Question

The following table shows some data for three zero-coupon bonds. The face value of each bond is $1,000. Bond Maturity (Years) Yield to Maturity Price $ 380 380 B 10% a. What is the yield to maturity of bond A? (Do not round intermediate calculations. Enter your answer as a percent rounded to 3 decimal places. Assume annual compounding.) Yield to maturity b. What is the maturity of B? (Do not round intermediate calculations. Round your answer to 2 decimal places. Assume annual compounding.) Maturity years c. What is the price of C? (Do not round intermediate calculations. Round your answer to 2 decimal places. Assume annual compounding.) Price

Answer 1

Price = Face Value / (1 + YTM)^N

Part (a)

Price = 380 = Face Value / (1 + YTM)^N = 1,000 / (1 + YTM)²⁰

Hence, (1 + YTM)²⁰ = 1,000 / 380 = 2.6316

Hence, YTM = 2.6316^1/20 - 1 = 4.957%

Part (b)

Price = 380 = Face Value / (1 + YTM)^N = 1,000 / (1 + 10%)^N

Hence, 1.1^N = 1,000 / 380 = 2.6316

Hence, Maturity = N = ln (2.6316) / ln (1.1) = 10.15 years

Part (c)

Price = 1,000 / (1 + 9%)¹⁸ = 211.99