bond's coupon rate (and thus its par rate at issuance) remains fixed.
Q5: How do premium and discount bonds relate to par rate?
A: Bonds trade at a premium when coupon rate > market rate, and at a discount when coupon rate < market rate. At par rate, they trade at face value.