The 6-month and 1 -year zero rates are both 5 % per annum....

The 6-month and 1 -year zero rates are both $5 \%$ per annum. For a bond that has a life of 18 months and pays a coupon of $4 \%$ per annum (with semiannual payments and one having just been made), the yield is $5.2 \%$ per annum. What is the bond's price? What is the 18-month zero rate? All rates are quoted with semiannual compounding.

Key Concepts

Coupon Payments

Coupon payments are periodic interest payments made to bondholders during the life of the bond. These payments, often expressed as a percentage of the face value, are an essential part of a bond's cash flow structure and must be accurately timed and discounted in the pricing process.

Zero Rates

Zero rates, or spot rates, are the interest rates used to discount a single cash flow occurring at a specific future time, reflecting the cost of money for that period. They are a fundamental input for pricing bonds since each cash flow is discounted at the rate corresponding to its maturity.

Bond Pricing

Bond pricing involves calculating the present value of all future cash flows, including coupon payments and the principal repayment, using appropriate discount factors derived from zero rates or yield curves. The bond's price reflects the sum of these discounted cash flows.

Yield to Maturity (YTM)

Yield to maturity is the rate of return anticipated on a bond if it is held until it matures. It takes into account all coupon payments and the redemption value, providing a single measure that equates the bond's current price with its future cash flows when using the appropriate compounding convention.

Semiannual Compounding

Semiannual compounding refers to the practice of compounding interest twice a year rather than once annually. This compounding convention is crucial in fixed-income markets and affects the conversion of annual rates into period-specific rates used in calculating the present value of cash flows.

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