Bond Price Calculator

A bond price is the amount an investor pays to purchase a bond in the market. It represents the present value of all future cash flows from the bond — periodic coupon payments plus the repayment of the face value at maturity. Bond prices fluctuate with interest rates: when rates rise, bond prices fall, and vice versa.

The bond price is calculated as the sum of the present values of all future coupon payments plus the present value of the face value at maturity. The formula discounts each cash flow using the yield to maturity (YTM) as the discount rate. Mathematically: Bond Price = Σ [Coupon / (1 + r)^t] + [Face Value / (1 + r)^n], where r is the periodic yield and n is the total number of periods.

A coupon is the periodic interest payment made to bondholders during the life of the bond. It is typically expressed as an annual percentage of the face value (the coupon rate). For example, a $1,000 bond with a 5% annual coupon rate pays $50 per year, split across payment intervals (e.g., $25 semi-annually).

Yield to Maturity (YTM) is the total annual return an investor can expect if the bond is held until it matures, assuming all coupon payments are reinvested at the same rate. It serves as the discount rate in the bond pricing formula. A bond's YTM changes constantly as its market price fluctuates.

Face value (also called par value) is the nominal value of the bond that the issuer promises to repay the bondholder at maturity. Most bonds have a face value of $1,000. The coupon rate is applied to this face value to determine the periodic interest payments.

When interest rates rise, bond prices fall. This is because new bonds issued at higher rates become more attractive, making existing lower-rate bonds less valuable. Investors demand a discount to hold the older bond. Conversely, when interest rates fall, existing bonds with higher coupon rates become more valuable and their prices rise above par.

A bond trades at a premium when its market price is above its face value, which happens when its coupon rate is higher than the current market yield. A bond trades at a discount when its price is below face value, meaning its coupon rate is lower than prevailing yields. A bond trades at par when its price equals its face value, meaning the coupon rate equals the YTM.

Yes, coupon frequency can slightly affect the bond price. More frequent payments (e.g., monthly vs. annually) mean the investor receives cash sooner, which has a marginally higher present value. Semi-annual compounding is the most common convention for US bonds, and calculators typically adjust the periodic rate and number of periods accordingly.