Year Year Forward Rate 1 4.6% 2 4.9% 3 5.2% 4 5.5% 5 6.8% What should the purchase price of a 3-year zero-coupon bond be if it is purchased today and has face value of $1,000?A. $966.87.B. $911.37.C. $950.21.D. $956.02.E. $945.51.

no option is correct, since the market value of the bond is $866.32

if the bond matured in 2 years instead of 3, then option B. $911.37 would be correct = $1,000 / [(1.046)x(1.052)] = $911.366 = $911.37

Explanation:

in order to determine the market value of the bond we need to determine the present value of its face value:

market value = PV = future value / [(1 + i₁) x (1 + i₂) x (1 + i₃)]

future value = $1,000

[(1 + i₁) x (1 + i₂) x (1 + i₃)] = [(1 + 4.6%) x (1 + 4.9%) x (1 + 5.2%)] = 1.154311

PV = $1,000 / 1.154311 = $866.32

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