Constant Yield Calculator
Buy a bond below face value and the tax system treats part of the discount as interest you earn a little at a time, even when no cash arrives. This constant yield calculator applies the IRS constant yield method to a discount bond: it computes the original issue discount (OID) for any accrual period, the daily OID, the adjusted basis after that period, cumulative OID, and how many compounding periods remain to reach face value. It covers discount bonds only, and the reason for that limit is stated plainly below, because the old version of this page got the premium case wrong.
Simplified zero-coupon model. Coupon bonds subtract the stated interest per period under the IRS method; this tool does not perform that subtraction, so check coupon-bond figures against your broker statement. Tax information, not tax advice; confirm against your 1099-OID.
Quick Answer
A $10,000 bond bought for $9,000 at a 6% yield to maturity, semi-annual accrual, accrues $270.00 of OID in period 1, $278.10 in period 2, and $286.44 in period 3, each taxable as ordinary interest income for that period. After three periods the adjusted basis is $9,834.54 and cumulative OID is $834.54 of the $1,000 total discount. Daily OID for the selected period 3 is $1.57 per day on the default 182.5 days. One compounding period remains to reach face value at this yield.
Key takeaways
- Constant yield means the yield stays fixed while the base grows. Each period’s OID equals beginning basis times the periodic yield, so the slices get bigger over time.
- OID is phantom income: taxed now, paid at maturity. You owe ordinary income tax on each period’s accrual even though no cash arrives until the bond matures.
- Your basis rises by each period’s OID. That prevents double taxation: at maturity, face value minus adjusted basis should leave no remaining discount gain.
- This tool is discount-only. A purchase price at or above face value now stops with an explanation instead of printing a positive OID alongside a “nothing to accrue” badge.
- Daily OID is only as good as the days figure you enter. It is a division, not a market day-count convention.
- Quick Answer
- How to use the constant yield calculator
- The formula, then the first-five-periods schedule
- Why the IRS insists on the constant yield method
- Discount bonds versus premium bonds: the mirror image, handled honestly
- What most constant yield calculators get wrong
- Frequently asked questions
- Add This Calculator to Your Website
- References
How to use the constant yield calculator
Six inputs give you one period’s OID and the running position. The results stay hidden until you calculate.
- Enter the face value: the amount payable at maturity. The worked example uses $10,000.
- Enter the purchase price: what you paid, which is your starting adjusted basis. It must be below face value. At or above face, the tool stops with an explanation and shows no OID figure.
- Enter the yield to maturity: the annual yield at purchase, in percent. The worked example uses 6%.
- Pick accrual periods per year: semi-annual (2) is the default, with annual, quarterly, and monthly options.
- Enter the accrual period number: counting from 1 at purchase. The worked example uses period 3.
- Enter the days in the accrual period: used only for the daily figure. The default 182.5 is the average semi-annual length, not a measured length for your bond.
- Click Calculate OID: read the selected period’s OID, the adjusted basis, the daily OID, cumulative OID, total OID, and periods remaining.
Invalid inputs are not rejected with an error message in the old tool’s style; they are silently reset to defaults, and that behaviour is kept here with the disclosure it deserves. A face value at or below zero resets to $10,000, a frequency at or below zero resets to 2, a period number below 1 resets to 1, and days at or below zero reset to 182.5. A negative yield resets to 0 and a negative price resets to 0. Check the fields after calculating if a result looks unlike the bond you entered, because a reset may have replaced your number.
The formula, then the first-five-periods schedule
Per accrual period, OID equals the adjusted basis at the start of the period times the periodic yield, which is yield to maturity divided by periods per year. For a coupon bond, the IRS method then subtracts any qualified stated interest for the period; this simplified tool does not perform that subtraction, so its schedule is a zero-coupon schedule. New basis equals old basis plus OID, and the next period starts from the higher base. Daily OID equals period OID divided by the days figure you entered.
OID for period k = adjusted basis at start of period k × periodic yield
New basis = old basis + OID; daily OID = period OID ÷ days in period
| Period | Beginning basis | OID (basis × 3%) | Ending basis |
|---|---|---|---|
| 1 | $9,000.00 | $270.00 | $9,270.00 |
| 2 | $9,270.00 | $278.10 | $9,548.10 |
| 3 | $9,548.10 | $286.44 | $9,834.54 |
| 4 | $9,834.54 | $295.04 | $10,129.58 |
| 5 | $10,129.58 | $303.89 | $10,433.47 |
Read periods 4 and 5 as a warning label on the model, not as tax figures to file. Once the basis passes face value, cumulative OID passes the $1,000 total discount: period 5 alone brings cumulative OID to $1,433.47. That happens because yield is an input here, not a rate solved from price and face value, so compounding at 3% per period does not land exactly on $10,000 at a whole number of periods. Use period numbers up to maturity only, and treat “periods remaining” as a count of compounding steps at the entered yield, never as a calendar date. To turn periods into time, divide by periods per year yourself: one remaining semi-annual period is about half a year.
Why the IRS insists on the constant yield method
Without a mandated method, a taxpayer could defer all tax on a bond discount until maturity, reporting nothing for years and then a lump sum. The constant yield method blocks that by recognizing the discount as it economically accrues, at a steady yield on a rising basis. A straight-line split would understate early income and overstate later income relative to the economics, which is why it is not the OID method. Your broker reports the annual total on Form 1099-OID, and this calculator’s cumulative figure should track that form for a zero-coupon discount bond held for whole periods. IRS Publication 1212 is the guide to OID instruments, and Publication 550 covers the reporting of investment income.
