Bond Calculator: What a Bond Is Really Worth
A bond is a loan you make, not one you take. You hand money to a government or a company, they pay you interest at fixed intervals, and at the end they hand your original money back. This bond yield calculator prices that stream of future payments, or runs the math backwards to find the yield hiding inside a price you already see.
What a bond is, in plain English
Picture a friend who needs $1,000 and promises to pay you $25 every six months for ten years, then return the full $1,000 at the end. You'd ask: is $25 twice a year a good deal for tying up $1,000 for a decade? It depends on what else you could earn. If other safe investments pay more, your friend's promise is worth less than $1,000 today, and if they pay less, it's worth more.
A bond is that deal in formal clothes. The borrower is the issuer, the $1,000 repaid at the end is the face value (par value), and the regular payments are coupons. The coupon rate is fixed at birth and never changes, even as market rates wander around it. The bond's end is maturity. The coupon stays fixed for life, but the price doesn't. A bond issued at $1,000 might later trade for $925 or $1,080, with nothing about the bond changed. Only rates moved, so the same payments are now worth more or less to a new buyer.
Every input, explained
Face value. The amount repaid at maturity. Our example uses $1,000, the most common single-bond face. Double it and you double every payment and the price.
Coupon rate. The annual rate on face value: 5% on $1,000 pays $50 a year. Don't mix this up with yield: the coupon is the bond's written promise, while yield is what you actually earn at the price you pay. They match only at par.
Years to maturity. How long until face value comes back, and longer bonds swing harder when rates move because there is more future cash to revalue.
Coupon frequency. How often coupons arrive. Most US bonds pay twice a year, so 5% on $1,000 means $25 every six months, not $50 once a year. Sooner money is worth more than later money.
Solve for price, or solve for yield. The calculator works both ways: yield in, price out; price in, yield out. The yield is the number for comparing bonds equally.
A worked example: pricing a 10-year bond at 6%
Take a real bond. It has a $1,000 face value, a 5% coupon paid semiannually, and 10 years left: 20 payments of $25, plus $1,000 at the end. Market yield: 6% a year.
- Split the yield into periods. A 6% annual yield paid semiannually means 3% per period, and each future payment is discounted at 3% per period.
- Value the coupons. Twenty payments of $25, each discounted back to today at 3% per period, add up to $371.69. The twentieth $25 payment, ten years out, is worth only about $13.84 today; the first, six months out, is worth $24.27.
- Value the face value. The $1,000 repaid in ten years, discounted 20 periods at 3%, is worth $553.68 today.
- Add them up. $371.69 + $553.68 = $925.61. A buyer paying $925.61 and collecting every payment earns exactly 6% a year.
The bond pays 5%, but the market demands 6%. Nobody pays full price for a 5% stream when 6% is on offer, so the price drops until the total return (coupons plus the $74.39 gain from buying below par) reaches 6%.
The round-trip check: run it backwards: feed in $925.61 and the yield it returns is 6.00%. If price and yield don't convert back into each other, something's off.
Premium, par, and discount: the one rule to remember
Compare coupon to market yield and you can predict the price in advance. Coupon above yield means a premium. Equal means par. Below means a discount. That's the whole rule: above-market bonds are worth extra, below-market ones must be cheaper.
Our bond shows all three. At 4%, its 5% coupon beats the market: premium at $1,081.76, or $81.76 above par. At 5%, coupon matches market: par at $1,000.00. At 6%, the coupon lags: discount at $925.61, or $74.39 below par. Note the asymmetry: a one-point yield fall from 5% lifts the price $81.76, while a one-point rise drops it only $74.39. Bond prices curve, a quirk called convexity.
| Yield to maturity | Price | Versus par |
|---|---|---|
| 4% | $1,081.76 | Premium of $81.76 |
| 5% | $1,000.00 | Par |
| 6% | $925.61 | Discount of $74.39 |
| 7% | $857.88 | Discount of $142.12 |
Yields and prices always move in opposite directions. Hold to maturity, though, and the seesaw stops mattering: you collect every coupon and the full $1,000 regardless.
