What it calculates

Bond pricing converts a fixed schedule of coupon payments and a final principal repayment into a present value today. It also runs in reverse: given a market price, it solves for the yield to maturity that makes the discounted cash flows equal that price.

How it is calculated

Each coupon is discounted at the yield for the number of periods until it is paid, and the face value is discounted from maturity. Price is the sum of those present values. Because price and yield move inversely and non-linearly, solving for yield from a price requires iteration rather than a closed formula. Duration measures the first-order sensitivity of price to yield; convexity captures the curvature that duration misses.

How to read the result

A bond trading above par is paying a coupon above current market yields, and below par the opposite. Duration tells you roughly how much the price moves for a one-point change in yield: a duration of 7 implies about a 7% price fall for a 100 basis point rise. That approximation degrades for large moves, which is exactly when convexity matters.

Worked example

A 5-year bond with a 5% annual coupon on 1,000 face, priced to yield 6%, pays 50 a year plus 1,000 at maturity. Discounting the five coupons and the principal at 6% gives roughly 957.88 - a discount to par, because the 5% coupon is below the 6% required yield.

Common questions

What is the difference between current yield and yield to maturity?

Current yield is just the annual coupon divided by the price, ignoring any gain or loss from holding to maturity. Yield to maturity includes that pull to par and is the total return if you hold the bond to the end and reinvest coupons at the same rate.

Why do bond prices fall when interest rates rise?

Because the coupon is fixed. If new bonds are issued paying more, the only way an older, lower-coupon bond can compete is to sell for less, so its yield rises to match the market.

Does duration equal the number of years to maturity?

Only for a zero-coupon bond. For a coupon bond, duration is shorter than maturity because some cash comes back before the end. The larger the coupon, the shorter the duration.