Question

Suppose that 6-month, 12-month, 18-month, and 24-month zero rates continuously compounded are 0.01, 0.04,0.02,and 0.02 per annum, respectively. Estimate the cash price of a bond with a face value of $1000 that will mature in 24 months pays a coupon of $85 per annum semiannually. Please write down the numerical answer with two decimal points and no dollar sign.

Answer 1

Answer:

1126.00

Explanation:

continuous compounding rate for these given periods;

6-month,  12-month,  18-month,    24-month  ;

  0.01,         0.04,           0.02,          0.02              per annum,

Estimate the cash price of a bond with face value of $1000 that will mature in 24 months ( 2 years )

 calculate the semiannual coupon payments = $85 /2 = 42.5

 discount factor = e^(-rate*year)

 coupon paid at maturity = semi annual payment + face value = $1042.5

 PV ( present value ) of coupon = coupon * discount factor

Hence cash price of the Bond = ∑ Pv of coupons

= 1125.9975 ≈ 1126.00

attached below is the detailed tabular solution