FRM Part I · FRM Exam Part I · Interest Rates
The market's 1-year and 2-year zero-coupon (spot) rates are 2.00% and 3.00% respectively, both expressed with annual compounding. What is the 2-year discount factor, rounded to four decimals?
The 2-year discount factor is 0.9426. It is found by discounting one unit at the 2-year spot rate of 3% compounded annually for two years, so 1/1.03 squared, or 1/1.0609. Averaging the spot rates or using simple interest gives wrong values.
- A0.9426Correct
- B0.9434
- C0.9709
- D0.9518
Explanation
The discount factor is 1/(1.03)^2 = 1/1.0609 = 0.9426. 0.9434 results from treating the rate as simple interest, 1/1.06. 0.9709 discounts for only one year at 3%. 0.9518 uses the average of the two spot rates, 2.5%, which is not the 2-year spot rate.
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