Bond Price
Price = Σ C/(1+r)^t + FV/(1+r)^n
Price a bond by discounting all coupon payments and the face value at the yield to maturity.
Variables
Periodic interest payment
YTM divided by payments per year
Par value returned at maturity
Years times payments per year
Example Calculation
Scenario
A 5-year bond with $1,000 face value, 6% annual coupon, and 8% YTM.
Given Data
Calculation
Price = 60/1.08 + 60/1.08^2 + 60/1.08^3 + 60/1.08^4 + 1060/1.08^5 = 920.15
Result
$920.15
Interpretation
The bond trades at a discount because its coupon (6%) is below market yield (8%).
When to Use This Formula
- ✓Fixed income homework
- ✓Comparing bonds with different coupons
- ✓Understanding premium vs discount pricing
Common Mistakes
- ✗Forgetting to adjust for semi-annual coupons
- ✗Using the wrong number of periods
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Common questions about this formula
When its coupon rate exceeds the current market yield, investors pay a premium for the higher payments.
Divide the annual coupon by 2 to get the semi-annual payment, divide YTM by 2 for the period rate, and multiply years by 2 for total periods. This is the standard convention for most corporate and government bonds.