Bond Investment Calculator

A Treasury bill does not pay regular coupons. For an illustrative 30-day bill with $10,000 face value purchased at 99.70% of par, you pay $9,970.00 and receive $10,000.00 at maturity. The gross return is $30.00, or 0.3009% over the holding period. It is not a 0.3009% annual return.

The bank discount yield divides $30.00 by $10,000.00 (face value) and multiplies by 360/30, giving 3.60%. The simple investment yield divides the same $30.00 by the purchase cost of $9,970.00 and multiplies by 365/30, giving about 3.66% for an ACT/365 example. The effective annualized investor rate is different again because it reflects compounding convention; costs and taxes can reduce the investor's return.

Using InvestCalcs: select “U.S. Treasury bill” in section 1, enter face value, price as percent of par, actual settlement and maturity dates, any broker fee and your own tax assumptions. Coupon and coupon-frequency controls disappear. The bill-rate panel explains the three different returns. The separate rolling-T-bills section is a comparison scenario, not the single bill entered.

U.S. Treasury rules calculate the investment rate for bills up to half-year maturity using a 365- or 366-day year depending on the one-year period. Longer bills require an additional market formula not reproduced in this introductory quote panel.

A bond is generally a debt contract. By purchasing a bond, you lend money to the issuer, which may be a government, company or other borrower. The issuer promises specified payments, commonly periodic interest (the coupon) and repayment of principal at a stated maturity date. Payments are contractual, but they are not guaranteed: an issuer can default or restructure its debt.

A bond is unlike a share in a business. A shareholder owns an interest in the business and participates in its residual profits and risks; a typical bondholder has contractual claims to specified payments. Some bonds have special features, but the calculator models fixed-rate, non-callable bonds repaid at face value on maturity.

Essential distinction: The coupon rate tells you what the bond pays relative to face value. The yield tells you what the bond earns relative to the price paid, subject to assumptions.

Open the calculator and choose Reset example if you have changed the inputs. Its default assumptions are:

These are illustrative assumptions, not historical market observations or appropriate tax rates for a particular investor.

Where the money goes

• Initial clean purchase cost: $10,000 × 95% = $9,500.00.
• Annual coupon: $10,000 × 4% = $400.00, paid once a year.
• Annual coupon tax: $400 × 25% = $100.00 under the simple model.
• Annual coupon after tax: $300.00.
• Redemption of principal at maturity: $10,000.00.
• Positive price gain on redemption: $10,000 − $9,500 = $500.00.
• Modeled tax on that gain: $500 × 25% = $125.00.
• Total after-tax cash receipts over five years: 5 × $300 + $10,000 − $125 = $11,375.00.
• Net nominal profit if coupons are held as cash: $11,375 − $9,500 = $1,875.00.

The after-tax annualized investor IRR is approximately 3.89%, and the modeled inflation-adjusted annual IRR is approximately 1.35%. These are annualized time-value measures, not the $1,875 cash profit expressed as a percentage.

The calculator's market YTM is approximately 5.16% in this annual-coupon example; with semiannual coupons, market YTM and effective annual yield can differ even when the bond trades at par.

Market YTM (nominal annual)

Yield to maturity (YTM) is the discount rate that equates the present value of promised future coupons and principal to the bond's dirty settlement price (clean price plus accrued interest). This calculator reports a nominal annual coupon-frequency quotation, before purchase fees and taxes. It uses a simplified regular-period/fractional-period method; some securities and markets use other quotation conventions.

YTM assumes the promised cash flows occur. It is not a guarantee of return. If you sell before maturity, the sale price changes the return. YTM should also not be interpreted as a guaranteed compounded terminal value: coupon reinvestment is a separate question.

Investor return after tax

This is the effective annual internal rate of return (IRR) calculated from the initial amount paid (including accrued interest and fees) and the dated after-tax cash flows. It accounts for when cash is paid and received. It is not the same as market-quoted YTM.

Real return after tax

The calculator converts the modeled after-tax annual IRR into purchasing-power terms using:

Real annual return = (1 + after-tax IRR) / (1 + expected inflation) − 1

At 3.89% after-tax IRR and 2.50% inflation, real return is about 1.35% annually. Inflation is an assumption; actual inflation could differ materially. This is an annual-rate adjustment, not an inflation-adjusted schedule of each cash receipt.

