Compute Yield to Maturity (YTM), current yield, coupon rate, and bond type from face value, market price, coupon, and maturity. Visualize the price–yield relationship on an interactive canvas.
A bond yield is the return an investor realizes on a bond. It can be expressed in several ways: Yield to Maturity (YTM), current yield, and coupon rate. Each metric provides a different lens for evaluating a bond's performance and risk. This calculator helps you compute all three instantly and visualizes the fundamental inverse relationship between bond prices and yields.
The bond price formula (present value of cash flows):
P = ∑ nt=1 C / (1 + r)t + FV / (1 + r)n
where P = market price, C = periodic coupon, r = periodic discount rate (YTM per period), n = number of periods, FV = face value.
The calculator solves for Yield to Maturity (YTM) by finding the discount rate r that equates the present value of all future cash flows (coupon payments and principal repayment) to the current market price. Because the equation is non‑linear, we use a numerical root‑finding method (Newton‑Raphson) to compute YTM to high precision.
Current yield is simply the annual coupon payment divided by the market price. It ignores the time value of money and any capital gain or loss, making it a quick but incomplete measure of return.
The coupon rate is the annual interest rate stated on the bond, expressed as a percentage of face value. It determines the periodic coupon payment.
The bond type is determined by comparing the market price to face value:
• Premium (Price > Par) – coupon rate > YTM
• Par (Price = Par) – coupon rate = YTM
• Discount (Price < Par) – coupon rate < YTM
| Metric | Definition | Use Case |
|---|---|---|
| Yield to Maturity (YTM) | The total return anticipated if the bond is held until it matures, assuming all coupon payments are reinvested at the same rate. | Primary metric for comparing bonds; reflects time value of money and all cash flows. |
| Current Yield | Annual coupon payment divided by the current market price. | Quick, simple measure; ignores capital gains/losses and time value. |
| Coupon Rate | The fixed annual interest rate paid by the bond issuer, based on face value. | Determines the periodic cash flow; does not change over the bond's life. |
| Yield to Call (YTC) | Return if the bond is called before maturity (not computed here). | Relevant for callable bonds; often higher than YTM. |
A corporation issues a 10‑year, 5% semiannual bond with a face value of $1,000. The bond is currently trading at $950. Using the calculator, the YTM is approximately 5.63%, the current yield is 5.26%, and the bond is classified as a discount bond (price < par). The investor's total return over the 10‑year period includes both coupon income ($500 total) and a capital gain of $50, for a nominal total return of 55% on the initial investment. The price–yield chart shows that if yields rise to 6%, the price would fall to about $925 – illustrating interest rate risk.
This analysis helps the portfolio manager decide whether the bond offers adequate compensation for its credit risk and interest rate sensitivity relative to other fixed-income alternatives.
Bond prices and yields move in opposite directions. This inverse relationship is non‑linear: the price curve is convex. Convexity measures the curvature of the price–yield relationship; bonds with higher convexity have better price appreciation when yields fall and less price depreciation when yields rise. Our interactive chart plots the price for a range of yields around the current YTM, showing this convexity visually.
For a given change in yield, the price change is approximated by duration (first‑order sensitivity) plus a convexity adjustment (second‑order). While our calculator does not explicitly compute duration and convexity, the chart provides an intuitive grasp of these concepts.