Question

Assuming semiannual compounding, what is the price of a zero coupon bond with 18 years to maturity paying $1,000 at maturity if the YTM is (Do not round intermediate calculations and round your answers to 2 decimal places, e.g., 32.16.): Please provide as many details on formulas as possible. Excel if possible. Thank you !

Answer 1

The question seems to be missing the YTM figure. So this will be solved with assumption of 3% YTM.

Price of zero coupon bond = present value of its maturity value, discounted at the YTM for 18 years

Since the compounding is semiannual, the semiannual YTM = 3% / 2 = 1.5%

Number of compounding periods = number of years * 2 = 18 * 2 = 36

Present value = future value / (1 + r)ⁿ,

where r = interest rate per period and n = number of compounding periods

Price of bond = $1000 / (1 + 1.5%)³⁶ = $585.09

As another example, let us say the YTM is 5%. Then, the semiannual rate = 5% / 2 = 2.5%

Price of bond = $1000 / (1 + 2.5%)³⁶ = $411.09