# A Bond Is Issued at Par Value When: Understanding Par, Premium, and Discount Bonds Published: 2026-04-18 Author: Warren Team URL: https://www.heywarren.com/blog/bond-issued-at-par --- A bond is issued at par value when the market interest rate equals the bond's coupon rate at the time of issuance. This seemingly simple condition has important implications for how bonds are priced, how returns are calculated, and why bond prices move inversely to interest rates. Here's a complete explanation. ## What Is Par Value of a Bond? A bond's **par value** (also called face value or principal) is the amount the issuer promises to repay to the bondholder at maturity. For most corporate bonds, the par value is $1,000 per bond. US Treasury bonds use $100 as par for price quoting purposes. Par value is distinct from market price: - **Par (100)**: Bond trades at exactly its face value - **Premium (>100)**: Bond trades above face value (e.g., at $1,050 for a $1,000 bond = 105) - **Discount (<100)**: Bond trades below face value (e.g., at $950 for a $1,000 bond = 95) ## When Is a Bond Issued at Par? **A bond is issued at par value when the coupon rate equals the prevailing market interest rate ([yield to maturity](/blog/formula-of-ytm)) for bonds of equivalent credit quality and maturity.** If an investor can earn 5% elsewhere for the same risk and maturity, a bond offering exactly 5% has no reason to trade at either a premium or discount — it's worth exactly its face value. **The mathematical proof**: Consider a 5-year bond with par value $1,000, coupon rate 5% (annual payments), when the market rate for similar bonds is also 5%: - Annual coupon: $50 - Present value of coupons: $50 / 1.05 + $50 / 1.05² + $50 / 1.05³ + $50 / 1.05⁴ + $50 / 1.05⁵ = $216.47 - Present value of principal: $1,000 / 1.05⁵ = $783.53 - **Total price = $216.47 + $783.53 = $1,000.00 = Par** When the discount rate (market rate) equals the coupon rate, the present value of all cash flows exactly equals par. ## When Is a Bond Issued at a Premium? A bond is issued at a **premium** when its coupon rate is **higher** than the current market interest rate. **Scenario**: Market rates for 5-year bonds = 3%, but a bond has a 5% coupon. - Investors pay more than par to obtain the above-market 2% coupon advantage - The premium is exactly the present value of the excess cash flows (the additional 2% per year) - At maturity, the bond repays exactly par — so a premium bond will lose the premium over time (this is "amortization of premium") **Example**: 5-year 5% coupon bond when market rate = 3%: Price = PV of coupons at 3% + PV of $1,000 at 3% = approximately **$1,091.59** (above par) ## When Is a Bond Issued at a Discount? A bond is issued at a **discount** when its coupon rate is **lower** than the current market interest rate. ![A 5% coupon bond priced at premium ($1,091.59) when market rate is 3%, and at discount ($918.01) when market rate is 7%.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20800%20210%22%20width%3D%22800%22%20height%3D%22210%22%20role%3D%22img%22%3E%3Ctitle%3EComparison%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Ctext%20x%3D%22230%22%20y%3D%2257.5%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EPremium%20%283%25%20mkt%29%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%2225%22%20width%3D%22450%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%232563eb%22%2F%3E%3Ctext%20x%3D%22702%22%20y%3D%2257.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%232563eb%22%3E%241.1K%3C%2Ftext%3E%3Ctext%20x%3D%22230%22%20y%3D%22152.5%22%20text-anchor%3D%22end%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EDiscount%20%287%25%20mkt%29%3C%2Ftext%3E%3Crect%20x%3D%22240%22%20y%3D%22120%22%20width%3D%22378.4429135481271%22%20height%3D%2255%22%20rx%3D%226%22%20fill%3D%22%237c3aed%22%2F%3E%3Ctext%20x%3D%22630.4429135481271%22%20y%3D%22152.5%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22%237c3aed%22%3E%24918%3C%2Ftext%3E%3C%2Fsvg%3E) *A 5% coupon bond priced at premium ($1,091.59) when market rate is 3%, and at discount ($918.01) when market rate is 7%.* **Scenario**: Market rates = 7%, but the bond has a 5% coupon. - No investor will pay full price for a below-market coupon - The bond's price falls below par to compensate — at a lower price, the effective yield rises to market rate - The discount accretes to par over time as the bond approaches maturity **Example**: 5-year 5% coupon bond when market rate = 7%: Price ≈ **$918.01** (below par) ## Why Bond Prices Move Inversely to Interest Rates This par/premium/discount mechanism explains the fundamental inverse relationship between bond prices and interest rates: - **Interest rates rise**: New bonds offer higher coupons; existing bonds with lower coupons become less attractive → prices fall (toward/below par) - **Interest rates fall**: New bonds offer lower coupons; existing bonds with higher coupons become more attractive → prices rise (above par) **Example**: - You hold a 10-year 4% bond (issued at par = $1,000) - Market interest rates rise to 6% - Your bond's $40/year coupon is now below-market; the bond must price at a discount to attract buyers - New price ≈ $851 (it now offers effective 6% yield to maturity) - The $149 loss from $1,000 to $851 compensates new buyers for the below-market coupon ## Zero-Coupon Bonds: The Extreme Discount Case A **[zero-coupon bond](/blog/zero-coupon-bond)** pays no coupons at all — it's issued at a deep discount and redeems at par. The entire return is the price appreciation from issuance to maturity. ![A 10-year zero-coupon bond grows from its $613.91 issue price to $1,000 par at maturity with no interim cash flows.