Question

The following is a list of prices for zero-coupon bonds of various maturities. a. Calculate the yield to maturity for a bond with a maturity of (i) one year; (ii) two years; (iii) three years; (iv) four years. (Do not round intermediate calculations. Round your answers to two decimal places.) YTM Maturity (Years) Price of Bond 920.90 $ 912.97 $ 826.62 $ 785.62 b. Calculate the forward rate for (i) the second year; (ii) the third year; (iii) the fourth year. (Do not round intermediate calculations. Round your answers to two decimal places.) Maturity (years) Price of Bond $ 920.90 912.97 826.62 785.62 Forward Rate Maturity (Years) Price of Bond $ 912.97 $ 826.62 $ 785.62

Answer 1

Answer:

a. Calculation of the yield to maturity for a bond with a maturity years

Yield to Maturity = [(Face value/Bond price)^(1/Time period)] - 1

i. One year = (1000/920.90) - 1 = 0.0858942339 = 8.59%

ii. Two year = (1000/912.97)^(1/2) - 1 = 0.04657835011 = 4.66%

iii. Three year = (1000/826.62)^(1/3) - 1 = 0.06552758403 = 6.55%

iv. Four year = (1000/785.62)^(1/4) - 1 = 0.06217693669 = 6.22%

b.  Calculation of the forward rate

Forward rate = [(1 + Next year YTM)^Period / (1+Previous year YTM)^Period} - 1

i. Second year = (1+4.66%)^2/(1+8.59%) - 1 = 0.00872231328 = 0.87%

ii. Third year = (1+6.55%)^2/(1+4.66%) - 1 = 0.08474130517 = 8.47%

iii. Fourth year = (1+6.22%)^2/(1+6.55%) - 1 = 0.05891022055 = 5.89%