Gross annual coupon

This equals face value × annual coupon rate, before tax. It does not change merely because the market price rises or falls. On a semiannual coupon bond, the annual coupon is divided into two scheduled installments; similarly for quarterly or monthly payments.

Clean price, dirty price and accrued interest

Suppose a bond has $10,000 face value and is quoted at 95. Its clean cost is $9,500, not $95 and not $10,000.

If you buy between coupon dates, the seller has usually earned a portion of the upcoming coupon. The buyer normally pays this amount as accrued interest in addition to the clean price. The dirty price is therefore:

Dirty price = Clean price + Accrued interest

Your actual initial cash outlay in this calculator is:

Initial outlay = Clean price + Accrued interest + Purchase fees

The purchaser subsequently receives the whole coupon on its payment date under the calculator's regular-coupon model. For real securities, check settlement rules, ex-coupon periods and applicable tax treatment.

Five day-count choices

• Actual/Actual (coupon period): Actual elapsed days as a proportion of the actual coupon period. This is the default.
• Actual/365 Fixed: Actual elapsed days using 365 days as annual denominator.
• Actual/360: Actual elapsed days using a 360-day year.
• 30/360 US (NASD): A specified U.S. 30/360 accrual convention.
• 30E/360 European: A specified European 30/360 accrual convention.

These are not interchangeable. Select the convention stated in the bond's terms. The calculator simplifies some irregular-date situations; it is not a full security-master or settlement engine.

Tax on gross coupon (%): Applied to each full coupon when paid.
Tax on positive price gain (%): Applied at maturity to the modeled gain between face value and clean purchase cost, optionally adjusting for fees.
Expected annual inflation (%): Converts after-tax IRR into real terms.
Extra unrecoverable withholding (%): Applied as an additional reduction of coupon income. Do not enter tax already accounted for elsewhere; the tool does not automatically net credits or refunds.
Are purchase fees part of the tax cost basis?: Choose Yes only where the applicable tax treatment permits that adjustment.

Important: This calculator is a scenario model, not a tax calculator for Switzerland, the Netherlands, South Africa, the U.S. or any other specific jurisdiction. Its simplified rules do not model tax relief for losses, tax treatment of premiums or original-issue discounts, adjustments for accrued interest, annual wealth taxes, creditable withholding, tax-payment delays or every issuer-specific rule. A zero-coupon discount is modeled as a gain taxed at redemption, which may be incorrect for a given jurisdiction.

A bond with a high coupon may have an attractive nominal income stream but a much lower real after-tax return. Always distinguish the two.

Repricing yield (nominal %) asks: What would this bond's modeled clean value be if the market required this yield instead? It is a scenario, not a live market quote or a predicted sale price.

Assumed rolling T-bill yield (nominal %) sets one assumed annual nominal yield for all future Treasury-bill renewals. Actual reinvestment rates are unknown.

T-bill earnings tax (%) reduces each modeled bill-period return.
T-bill rollover interval sets how often the model renews bills (monthly, quarterly or annually).
Comparable cash-flow treatment chooses whether cash receipts are held at 0% or reinvested at the assumed after-tax bill rate.

The comparison starts both strategies with exactly the same initial capital and runs them to the bond maturity date. This helps make the figures comparable, but does not eliminate differences in risk, liquidity, taxes or future interest rates.

Technical limitation: The T-bill calculation assumes a constant proportional nominal yield and simplified rollover mechanics, including partial final intervals. It is not a security-by-security simulation of actual bill prices, auction discount conventions or future term structures.

The top boxes give four quick answers. Beneath them, Investment economics explains the mechanics:

• Settlement → maturity and years remaining: Your modeled holding period.
• Clean bond cost: Face value × clean price percentage.
• Accrued interest paid: Interest attributed to the period before settlement, according to the selected convention.
• Purchase fees / total initial outlay: Money that leaves your account to acquire the bond.
• Tax basis includes fees?: The selected tax-model assumption.
• Effective annual market yield: The annual compounded equivalent of market-quoted nominal YTM.
• Investor IRR before tax (after fees): Annualized dated cash-flow return with transaction costs, before the simplified coupon/gain taxes.
• Current yield: Annual gross coupon divided by clean cost. This ignores the redemption gain/loss and cash-flow timing; it is not YTM.
• Total tax modeled: Sum of simplified coupon taxes/withholding plus positive-gain tax.
• Net profit (coupons held): Total modeled after-tax cash receipts minus initial outlay, without reinvesting the coupons.