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20800%20149%22%20width%3D%22800%22%20height%3D%22149%22%20role%3D%22img%22%3E%3Ctitle%3ETimeline%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Cline%20x1%3D%22137.5%22%20y1%3D%2255%22%20x2%3D%22662.5%22%20y2%3D%2255%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%223%22%2F%3E%3Ccircle%20cx%3D%22137.5%22%20cy%3D%2255%22%20r%3D%2224%22%20fill%3D%22white%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22137.5%22%20y%3D%2260%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2215%22%20font-weight%3D%22700%22%20fill%3D%22%230f172a%22%3E1%3C%2Ftext%3E%3Ctext%20x%3D%22137.5%22%20y%3D%22101%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2212%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EIssue%3C%2Ftext%3E%3Ctext%20x%3D%22137.5%22%20y%3D%22119%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3E%24613.91%20paid%3C%2Ftext%3E%3Ccircle%20cx%3D%22312.5%22%20cy%3D%2255%22%20r%3D%2224%22%20fill%3D%22white%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22312.5%22%20y%3D%2260%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2215%22%20font-weight%3D%22700%22%20fill%3D%22%230f172a%22%3E2%3C%2Ftext%3E%3Ctext%20x%3D%22312.5%22%20y%3D%22101%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2212%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EYear%203%3C%2Ftext%3E%3Ctext%20x%3D%22312.5%22%20y%3D%22119%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EPrice%20accretes%3C%2Ftext%3E%3Ccircle%20cx%3D%22487.5%22%20cy%3D%2255%22%20r%3D%2224%22%20fill%3D%22white%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22487.5%22%20y%3D%2260%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2215%22%20font-weight%3D%22700%22%20fill%3D%22%230f172a%22%3E3%3C%2Ftext%3E%3Ctext%20x%3D%22487.5%22%20y%3D%22101%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2212%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EYear%206%3C%2Ftext%3E%3Ctext%20x%3D%22487.5%22%20y%3D%22119%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EPrice%20accretes%3C%2Ftext%3E%3Ccircle%20cx%3D%22662.5%22%20cy%3D%2255%22%20r%3D%2224%22%20fill%3D%22%232563eb%22%20stroke%3D%22%232563eb%22%20stroke-width%3D%223%22%2F%3E%3Ctext%20x%3D%22662.5%22%20y%3D%2260%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2215%22%20font-weight%3D%22700%22%20fill%3D%22white%22%3E4%3C%2Ftext%3E%3Ctext%20x%3D%22662.5%22%20y%3D%22101%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2212%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EMaturity%3C%2Ftext%3E%3Ctext%20x%3D%22662.5%22%20y%3D%22119%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3E%241%2C000%20received%3C%2Ftext%3E%3C%2Fsvg%3E) *A 10-year zero-coupon bond grows from its $613.91 issue price to $1,000 par at maturity with no interim cash flows.* **Example**: A 10-year zero-coupon Treasury bond with par value $1,000, when market yield = 5%: - Issue price = $1,000 / (1.05)^10 = **$613.91** - Investor pays $613.91, receives $1,000 in 10 years Zero-coupon bonds have the highest duration (price sensitivity to interest rate changes) of any bond structure — they're pure time value of money instruments with no cash flows until maturity. ## Par Value in the Primary Market vs. Secondary Market **Primary market (new issuance)**: Bonds are typically priced at or very close to par when first issued, because underwriters and issuers set the coupon rate to match current market rates. The goal is to price at par to simplify accounting and investor familiarity. **Secondary market**: After issuance, bonds trade at prices reflecting current interest rates. A bond issued at par five years ago will trade at a premium today if rates have fallen (its coupon is now above-market) or at a discount if rates have risen (its coupon is now below-market). ## Yield to Maturity (YTM) and the Par Relationship **Yield to maturity** is the total return an investor earns by holding a bond to maturity, accounting for the current price, all coupon payments, and the principal repayment. ![How a bond's yield to maturity compares to its coupon rate depending on whether it trades at par, premium, or