What this calculator does
A bond is a stream of coupon payments plus the return of face value at maturity. Its price is simply the present value of that stream, discounted at whatever yield the market currently demands. When market yields rise above the coupon rate, the price falls below face value; when they fall, the price rises above it.
That inverse relationship is the single most important thing about bonds, and this calculator makes it visible. Holding everything else constant and moving the yield shows exactly how much price risk a bond carries: and longer maturities carry considerably more of it.
The formula
Each coupon is discounted at the periodic yield according to how far away it is, and the face value is discounted from maturity. The coupon stream is an annuity, so it collapses into a closed form; the face value is a single discounted amount added on top.
| Term | Meaning |
|---|---|
| F | Face or par value: repaid at maturity. |
| C | The coupon payment per period: face value × coupon rate ÷ payments per year. |
| i | The market yield per period. |
| N | Total number of coupon periods remaining. |
| Current yield | Annual coupon income ÷ current price. |
The inputs explained
| Field | What to enter |
|---|---|
| Face value ($) | The amount repaid at maturity, commonly 1,000 or 100 per unit. |
| Coupon rate (%) | The coupon rate printed on the bond. This is fixed for the life of the bond and does not change with the market. |
| Market yield (%) | The yield the market currently demands for bonds of this risk and maturity. This is the input that moves. |
| Years to maturity | Years remaining until maturity. |
| Payments per year | How often coupons are paid. Semi-annual is the most common convention. |
When to use it
Valuing a bond you already hold
Enter its coupon and the yield now available on comparable bonds. If the market yield has risen since you bought, the price will have fallen, and vice versa.
Understanding interest rate risk
Run the same bond at several yields and note how much the price moves. Then repeat with a longer maturity: the price swings become much larger, which is duration in action.
Comparing a bond against a term deposit
A bond held to maturity returns its yield regardless of price movements along the way. The current yield line shows the income relative to what you would pay today.
Deciding between premium and discount bonds
A high-coupon bond trading at a premium returns more income but a capital loss at maturity. A discount bond does the reverse. At the same yield they are economically equivalent: but the tax treatment often is not.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Bond price as the market yield changes
A ten-year bond with a 5% coupon paying semi-annually, priced at a range of market yields.
| Market yield | Bond price | Trading at | Current yield |
|---|---|---|---|
| 2% | $1,270.68 | a premium | 3.93% |
| 3% | $1,171.69 | a premium | 4.27% |
| 4% | $1,081.76 | a premium | 4.62% |
| 5% | $1,000.00 | par | 5.00% |
| 6% | $925.61 | a discount | 5.40% |
| 8% | $796.15 | a discount | 6.28% |
How maturity amplifies price risk
The same 5% coupon bond at a 7% market yield, across different maturities.
| Years to maturity | Bond price | Current yield | Total coupons to maturity |
|---|---|---|---|
| 1 year | $981.00 | 5.10% | $50.00 |
| 3 years | $946.71 | 5.28% | $150.00 |
| 5 years | $916.83 | 5.45% | $250.00 |
| 10 years | $857.88 | 5.83% | $500.00 |
| 20 years | $786.45 | 6.36% | $1,000.00 |
| 30 years | $750.55 | 6.66% | $1,500.00 |
The effect of the coupon rate
Ten-year bonds with different coupons, all priced at the same 6% market yield.
| Coupon rate | Bond price | Trading at | Coupon payment | Current yield |
|---|---|---|---|---|
| 0% | $553.68 | a discount | $0.00 every 6 months | 0.000% |
| 2% | $702.45 | a discount | $10.00 every 6 months | 2.85% |
| 4% | $851.23 | a discount | $20.00 every 6 months | 4.70% |
| 6% | $1,000.00 | par | $30.00 every 6 months | 6.00% |
| 8% | $1,148.77 | a premium | $40.00 every 6 months | 6.96% |
| 10% | $1,297.55 | a premium | $50.00 every 6 months | 7.71% |
Questions
Why do bond prices fall when interest rates rise?
Because a bond’s coupon is fixed. If new bonds are issued paying more, the old one is only attractive at a lower price: one that brings its effective return up to the new market yield.
What is the difference between coupon rate and yield?
The coupon rate is fixed at issue and determines the cash payments. The yield is what the market currently demands, and it moves constantly. They are equal only when the bond trades exactly at par.
What is current yield?
Annual coupon income divided by the current price. It measures income relative to what you pay, but ignores any capital gain or loss at maturity, so it overstates the return on a premium bond and understates it on a discount one.
Does this calculate yield to maturity?
Not directly. It prices a bond from a given yield. To find yield to maturity, adjust the yield until the calculated price matches the market price you were quoted.
What is accrued interest?
Interest earned since the last coupon date, which a buyer pays on top of the quoted price. This calculator prices the bond on a coupon date, so accrued interest is zero.
For the discounting principle behind this, see present and future value. For share positions instead, use the average share cost calculator.