A bond's value is the present value of everything it will pay you: each coupon payment, plus the face value at maturity, all discounted at the current market rate for bonds of similar risk and term. Price the coupons, price the final repayment, add the two — that sum is what the bond is worth today. Everything on this page is that one idea, applied carefully.
You need the calculation whenever a problem asks what a bond is worth after it has been issued. The coupon rate was fixed on the issue date, but market interest rates move every day, so the price is what adjusts. The formula below turns the bond's fixed cash flows and today's market rate into that price.
P = Σ [ C ÷ (1 + r)^t ] + F ÷ (1 + r)^n
P — Price of the bond today (its present value)
C — Coupon payment per period (face value × coupon rate, split across the year's payments)
r — Market rate (required yield) per period — not the coupon rate
t — The period each coupon arrives in (1, 2, and so on up to n)
F — Face (par) value repaid at maturity, usually $1,000
n — Total number of payment periods (years × payments per year)
The summation sign just means: discount every coupon back to today, one at a time, then add them up. The second term does the same for the single face-value repayment. Two present values, one price.
C, the coupon payment. Multiply the face value by the coupon rate. A $1,000 bond with a 6% coupon pays $60 a year; if it pays semiannually, as most US bonds do, each payment is $30. The coupon rate is written into the bond's contract and never changes, no matter what interest rates do afterward.
r, the market rate. This is the return investors currently require on comparable bonds, and it is the discount rate for every cash flow. It is not the coupon rate — that distinction decides whether your answer is right. The coupon rate tells you what cash the bond pays; the market rate tells you what that cash is worth today. If you know the price and need to solve for this rate instead, that reverse problem is yield to maturity.
F and n, the face value and the period count. F is the lump sum repaid at maturity, usually $1,000. n counts payment periods, not years — a 5-year bond that pays twice a year has 10 periods, and its last coupon lands in the same period as the face value.
The semiannual convention. When coupons arrive twice a year, convert every input to per-period terms: halve both rates and double the count. A 6% coupon becomes $30 every six months, an 8% market rate becomes 4% per period, and 5 years becomes 10 periods. Do all three conversions or none — mixing annual and semiannual inputs is the most common calculation error in this topic.
Take a bond an instructor could assign tomorrow: $1,000 face value, 6% coupon paid semiannually, 5 years to maturity, and a market rate of 8%. In per-period terms that is a $30 coupon, a 4% discount rate, and 10 periods. Discount each payment back to today:
| Period | Cash flow | Discount factor at 4% | Present value |
|---|---|---|---|
| 1 | $30 coupon | 0.961538 | $28.85 |
| 2 | $30 coupon | 0.924556 | $27.74 |
| 3 | $30 coupon | 0.888996 | $26.67 |
| 4 | $30 coupon | 0.854804 | $25.64 |
| 5 | $30 coupon | 0.821927 | $24.66 |
| 6 | $30 coupon | 0.790315 | $23.71 |
| 7 | $30 coupon | 0.759918 | $22.80 |
| 8 | $30 coupon | 0.730690 | $21.92 |
| 9 | $30 coupon | 0.702587 | $21.08 |
| 10 | $30 coupon | 0.675564 | $20.27 |
| 10 | $1,000 face value | 0.675564 | $675.56 |
| Total | Price of the bond | $918.90 |
The bond is worth $918.89 — $918.90 if you sum the rounded rows. Notice where the value sits: the ten coupons together contribute $243.34, while the single face-value repayment contributes $675.56. Even on a 5-year bond, most of the price is the promise to return the principal.
Bond prices and market rates move in opposite directions. This bond pays a 6% coupon while the market demands 8%, so nobody pays the full $1,000 — the price falls to $918.89, a discount of $81.11 below par, and a buyer at that lower price earns the market's 8% after all. Flip the situation and the logic flips: if the market rate dropped to 4%, those same $30 coupons would look generous, and the price would rise above face value.
That gives you three cases and one rule. Coupon rate below the market rate: the bond trades at a discount, like ours. Coupon rate above the market rate: it trades at a premium. The two rates equal: it trades at par, because discounting a 6% coupon stream at exactly 6% hands back the $1,000 face value. Before you compute anything on an exam, compare the two rates and predict which side of par the answer must land on — it is a free error check.
Use the coupon rate as the discount rate and the arithmetic collapses: every bond comes out worth exactly its face value, always. The calculation stops saying anything. If your answer to a pricing problem is exactly $1,000, check which rate you fed into the discount factors before you check anything else.
Discounting $60 annual coupons at 8% over 5 years gives about $920.15 — barely a dollar off the correct $918.89 here, which is exactly why this mistake survives: the wrong answer looks plausible. The gap widens on longer bonds and wider rate spreads, and instructors pick numbers that expose it. When the problem says semiannual, halve the rates and double the periods every time.
The period count trips students two ways. First, counting years instead of payments — a 5-year semiannual bond has 10 periods, not 5. Second, misreading time remaining: a 10-year bond issued 7 years ago has 6 semiannual periods left, and only those remaining payments enter the formula. The first coupon you discount arrives one period from now; nothing is paid at time zero.
The coupon rate sets a bond's cash flows; the market rate sets what they are worth. Discount every coupon and the face value at the market rate per period — never the coupon rate — and the sum of those present values is the price.
Bond valuation is finding the fair price of a bond by discounting its future cash flows — every remaining coupon payment plus the face value at maturity — at the current market rate for bonds of similar risk and term. The result is the most a rational investor should pay for the bond today.
Use the market rate — the yield investors currently require on comparable bonds — never the bond's own coupon rate. The coupon rate only sets the size of the cash payments. Discounting at the coupon rate returns face value every time, which tells you nothing about what the bond is worth.
A bond trades at a discount when its coupon rate is below the current market rate. Its fixed coupons pay less than new bonds offer, so the price drops until a buyer at that lower price earns the full market rate. In the worked example, a 6% coupon against an 8% market rate prices the bond at $918.89 versus $1,000 face.
Convert every input to per-period terms: halve the coupon rate, halve the market rate, and double the number of periods. A 6% semiannual coupon on $1,000 face value means $30 each period, an 8% market rate becomes 4% per period, and 5 years becomes 10 periods.
Use the PV function with per-period inputs. For the bond in the example, =PV(4%, 10, -30, -1000) returns 918.89: the rate is the per-period market rate, 10 is the number of periods, 30 is the coupon, and 1000 is the face value. The coupon and face value are entered as negatives so the price comes out positive.
By the FinanceBrain Team · Last verified July 11, 2026 · How we produce and verify articles