discount.](data:image/svg+xml,%3Csvg%20xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F2000%2Fsvg%22%20viewBox%3D%220%200%20600%20211%22%20width%3D%22600%22%20height%3D%22211%22%20role%3D%22img%22%3E%3Ctitle%3EHierarchy%3C%2Ftitle%3E%3Crect%20width%3D%22100%25%22%20height%3D%22100%25%22%20fill%3D%22%23f8fafc%22%2F%3E%3Crect%20x%3D%22220%22%20y%3D%2220%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22%232563eb%22%2F%3E%3Ctext%20x%3D%22300%22%20y%3D%2254%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2214%22%20font-weight%3D%22700%22%20fill%3D%22white%22%3EBond%20Price%3C%2Ftext%3E%3Cpath%20d%3D%22M%20300%2078%20L%20300%20105.5%20L%20120%20105.5%20L%20120%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%2240%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22120%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EAt%20Par%3C%2Ftext%3E%3Ctext%20x%3D%22120%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EYTM%20%3D%20coupon%20rate%3C%2Ftext%3E%3Cpath%20d%3D%22M%20300%2078%20L%20300%20105.5%20L%20300%20105.5%20L%20300%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%22220%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22300%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EAt%20Premium%3C%2Ftext%3E%3Ctext%20x%3D%22300%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EYTM%20%26lt%3B%20coupon%20rate%3C%2Ftext%3E%3Cpath%20d%3D%22M%20300%2078%20L%20300%20105.5%20L%20480%20105.5%20L%20480%20133%22%20stroke%3D%22%23cbd5e1%22%20stroke-width%3D%222%22%20fill%3D%22none%22%2F%3E%3Crect%20x%3D%22400%22%20y%3D%22133%22%20width%3D%22160%22%20height%3D%2258%22%20rx%3D%228%22%20fill%3D%22white%22%20stroke%3D%22%230891b2%22%20stroke-width%3D%222%22%2F%3E%3Ctext%20x%3D%22480%22%20y%3D%22158%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2213%22%20font-weight%3D%22600%22%20fill%3D%22%230f172a%22%3EAt%20Discount%3C%2Ftext%3E%3Ctext%20x%3D%22480%22%20y%3D%22176%22%20text-anchor%3D%22middle%22%20font-family%3D%22system-ui%2C-apple-system%2Csans-serif%22%20font-size%3D%2210%22%20fill%3D%22%2364748b%22%3EYTM%20%26gt%3B%20coupon%20rate%3C%2Ftext%3E%3C%2Fsvg%3E) *How a bond's yield to maturity compares to its coupon rate depending on whether it trades at par, premium, or discount.* - **Bond trading at par**: YTM = coupon rate - **Bond trading at premium**: YTM < coupon rate (you're paying extra upfront, reducing total return) - **Bond trading at discount**: YTM > coupon rate (you're getting a capital gain at maturity, boosting total return) **Example**: A 5% coupon bond trading at $950: - Annual coupon: $50 - Capital gain at maturity: $50 (from $950 to $1,000) - YTM > 5% (capital gain component adds to total return) The YTM calculation is the present value formula solved for the discount rate — the rate that makes the present value of all cash flows equal to the current price. ## Practical Implications for Bond Investors **Duration and price sensitivity**: Premium bonds (high coupon, low duration component) are less sensitive to rate changes than discount bonds (low coupon, higher duration). Zero-coupon bonds have the highest price sensitivity. **Tax considerations**: For taxable bonds: - **Discount bonds**: The "market discount" (buying below par in the secondary market) is treated as ordinary income when recognized (either annually via accretion or at sale/maturity) under [IRS](https://www.irs.gov/) rules - **Premium bonds**: The premium can be amortized as an offset to interest income annually, or written off at sale/maturity This tax asymmetry means the after-tax yield on discount vs. premium bonds differs from the pre-tax YTM, which matters for taxable account investors. **[Current yield](/blog/current-yield-on-bond-formula) vs. YTM**: A premium bond's current yield (coupon / current price) is higher than its YTM because you're paying more than you'll get back at maturity. A discount bond's current yield understates YTM because the capital gain component is excluded. ## Conclusion A bond is issued at par when its coupon rate matches the prevailing market interest rate — a simple condition with elegant mathematics underpinning it. Understanding par, premium, and discount bonds is the foundation for bond price sensitivity, yield calculations, and the inverse price-rate relationship that governs all fixed income investing. Every bond price change after issuance is simply the market repricing a fixed cash flow stream to reflect new prevailing interest rates. For related bond and fixed income topics, see our guides on [accrued interest](/blog/accrued-interest), [weighted average maturity](/blog/weighted-average-maturity), and [bearer bonds](/blog/bearer-bonds). Warren at [heywarren.com](https://heywarren.com) helps you analyze fixed income investments and understand how bond pricing fits into your overall portfolio strategy. --- ## Related Reading **More from Warren**: - [Weighted Average Maturity (WAM): Definition, Formula, and Why It Matters for Bond Investors](/blog/weighted-average-maturity) - [Bearer Bonds: What They Were, Why They Disappeared, and Their Legacy](/blog/bearer-bonds) - [Accrued Interest: What It Is, How to Calculate It, and Why It Matters for Bond Investors](/blog/accrued-interest) **Authoritative sources**: - [TreasuryDirect — Bonds and Securities](https://www.treasurydirect.gov/marketable-securities/) - [SEC — Bonds](https://www.investor.gov/introduction-investing/investing-basics/investment-products/bonds-or-fixed-income-products/bonds) - [FINRA — Bond Basics](https://www.finra.org/investors/learn-to-invest/types-investments/bonds)