Explain it like I’m 5
A bond is like an IOU note. You lend a company or the government some money — usually $1,000. In return, they promise two things: they’ll pay you a little “thank you” money every six months (the coupon), and they’ll give your $1,000 back on a set day in the future (maturity).
Now imagine you want to sell your IOU to a friend before that day. If new IOUs being handed out today pay more thank-you money than yours, your friend won’t pay the full $1,000 for yours — they’d pay less. If new IOUs pay less, yours is the better deal, and your friend would happily pay more than $1,000.
That’s the whole secret of bond prices: when interest rates go up, bond prices go down, and when rates go down, bond prices go up — like two kids on a seesaw. This calculator works out exactly how much a bond is worth for any interest rate.
Words you’ll see, in plain English
- Bond
- An IOU. You lend money to a government or company; they pay you interest along the way and give your money back at the end.
- Face value (par)
- The amount a bond pays back at the end — usually $1,000 per bond.
- Coupon
- The interest a bond pays you, usually twice a year. A $1,000 bond with a 5% coupon pays $50 a year.
- Maturity
- The day an investment “finishes” and you get your money back — like the end date on a CD or a bond.
- Yield to maturity (YTM)
- Your total yearly return if you buy a bond today at its current price and keep it until it pays you back.
- Current yield
- A bond’s yearly interest divided by today’s price — a quick, simpler version of the return.
- Premium / discount bond
- A bond selling for more than its face value (premium) or less than it (discount).
- Duration
- A way to measure how much a bond’s price will wobble when interest rates change. Bigger duration = bigger wobble.
More money words explained simply in our glossary.
How to use the bond calculator
- Choose what you know. If you know the yield you want, the calculator finds the price. If you see a bond’s price (for example in your brokerage), it finds the yield.
- Face value is what the bond pays back at the end — almost always $1,000 per bond (bond prices are often quoted per $100, so a quote of 95 means $950).
- Coupon rate is the yearly interest printed on the bond, as a percent of face value.
- Years to maturity and how often interest is paid — most US bonds pay twice a year.
The math, step by step
Example: a $1,000 bond with a 4% coupon, paid twice a year, maturing in 10 years, when similar bonds yield 5%.
- Interest per payment: 4% × $1,000 ÷ 2 = $20, paid 20 times (10 years × 2).
- Yield per period: 5% ÷ 2 = 2.5%.
- Value the $1,000 at the end: $1,000 ÷ 1.02520 = $610.27. Money you get later is worth less than money today.
- Value all 20 coupons the same way and add them up: $311.78.
- Price = $922.05. The bond sells at a discount because its 4% coupon is below the 5% market yield.
Price = C × [1 − (1 + y)−n] ÷ y + F × (1 + y)−n
C = coupon per period, y = yield per period, n = number of payments, F = face value. Finding the yield from a price has no simple formula, so the calculator searches for the yield that makes this equation match the price.
The seesaw in numbers
| Market yield | Price of the 4%, 10-year bond | Sells at |
|---|---|---|
| 3% | $1,085.84 | Premium |
| 4% | $1,000.00 | Par |
| 5% | $922.05 | Discount |
| 6% | $851.23 | Discount |
Current yield vs. yield to maturity
For the example bond at $922.05, the current yield is $40 ÷ $922.05 =4.34%. The yield to maturity is higher (5%) because you also gain$77.95 when the bond pays back its full $1,000 at the end. Use YTM to compare bonds.
What this calculator assumes
- Prices are calculated on a coupon date, so there’s no accrued interest. Between coupon dates, the price you pay includes interest built up since the last payment.
- The bond is held to maturity, isn’t called early, and the issuer pays everything on time.
- Taxes and trading costs aren’t included.
Frequently asked questions
How do you calculate the price of a bond?
Add up the present value of every future payment: each coupon payment and the face value at the end, each discounted at the market yield. Price = coupon × [1 − (1 + y)^−n] ÷ y + face × (1 + y)^−n, where y is the yield per period and n is the number of payments.
What is yield to maturity?
Yield to maturity (YTM) is the yearly return you would earn if you bought a bond at today’s price, received every coupon, reinvested them at that same rate and held the bond until it paid back its face value. It is the single best number for comparing bonds with different prices and coupons.
Why do bond prices fall when interest rates rise?
A bond’s coupon is fixed. If new bonds start paying more, nobody will pay full price for an older bond paying less — so its price drops until its yield matches the new market rate. When rates fall, the opposite happens and older, higher-paying bonds become worth more.
What is the difference between current yield and yield to maturity?
Current yield is simply the annual coupon divided by today’s price. Yield to maturity also counts the gain (or loss) you get when the bond pays back its face value at the end, and the timing of every payment. For a bond bought at a discount, YTM is higher than current yield; for a premium bond, it is lower.
What does duration mean?
Duration measures how sensitive a bond’s price is to interest-rate changes. This calculator shows modified duration: roughly the percent the price moves when yields change by one percentage point. A duration of 8 means a 1-point rise in yields cuts the price by about 8%.
These results are estimates for education only, based on the assumptions you enter. They are not financial, investment or tax advice. Real returns, rates and taxes vary. See our methodology anddisclaimer.