Given the yield on a 3-year zero-coupon bond is 7.2% and forward rates of 6.1% in year 1 and 6.9% in year 2, what must be the forward rate in year 3?
A)8.4%
B)8.6%
C)8.1%
D)8.9%

Question

Quizplus · Accepted Answer

Using the formula for calculating the yield on a zero-coupon bond:

Yield = (Face Value / Present Value)^(1/n) -1

Where Face Value is $100, n is the number of years, and Present Value is the price that the investor is willing to pay for the bond today.

Assuming a Face Value of $100 and solving for Present Value:

Present Value = Face Value / (1 + Yield)^n

Present Value for a 3-year zero-coupon bond with a yield of 7.2% would be:

Present Value = $100 / (1 + 0.072)^3 = $78.55

Using the formula for calculating the forward rate:

Forward Rate = [(1 + r2)^2 / (1 + r1)] - 1

Where r1 is the rate for the first period, r2 is the rate for the second period, and Forward Rate is the rate for the third period.

Substituting the given values:

Forward Rate = [(1 + 0.069)^2 / (1 + 0.061)] - 1 = 0.086 or 8.6%

Therefore, the answer is B) 8.6%.

Given the Yield on a 3-Year Zero-Coupon Bond Is 7