Bond Price Calculator

What Is a Bond?

A bond is a debt instrument issued by governments or corporations to raise money. When you buy a bond, you are lending money to the issuer. In return, the issuer promises to pay you periodic coupon payments (interest) and return your face value (principal) at maturity.

Key Bond Terms

• Face value (par value): The amount returned at maturity — usually $1,000 per bond.
• Coupon rate: The annual interest rate stated on the bond. A 5% coupon on a $1,000 bond pays $50 per year.
• Yield to Maturity (YTM): The total annual return if you hold the bond to maturity and reinvest all coupons — the market-determined required rate of return.
• Maturity: The date (or years until the date) when the face value is repaid.

Bond Pricing Formula

A bond is priced as the present value of all future cash flows — coupons plus face value — discounted at the required yield:

Bond Price = Σ [C / (1 + r)^t] + F / (1 + r)^n

Where: C = periodic coupon payment, r = period yield (YTM / periods per year), F = face value, n = total periods, t = period number.

The Fundamental Inverse Relationship

When interest rates rise, bond prices fall. When interest rates fall, bond prices rise.

This is the single most important concept in fixed income investing. Here is why: If market yields rise to 6% but your bond pays only 5%, no one will pay full price for a 5% bond when they can get 6% elsewhere. So the bond price drops until its effective yield (total return at the lower price) matches the market rate of 6%.

Premium, Par, and Discount Bonds

• At par: Coupon rate = YTM → Price = Face value
• At premium: Coupon rate > YTM → Price > Face value (bond pays more interest than the market requires)
• At discount: Coupon rate < YTM → Price < Face value (bond pays less interest than the market requires)

Duration: two numbers, and only one of them is the rule of thumb

Macaulay duration is the weighted average time, in years, to receive the bond’s cash flows. It is a measure of when you get paid.

Modified duration is Macaulay divided by (1 + yield per period), and it is the one that estimates price movement. A bond with a modified duration of 7 loses roughly 7% of its value if yields rise by 1%.

The two get used interchangeably and they are not the same. On a 10-year bond yielding 6% semi-annually the Macaulay figure is 7.89 and the modified figure is 7.66, so quoting Macaulay overstates the price move by about 3%. On a long bond at a high yield the gap is wider. The calculator shows both and uses the modified figure for the estimate.

Longer duration means greater interest rate risk, whichever measure you use.

Worked Example

A $1,000 bond with a 5% coupon, paying semi-annually, yielding 6%, with 10 years to maturity.

Period coupon = 5% × $1,000 ÷ 2 = $25, paid 20 times. Period yield = 6% ÷ 2 = 3%. Price = sum of $25 discounted over 20 periods, plus $1,000 discounted over 20 periods = $925.61.

It trades at a discount because the 5% coupon is below the 6% the market wants. Current yield is $50 ÷ $925.61 = 5.40%, which sits between the coupon rate and the YTM, as it always does for a discount bond. Modified duration is 7.66, so a rise to 7% would take the price to roughly $854.

Current Yield

Current yield = Annual coupon / Current price. This is simpler than YTM and ignores capital gain or loss at maturity. It is useful for a quick comparison but YTM is more complete.

Bond Ratings

Investment-grade bonds (BBB/Baa and above) are considered safe enough for institutional investors. Below investment-grade (“junk” or “high-yield”) bonds offer higher yields to compensate for higher default risk. US Treasury bonds carry essentially no default risk and serve as the “risk-free” rate benchmark.