Bond Price Calculator
Calculate the fair price of a bond as the present value of its future coupon payments plus its face value. Enter the face value, coupon rate, market yield, and years to maturity to see the bond's price.
Formula
Price = Σ [Coupon ÷ (1 + y)^t] + Face ÷ (1 + y)^n, where Coupon = Face × Coupon Rate and y = market yield
- A bond's price is the present value of every future cash flow discounted at the market yield.
- Each coupon is discounted by the number of years until it is paid; the face value is discounted over the full term.
- If the coupon rate exceeds the market yield, the bond trades at a premium; if it is lower, at a discount.
- When the coupon rate equals the yield, the price equals face value (par).
- This model assumes annual coupons and a single flat discount rate to maturity.
$1,000 bond, 5% coupon, 6% yield, 10 years
Inputs
- Face Value: 1000
- Annual Coupon Rate: 5 %
- Market Yield (Discount Rate): 6 %
- Years to Maturity: 10 years
The 5% coupon is below the 6% market yield, so the bond prices at about $926 — a discount to its $1,000 face value.
Frequently asked questions
How is a bond's price determined?
It is the present value of all future coupon payments plus the face value, each discounted at the market yield to maturity.
Why does a bond trade at a discount or premium?
If a bond's coupon rate is below current market yields, buyers pay less than face value (a discount); if it is higher, they pay more (a premium).
What is the market yield?
It is the return investors currently require for bonds of similar risk and maturity — the rate used to discount the bond's cash flows.
Why does price fall when yields rise?
Higher discount rates reduce the present value of fixed future payments, so the bond is worth less today.
Does this assume annual coupons?
Yes. This calculator discounts one coupon per year. Semi-annual bonds split the coupon and yield across two periods per year.