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Suppose that 6-month, 12-month, 18-month, and 24-month zero rates continuously compounded are 0.01, 0.01,0.04,and 0.01 per...

Suppose that 6-month, 12-month, 18-month, and 24-month zero rates continuously compounded are 0.01, 0.01,0.04,and 0.01 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 $87 per annum semiannually. Please write down the numerical answer with two decimal points and no dollar sign.

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Answer #1

Given given continuous compounding rates, price of the bond is calculated as follows:

coupon paid semiannually = $87/2 = $43.50

It maturity, Face value of $1000 will also be paid so, total cash flow at maturity = $1000 + 43.5 = $1043.5

discount factor = e^(-rate*year)

PV of coupon = discount factor*coupon,

Price of bond is sum of PV of all coupons = $1150.15

Year Period rate Coupon discount factor PV of coupon
0.5 1 1.00% 43.5 0.9950 43.2830
1 2 1.00% 43.5 0.9900 43.0672
1.5 3 4.00% 43.5 0.9418 40.9668
2 4 1.00% 1043.5 0.9802 1022.8373
Price 1150.1543
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