The nearby explanatory box interprets the market YTM, effective yield, after-tax IRR and real after-tax IRR for the current inputs.

The bond promises fixed contractual payments. If new comparable investments offer a higher yield, an existing low-coupon bond generally has to sell at a lower price to be competitive. Conversely, if required yields fall, its value generally rises.

Example: A hypothetical five-year bond with $10,000 face value, 4% annual coupon and five full years remaining is worth exactly $10,000 at a 4% required annual yield. A change in the required yield reprices those fixed promised payments, even though their amounts have not changed.

The calculator shows:

• Repricing yield: the hypothetical new required yield.
• Clean value at repricing yield: the bond's repriced value excluding accrued interest.
• Change versus purchase clean cost: an illustrative price difference, not an actual realized total profit/loss.
• Macaulay duration: weighted-average present-value timing of promised bond payments, expressed in years.
• Modified duration: a measure of local price sensitivity to a small change in yield.
• Clean price if yield +1 pp / −1 pp: repriced clean prices for a one-percentage-point increase or decrease in yield from the modeled market YTM.

Duration rule of thumb: If modified duration is 4.5, a small 1 percentage-point increase in yield implies an approximate 4.5% decrease in price, all else equal. It is an approximation; the exact modeled +1 pp and −1 pp price results account for the curve's nonlinearity (convexity).

Do not confuse a 1 percentage-point change with a 1% relative change. A yield moving from 4% to 5% has risen 1 percentage point, or 25% relative to 4%.

The model assumes contractual payments and unchanged credit risk. Real sale prices also depend on the issuer, liquidity, bid–ask spreads, market conventions and trading conditions.

• Horizontal axis: Nominal annual market yield.
• Vertical axis: Modeled clean bond price in the selected currency.
• Downward-sloping line: Bond prices generally decline as required yields rise.
• Dashed vertical line: The bond's calculated market YTM from the inputs.
• Highlighted point: The selected repricing yield, if it lies within the graph's displayed range.
• Hover or tap: View exact yield and calculated clean price at a point on the curve.

Exercise: Keep face value, coupon and dates unchanged. Increase Repricing yield from 5% to 7%. Observe the calculated market value drop. Then reduce it to 3%. Notice that the bond can rise above its purchase price even though its coupon amount never changes.

This section addresses opportunity cost: What if the same initial capital went into a series of short-term government bills?

The comparison displays:

When “hold cash” is selected: Interim after-tax coupon receipts and bill earnings do not earn any further return. The bill principal continues to roll under the simplified model.

When “reinvest/compound” is selected: After-tax bond coupons are reinvested at the assumed after-tax T-bill rollover rate until the horizon; the bill strategy also compounds at that assumed rate.

Critical distinction: A fixed-rate bond locks in promised coupons and redemption, subject to issuer performance. A future series of T-bill yields is not known today. This model holds the modeled T-bill rate constant; that is a scenario, not a forecast or a guaranteed alternative outcome.

Each line is a future scheduled payment:

The Totals row adds future receipts. To calculate the no-reinvestment profit, subtract Total initial outlay from total after-tax receipts.

Export CSV downloads the payment table for audit or spreadsheet use. Its rows are future cash receipts; the initial negative purchase outlay is not a row in this export.

These are separate questions:

1. Market YTM: At this price, what annualized yield is implied by the promised contractual payments, before fees and tax?
2. Investor IRR: Given the exact money I pay and when I receive after-tax cash, what is my annualized return?
3. Total profit: How much more money will I receive than I paid, assuming coupons are held and not reinvested?
4. Real return: After considering assumed inflation, how fast does my modeled purchasing power grow on an annualized basis?

A large nominal cash profit can coexist with a modest real annualized return, particularly when payments are far in the future.

Experiment A — Premium, par and discount

Hold face value at $10,000, coupon at 4%, annual payments and five years remaining. Change clean purchase price from 100 to 95, then to 105.

