How a bond turns fixed cash flows into a price
Every plain-vanilla bond promises the same two things: a series of fixed coupon payments at regular intervals, and the return of its face value on the maturity date. Pricing it is therefore a discounting exercise — the same logic behind anypresent value calculator. Each future payment is worth less than its face amount today, and the further away it is, the more it is discounted. The coupons form a level annuity that collapses into a single closed-form term, while the face value is discounted as one lump sum at maturity. Add them together at the bond’s yield and you have its price; rearrange the problem to find the yield that reproduces a known price and you have the yield to maturity.
The bond pricing formula
price = C · [ 1 − (1 + i)−n ] / i + F / (1 + i)n
where C = coupon per period, F = face value,i = yield per period (YTM ÷ frequency), and n = total number of periods (years × frequency). The first term is the present value of the coupon annuity; the second is the present value of the face value repaid at maturity.
What makes this calculator different
- It solves both directions. Enter a yield to get the price, or enter a market price and it inverts the equation numerically to find the yield to maturity — there is no algebraic shortcut for YTM.
- It classifies the bond automatically. The result tells you whether the bond is trading at a premium, at par, or at a discount, based on how the yield compares to the coupon rate.
- It shows current yield too. Alongside YTM you see the current yield (annual coupon ÷ price), making the gap between the two measures explicit instead of hidden.
- It lays out the cash flows. The coupon stream and the final face-value repayment are shown, so you can see exactly which payments are being discounted and by how much.
Frequently asked questions
How is a bond priced?+
A bond’s price is simply the present value of everything it pays you. That’s the stream of fixed coupon payments plus the return of the face value at maturity, each cash flow discounted back to today at the bond’s yield. The coupons form an annuity, so they collapse into a neat closed-form term, while the face value is discounted as a single lump sum. Add the two together and you have the price an investor should be willing to pay to earn that yield.
What is yield to maturity (YTM)?+
Yield to maturity is the single discount rate that makes the present value of all the bond’s future cash flows equal to its current market price. In other words, it is the internal rate of return you earn if you buy the bond today and hold it to maturity, reinvesting coupons at that same rate. Because the pricing equation cannot be rearranged to isolate the yield, YTM has no algebraic solution and must be found numerically. This calculator solves for it iteratively when you enter a market price.
Why do bond prices and yields move inversely?+
A bond’s coupon and face value are fixed the day it is issued, so the only thing that can change to reflect new market rates is its price. When prevailing yields rise, the fixed cash flows are discounted more heavily, so each future payment is worth less today and the price falls. When yields fall, those same cash flows are discounted more gently and the price rises. The relationship is mechanical: price is the present value of fixed cash flows, and raising the discount rate always lowers a present value.
What’s the difference between coupon rate, current yield, and YTM?+
The coupon rate is fixed at issuance and is the annual coupon as a percentage of face value — it never changes. Current yield is the annual coupon divided by the bond’s current price, so it reflects today’s price but ignores any gain or loss at maturity. Yield to maturity is the most complete measure: it accounts for the coupons, the time value of money, and the difference between the purchase price and the face value repaid at maturity. For a bond bought at par all three are equal; otherwise they diverge.
What makes a bond trade at a premium versus a discount?+
It comes down to how the bond’s coupon rate compares to the yield investors currently demand. If the yield is below the coupon rate, the bond pays more than the market requires, so buyers bid its price above face value and it trades at a premium. If the yield is above the coupon rate, the bond underpays relative to the market, so its price falls below face value and it trades at a discount. When yield equals the coupon rate the bond trades exactly at par.
Disclaimer: This calculator is foreducation and illustration only. It uses standard bond pricing conventions and does not account for accrued interest, day-count nuances, credit risk, embedded options, or live market data. Its output is not a tradeable quote and real bond prices will differ. Nothing here is investment, tax, or trading advice.