π Bond Calculator
Bond price, current yield, and yield to maturity from real bond math.
Estimated Bond Price
Estimates for planning only, not financial advice.
How to Use This Calculator
Price a bond from its terms and the market yield, or work backwards from a market price to find the yield to maturity. Enter the face value, annual coupon rate, years to maturity, and payment frequency, then choose which direction to calculate. The results include the price, the current yield, and a year-by-year schedule of the cash flows.
Enter the Face Value (usually $1,000), the Annual Coupon Rate, the Years to Maturity, and how many coupon Payments Per Year the bond makes.
To find the price, choose "Price from yield to maturity" and enter the market YTM. To find the yield, choose "Yield to maturity from market price" and enter the price you would pay.
Read the price, the annual coupon in dollars, the current yield, and whether the bond trades at a premium or discount to face value.
Scan the cash flow schedule to see every payment and its present value, which shows exactly how much of the price comes from coupons versus the final principal repayment.
The Bond Pricing Formula
The first term is the present value of an annuity: all the coupon payments discounted at the per-period yield. The second term is the present value of the face value repaid at maturity. Together they equal what a rational buyer pays today for those future cash flows. When the coupon rate equals the YTM, the two forces balance and the price equals face value exactly. A coupon above the YTM pulls the price above par (a premium bond); a coupon below the YTM pushes it below par (a discount bond).
Worked Example
Price a $1,000 bond with a 5 percent annual coupon, semiannual payments, 10 years to maturity, when the market YTM is 4 percent. Each coupon is $25, there are 20 periods, and the per-period yield is 2 percent. Present value of coupons = $25 x (1 - 1.02^-20) / 0.02 = $25 x 16.3514 = $408.79. Present value of face = $1,000 / 1.02^20 = $672.97. Price = $408.79 + $672.97 = $1,081.76, a premium bond because the 5 percent coupon beats the 4 percent market yield. Current yield = $50 / $1,081.76 = 4.62 percent. Run the calculator in reverse with a market price of $1,081.76 and it recovers a YTM of 4.00 percent.
Finding YTM by Search
There is no algebra that isolates the yield in the pricing formula, so the calculator brackets it: it finds a low yield whose price is above your target and a high yield whose price is below it, then repeatedly halves the interval until the price matches to within a fraction of a cent. This binary search always converges because bond price falls smoothly as yield rises. If no yield in a sane range reproduces your price, for example a negative price or a price wildly above any reasonable value, the calculator tells you plainly instead of inventing a number.
Estimates for planning only, not financial advice.
Frequently Asked Questions
How is a bond priced?
A bond is worth the present value of everything it will pay you: every coupon payment plus the face value at maturity, each discounted back at the yield to maturity. The formula is price = C x (1 - (1+y)^-n)/y + F/(1+y)^n, where C is the coupon per period, y is the yield per period, n is the number of periods, and F is the face value. When market yields rise, the discount rate rises and the price falls.
What is yield to maturity (YTM)?
Yield to maturity is the single annualized return you earn if you buy the bond at its current price, hold it to maturity, and reinvest every coupon at the same yield. It is the discount rate that makes the present value of all future payments exactly equal the market price. Because the price formula cannot be rearranged to isolate the yield, it is found by numerical search, which this calculator does for you.
What is current yield and how is it different from YTM?
Current yield is simply the annual coupon divided by the current price, so a $50 annual coupon on a $1,081.76 bond gives a 4.62 percent current yield. Unlike YTM, it ignores the gain or loss you realize when the face value is repaid at maturity. Current yield is a quick income snapshot; YTM is the true total return.
Why do bond prices fall when interest rates rise?
A bond's coupon payments are fixed, so when new bonds pay higher rates, the old bond's fixed payments look less attractive and buyers will only pay less for them. The price drops until the old bond's yield to maturity matches what the market demands. Longer-maturity bonds swing more because more of their value sits far in the future, where discounting hits hardest.
What does it mean to buy a bond at a premium or discount?
A bond trades at a premium when its price is above face value, which happens when its coupon rate is higher than current market yields. It trades at a discount when its coupon is below market yields. At maturity you always receive exactly the face value, so premium buyers accept a small capital loss and discount buyers enjoy a capital gain, both reflected in the YTM.
How do semiannual coupons change the math?
Most US corporate and Treasury bonds pay coupons twice a year, so a 5 percent annual coupon on a $1,000 bond means $25 every six months. The formula then uses 20 half-year periods and a per-period yield of YTM/2. The calculator annualizes the result back to a standard YTM. Using annual periods on a semiannual bond would give you the wrong price, so the payment frequency matters.