At 100, the price is $10,000; at 95, the price is $9,500; at 105, the price is $10,500. At maturity the issuer still repays $10,000, provided it pays as promised. Thus the discounted purchase builds in a $500 redemption gain, whereas the premium purchase builds in a $500 redemption loss. The coupon remains $400 per year.

Observe that current yield is not enough to understand the return: it ignores those maturity gains and losses.

Experiment B — Interest-rate sensitivity and duration

With the bond unchanged, vary only Repricing yield and inspect the graph and risk panel. Longer-maturity bonds and lower-coupon bonds generally have greater sensitivity to a comparable change in yield, all else equal.

Then change maturity farther into the future and compare modified duration. Beware: changing maturity also changes the contractual cash-flow schedule, so use matched examples when isolating effects.

Experiment C — The tax-and-inflation hurdle

Use the default bond. First set all taxes and inflation to zero; record Investor return after tax and Real return after tax. Then restore coupon tax 25%, price-gain tax 25%, and inflation 2.5%.

This shows why nominal yield is not the same as increased purchasing power. The default is a hypothetical example, not a recommendation of those tax rates.

Bond yields are prices for receiving money at different dates and under different risks. Sovereign yields often serve as reference points for corporate borrowing, mortgage funding, asset valuation and the opportunity cost of holding equities or real estate.

Time value: A dollar received today is usually worth more than the same nominal dollar years later because it can be invested, consumed or retained for flexibility.
Credit: An issuer with a higher perceived chance of default usually must offer more yield than a safer borrower, all else equal.
Inflation: Fixed future nominal money may buy less when finally received.
Liquidity: An investment that is difficult to sell quickly may require a yield premium.
Term structure: Short and long maturities can have very different yields; this pattern is the yield curve. The calculator does not model the live yield curve.

A government bond can be comparatively safe from default in its own currency and still be a poor investment at a particular price if inflation, taxation or interest-rate risk overwhelms its return. Conversely, a bond can produce attractive returns if purchased at a sufficiently advantageous price, provided payments are made.

Enter Annual coupon = 0. The calculator then models a single contractual payment of face value at maturity. The investor generally purchases at a discount and earns the difference over time.

Example: Pay $9,000 for a $10,000 zero-coupon bond redeeming in five years. The $1,000 nominal gain is not a 1,000/9,000 ÷ 5 simple annual return: its annualized compounded pre-tax return is approximately ($10,000 / $9,000)^(1/5) − 1, or 2.13%.

In real markets, Treasury-bill discount yields and bond-equivalent yields may use different day-count and pricing conventions. The calculator's zero-coupon market-yield display is a periodic-compounding equivalent, not necessarily the published discount yield for a particular T-bill. Zero-coupon income can also be taxable before redemption in certain jurisdictions; the calculator does not model that.

Do not treat the calculator as a live trading screen. It does not retrieve market bond prices; verify prices, accrued interest and issuer information independently. It does not model default or recovery, callable or floating-rate bonds, foreign-exchange changes, liquidity spreads, irregular first/last coupons, ex-coupon settlement, every market-specific yield quotation, automatic withholding-tax credits, wealth tax, or jurisdiction-specific tax rules.

The sensitivity graph is a static repricing calculation with remaining cash flows held fixed. It is not a simulated portfolio P&L across future dates. The T-bill comparison assumes an unchanged rollover rate and simplified timing. The after-tax IRR is based on dated investor cash flows, whereas the coupon-frequency YTM follows a different quotation convention; their numerical difference is not necessarily caused solely by tax and fees.

Before relying on any result, identify the exact security, issuer, currency, face value, coupon, maturity, payment frequency, call features, day-count convention, settlement date, price quotation and fees. Then establish the applicable tax treatment and ask whether you can hold to maturity without needing the capital. Evaluate creditworthiness, inflation exposure, market-price sensitivity and realistic alternatives.

The final question is not merely “What is the coupon?” It is:

What cash will I pay, what cash might I receive, when will I receive it, what can go wrong, how much purchasing power will remain, and what else could I do with the same capital?

InvestCalcs educational note: All examples are illustrative. The tool assumes promised payments occur. Verify the bond's official terms, market quote and your tax circumstances before investing. The examples are educational scenarios and are not live investment quotations.