Discount bonds versus premium bonds: the mirror image, handled honestly
A discount bond starts below face value and its basis climbs toward face as OID accrues. A premium bond starts above face value and its basis falls toward face as the premium amortizes. For premium bonds, the IRS constant yield amortization for a period is the yield accrual minus the qualified stated interest for that period, and the basis falls by that amortization amount. That formula needs a coupon, which this tool never asks for. The old page printed a positive OID for premium bonds while its badge said “nothing to accrue”, which was wrong in both directions at once: the number rose when it should fall, and the badge denied the very accrual the number showed. The fix is a scope guard, not a fudged number: enter a price at or above face value and the tool refuses the calculation and explains the premium formula instead. If you hold a premium bond, use a premium amortization calculation that takes your coupon, or work from your broker’s amortization schedule.
For the coupon side of bond math, the coupon rate calculator computes the coupon rate from annual payment and face value. To convert a coupon and price into a yield in the first place, the rate to yield calculator is the companion step. After tax, the after-tax yield calculator adjusts a yield for your tax rate, which is a different question from how much OID accrues in a period.
What most constant yield calculators get wrong
- They label current yield as constant yield: coupon divided by price is a snapshot, not an accrual schedule. It never produces a period-by-period basis.
- They split the discount evenly: straight-line OID is simple and wrong for OID purposes, understating early periods and overstating later ones.
- They hide the coupon subtraction: a schedule that never mentions qualified stated interest will overstate OID for every coupon bond it touches.
- They print premium OID as if it were discount OID: the old version of this page did exactly that, with a badge contradicting its own number. This rewrite refuses the premium case rather than dressing it up.
- The gap this page fills: a period-by-period zero-coupon schedule with daily OID, cumulative OID, adjusted basis, and periods remaining, plus the premium guard and the overshoot warning that keep the simplified model from being mistaken for a filing figure.
Frequently asked questions
Original issue discount is the difference between a bond’s face value and the lower price at which it was issued or bought. The tax system treats that discount as interest earned gradually over the bond’s life, so each period’s slice is ordinary interest income even though no cash arrives until maturity or sale.
Each period’s OID equals the adjusted basis at the start of the period times the periodic yield, then the basis rises by that OID, so later periods accrue larger dollar amounts at the same yield.
Because at face value there is no discount to accrue, and a premium bond’s basis falls as its premium amortizes. That amortization equals stated interest minus the yield accrual, which needs a coupon input this tool does not have. Showing a positive rising OID for either case would be wrong, so the tool stops and explains the premium formula instead.
It counts compounding periods, at the yield you entered, until the basis reaches face value. It is not a calendar date and not a maturity date. Divide it by periods per year to get an approximate time: one remaining semi-annual period is about half a year.
Because yield is an input here, not a rate solved from price and face value, so compounding at the entered yield does not land exactly on face value at a whole number of periods. Only use period numbers up to maturity, and never file a cumulative figure that exceeds the total discount.
Only as a simplified zero-coupon schedule. The IRS method subtracts qualified stated interest for the period before arriving at OID, and this tool does not perform that subtraction. For a coupon bond, check the result against your broker statement or 1099-OID.
Yes. It runs entirely in your browser, needs no account, and stores nothing. Copy the result with “Copy my results” or send it to another app with “Share results”.
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References
- Internal Revenue Service. Publication 1212, Guide to Original Issue Discount (OID) Instruments (constant yield method: OID for an accrual period equals adjusted acquisition price at the start of the period times yield to maturity divided by accrual periods per year; premium amortization as yield accrual minus qualified stated interest). Accessed October 24, 2026.
- Internal Revenue Service. Publication 550, Investment Income and Expenses (OID and market discount reporting, constant yield election for market discount, ordinary-income character of accrued discount). Accessed October 24, 2026.
- Internal Revenue Service. Publication 1212 (January 2022), Guide to Original Issue Discount Instruments (accrual period rules, daily OID allocation, and the constant yield formula for debt instruments issued after July 1, 1982). Accessed October 24, 2026.
- Manuals.plus, archived copy of IRS Publication 1212. Publication 1212, Original Issue Discount Instruments: User Guide (constant yield steps for debt instruments issued after July 1, 1982, daily OID allocation, acquisition premium reduction). Accessed October 24, 2026.
- UncleFed, archived IRS Publication 550 text. Publication 550: Bond Premium Amortization (constant yield premium amortization steps: yield, accrual periods, premium for the period as yield accrual minus qualified stated interest). Accessed October 24, 2026.
- LegalClarity, explainer with IRS citations. What Is Original Issue Discount and How Is It Taxed? (OID as face minus issue price, constant yield accrual growing over time, Form 1099-OID reporting). Accessed October 24, 2026.
- LegalClarity, explainer. 1099-OID Meaning: What Is Original Issue Discount? (when a broker issues Form 1099-OID, the $10 threshold, and OID as interest earned gradually). Accessed October 24, 2026.
- LegalClarity, explainer. How to Calculate and Report Original Issue Discount (yield to maturity as the discount rate equating present value to issue price, adjusted issue price rising by prior OID, coupon subtraction step). Accessed October 24, 2026.
- Internal Revenue Service. About Form 1099-OID, Original Issue Discount (when Form 1099-OID must be filed, including the at-least-$10 OID threshold). Accessed October 24, 2026.
- Internal Revenue Service Publication 550, archived PDF copy. Publication 550 (2025), Investment Income and Expenses (market discount constant yield election, and the ordinary-income character of accrued discount). Accessed October 24, 2026.