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# P1.T4.313. Forward and par rates

#### Fran

AIMs: Define and interpret the forward rate, and compute forward rates given spot rates. Define par rate and describe the equation for the par rate of a bond. Interpret the relationship between spot, forward and par rates.

Questions:

313.1. For the 1.5 year swap rate curve, assume the following swap rates and discount factors:

Expressed with semi-annual compounding, which is nearest to the six-month forward rate in six months; i.e., f(.5, 1.0) or f(0, 0.5, 1.0)?

a. 0.40%
b. 0.60%
c. 0.85%
d. 1.00%

313.2. Assume we observe the following 1.5 year swap rate curve and associated discount factors (but we are not given the spot rates):

Which is nearest to the 1.5 year semi-annual par rate; i.e., the 1.5 year par rate with semi-annual compound frequency?

a. 0.50%
b. 0.55%
c. 0.70%
d. 0.91%

313.3. We are given the 1.5 year discount function (i.e., set of discount factors) below. Also, below is the mathematical definition of the semi-annual par rate: the par rate, C(T), is the coupon rate such that the present value of the bond equals par.

Given these discount factors, which is nearest to the 1.5 year par rate, C(1.5)?

a. 1.33%
b. 1.50%
c. 1.80%
d. 2.40%