Quick answer: A 1,000 bond paying a 5% coupon twice a year with 10 years left is worth 925.61 at a 6% yield to maturity; it trades at a discount because its coupon is below the market yield.
How it's calculated
Price = C × (1 − (1 + y)^−N) ÷ y + F × (1 + y)^−N, where C is each coupon (face × coupon rate ÷ coupons a year), y the yield per period, N the number of coupons left and F the face value repaid at maturity.
Yield to maturity (YTM) is the single rate that makes this price equal the market price; it is found numerically. Price and yield move in opposite directions: when yields rise, prices fall.
Current yield is the yearly coupon ÷ price. Macaulay duration is the weighted average time to the cash flows; modified duration estimates the percentage price change for a 1-point change in yield (about 7.7% here).
Worked examples
- 1,000 face, 5% semi-annual, 10 years, YTM 6%: price = 925.61
- Same bond priced at 1,050: YTM = 4.377%
Frequently asked questions
Why does a bond sell below face value?
When its coupon is lower than the yield new bonds offer, buyers pay less so that their total return matches the market.
Does this work for sukuk?
Yes, for fixed-rate sukuk with periodic distributions and the face amount at maturity, the pricing maths is the same.
What about accrued interest?
Prices here are on a coupon date. Between coupons, the buyer also pays the coupon earned since the last payment.
Why do bond prices fall when yields rise?
A bond's coupon is fixed. When new bonds pay more, an older bond must sell for less so that its buyer earns the same yield.
What is the difference between the coupon rate and the yield?
The coupon rate is the fixed interest on the face value. Yield to maturity is the return you earn at today's price if you hold to the end.
Why are longer bonds more sensitive to rates?
More of their value lies in payments far in the future, and those lose more value when the yield rises.