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 1 $ 978.43 $ 924.97 $ 840.12 | $ 784.39 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 $ 978.43 924.97 840. 12 784.39 Forward Rate Maturity (Years) Price of Bond $ 924.97 3 $ 840.12 $ 784.39

Answer 1

a)

future value = present value (1 + y)^n

where future value = $1000

present value = price of the bond

y = yield to maturity

n = number of years to maturity

re - writing above formula

y = (future value / present value)^1/n - 1

D12 - А 1 maturity Price of the bond YTM 2 1 978.43 =(1000/2)^(1/A2)-1 3 2 924.97 = (1000/B3)^(1/A3)-1 4 3 840.12 =(1000/B4)^(1/A4)-1 5 4 784.39 1=(1000/85)^(1/A5)-1|

the above image shows formulas

с А В maturity Price of the bond YTM 1 | | 978.43 2.20% | 2 924.97 3.98% ) 840.12 5.98% 784.39 6.26% |

b)

forward rate = [(1 + yn)n / (1 + yn-1)n-1] - 1

where yn = YTM of current year

yn-1 = YTM of previous year

C maturity Price of the bond YTM forward rates 978.43 =(1000/B2)^(1/A2)-1 924.97 =(1000/B3)^(1/A3)-1 =((1+C3) A3/(1+C2))-1 840.12 =(1000/B4)^(1/A4)-1 =((1+C4)^A4/(1+C3)^2)-1 784.39 =(1000/B5)^(1/A5)-1 =((1+C5)^A5/(1+C4)^3)-1

above image shows formulas

A B C maturity Price of the bond YTM forward rates 1 9 78.43 2.20% 2 924.97 3.98% 5.78% 3 840.12 5.98% 10.10% 4 784.39 6.26% 7.10%