Current yield is not yield to maturity
At our $925.61 price, the bond pays $50 a year in coupons. Divide $50 by $925.61 and you get 5.40%. That's the current yield: income return only. It ignores the $74.39 you'll gain at maturity, when $1,000 comes back for a bond bought at $925.61. Spread over ten years, that gain lifts your true return from 5.40% to 6.00%.
For premium bonds the gap reverses. Buy at $1,081.76 and current yield is just 4.62%, but you'll also lose $81.76 at maturity, so true yield to maturity is 4.00%, below current yield. Current yield is this year's income; yield to maturity is the whole story. One wrinkle: yield to maturity assumes you reinvest every coupon at that same yield, which rarely happens exactly, so treat it as a comparison number rather than a promise.
Duration: how hard a rate rise hits the price
Macaulay duration is the average wait until your money comes back, weighted by each payment's present value. For our bond at 6%, it's about 7.89 years, though the bond runs ten, and it doubles as a sensitivity gauge: a 1% yield rise should move price by roughly the duration in percent, the other way.
Check it: yield rises 6% to 7%, price falls from $925.61 to $857.88, a 7.32% drop against duration's rough 7.89% prediction. Close, but not exact, because duration is a linear approximation and the curve bends (convexity again). Treat duration as an approximation. Two things stretch it out: longer maturities, and lower coupons, since less early cash means a longer average wait. Short, high-coupon bonds are calm. Long, low-coupon bonds are wild.
Common mistakes
- Confusing current yield with yield to maturity. The 5.40% current yield looks like the return. The true return is 6.00%, because the discount gain at maturity counts.
- Forgetting semiannual timing. Pricing a semiannual bond as annual gives a wrong price. Check frequency before trusting any number.
- Assuming the price stays put until maturity. It won't. A bond bought at $925.61 could trade at $880 or $980 next year with nothing going wrong. If you might need the money early, that swing is your risk.
- Ignoring credit risk. Every number here assumes the issuer pays in full and on time. A shaky company offers a juicy yield precisely because its payments are less certain; a higher yield usually means somebody is worried.
Practical tips
Compare yield, not coupon, when you shop, because two bonds with the same 5% coupon can offer very different returns once price enters the picture. A bond ladder helps with rate risk: split money across bonds maturing in two, four, six, eight, and ten years, so some comes back regularly for reinvestment at prevailing rates. Match the bond to the job: money needed next year belongs in short bonds or cash, not a 30-year bond that could be down double digits by then. Before buying, run the price both ways and confirm they agree, as our $925.61 and 6.00% do. It takes ten seconds.
Frequently asked questions
Why does my bond lose value when interest rates rise?
Because new bonds pay more, so your older bond must get cheaper before anyone buys it. Hold to maturity and you'll still collect every coupon and the full face value; the paper loss only becomes real if you sell early.
What's the difference between coupon rate and yield?
The coupon is fixed at issue: 5% on $1,000 means $50 a year, regardless of price. Yield depends on what you pay: below par it beats the coupon, above par it trails it, matching only at par.
Can a bond's price go above its face value?
Yes. That's a premium bond, whenever market yield drops below the coupon rate. Our example trades at $1,081.76 at a 4% yield. You'll still only get $1,000 back at maturity, so the premium fades over its remaining life.
Is yield to maturity guaranteed?
No. It holds only if the issuer pays on schedule, and it assumes you reinvest each coupon at the same yield, which rarely happens exactly. Treat it as a comparison number, not a guaranteed return.
What does duration actually tell me as an investor?
Roughly how much price moves when rates move: near 7.89 years, a 1% rate rise should knock price down close to 7.89%, before convexity softens the blow. Longer duration, bigger swings.
Related calculators: Annuity Calculator, Annuity Payout Calculator and Finance Calculator.
Bonds sit next to annuities and savings in most portfolios. Their guides, with the same worked examples, are on the CalcMega Blog.
For general information only, and not financial advice. Prices, yields, and creditworthiness change, so check current market data before any investment decision.
Further reading: TreasuryDirect, the US Treasury's bond portal, from the US Department of the Treasury.