Suppose you observe the following zerocoupon bond prices per

Suppose you observe the following zero-coupon bond prices per $1 of maturity payment: 0.95184 (1-year), 0.89472 (2-year), 0.83089 (3-year). Compute r₀(1,3), the implied forward rate for a loan made at the end of year 1 and maturing at the end of year 3.

7.68%

7.28%

7.03%

6.38%

7.15%

7.68%

please explain in steps

Suppose you observe the following zero-coupon bond prices per $1 of maturity payment: 0.95184 (1-year), 0.89472 (2-year), 0.83089 (3-year). Compute r0(1,3), the implied forward rate for a loan made at the end of year 1 and maturing at the end of year 3.

Selected Answer: e. 7.68% Answers: a. 7.28% b. 7.03% c. 6.38% d. 7.15% e. 7.68%

Solution

A B C = B/A Time Price/$ Discount Implied interest rate 1 0.95184 0.04816 0.050596739 2 0.89472 0.10528 0.117668097 3 0.83089 0.16911 0.203528746 1.20353 = (1 + .0506) * (1 + x)2 (1+r3)^3 = (1+r1) x (1+x)^2 Divide both sides by 1.0506 Here, cumulative value of (1+r3)^3 = 1.20353 1.145564 = (1 + x)2 r3 is rate for 3 years Take the square root of both sides to get ride of the 2 1.07031 = 1 + x x = .07031 or 7.03%