Prices of zero-coupon bonds reveal the following pattern of forward rates: Year Forward Rate 1 5 % 2 6 3 7 In addition to the zero-coupon bond, investors also may purchase a 3-year bond making annual payments of $50 with par value $1,000. a. What is the price of the coupon bond? (Do not round intermediate calculations. Round your answer to 2 decimal places.)

The price of the coupon bond is $ 1,232.30

Explanation:

The forward rates are:

year 1 5%

year 2 6%

year 3 7%

In determining the price of the bond, we discount the coupon and the face value of the bond as below:

price=coupon / (1+f1) + coupon / (1+f1) * (1+f2) + (coupon+face value) / (1+f1) * (1+f2) * (1+f3)

price=50 / (1+5%) + 50 / (1+5%) * (1+6%) + 1050 / (1+5%) * (1+6%) * (1+7%) = $1,232.30

The price of the bond using the forward rates provided is $ 1,232.30

This implies that an increasing forward rates led to the bond been issued at a premium of $232.30 when compared to its face value of $1000 i. e $ 1,232.30-$1,000.00