Bond Yield to Maturity (YTM) Calculator
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Coupon Frequency
Yield to Maturity (YTM)5.66%
Current Yield5.26%
Annual Coupon$50.00
Bond PricingDiscount (price < face)
Yield to Maturity (YTM) is the single discount rate that makes the present value of a bond future coupon payments plus its face value equal to the price you pay today. This calculator solves for that rate iteratively: you supply the par value, coupon rate, years remaining, market price, and payment frequency, and it searches for the yield that exactly reprices the bond. Unlike a bond pricing tool that starts from a known yield, this works the problem in reverse from the observed price.
Formula
Price = Σ [ C / (1 + y/m)^(m·t) ] + F / (1 + y/m)^(m·T); solve for y
- C
- Coupon payment per period
- F
- Face (par) value repaid at maturity
- y
- Yield to maturity (annual, the unknown being solved)
- m
- Coupon payments per year
- T
- Years to maturity
How it works
- Enter the face value, annual coupon rate, years to maturity, the current market price you would pay, and how often coupons are paid each year.
- The engine discounts every coupon and the final principal repayment at a trial yield, then uses bisection to adjust that yield until the discounted total matches your market price to within a fraction of a cent.
- It also reports the simpler current yield (annual coupon divided by price) and flags whether the bond trades at a premium, a discount, or at par.
Worked example
A $1,000 bond with an 8% coupon, 5 years to maturity, paying semiannually, currently sells for $960.
- Annual coupon = 1000 × 8% = $80, paid as $40 every six months.
- Because the price ($960) is below par, the bond trades at a discount and the YTM must exceed the 8% coupon.
- Bisection converges on the rate that discounts ten $40 coupons plus the $1,000 principal back to $960.
A yield to maturity of about 9.01%, versus a current yield of 8.33%.
Frequently asked questions
- How is YTM different from the current yield?
- Current yield is just the annual coupon divided by the price and ignores any gain or loss versus par. YTM also accounts for the price you paid converging to face value at maturity, so it is the more complete total-return measure.
- Why is YTM solved iteratively instead of with a formula?
- The pricing equation cannot be rearranged to isolate the yield in closed form because the rate appears in multiple discounted terms with different exponents. This tool uses bisection, which reliably converges by repeatedly narrowing the rate range.
- Why does a discount bond have a higher YTM than its coupon?
- Buying below par means you also earn the price appreciation back to face value at maturity. That extra gain lifts the total return above the coupon rate, so a discount bond YTM exceeds its coupon while a premium bond YTM falls below it.
- How does this differ from a bond price calculator?
- A bond price calculator takes a yield you already know and computes the fair price. This calculator does the inverse: it takes the market price you observe and solves for the yield that justifies it.