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# P1.T4.415. Spot and forward rates

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Concept: These on-line quiz questions are not specifically linked to AIMs, but are instead based on recent sample questions. The difficulty level is a notch, or two notches, easier than bionicturtle.com's typical AIM-by-AIM question such that the intended difficulty level is nearer to an actual exam question. As these represent "easier than our usual" practice questions, they are well-suited to online simulation.

Questions:

415.1. The price of a six-month zero-coupon bond is $99.30 . The price of a one-year 6.0% coupon bond is$101.98. The face value of both bonds is $100.00 and the rates are expressed per annum with semi-annual compounding; aka, bond-equivalent basis. Which is nearest to the implied one-year spot rate? a. 1.00% per annum with semi-annual compounding b. 2.00% per annum with semi-annual compounding c. 3.00% per annum with semi-annual compounding d. 4.00% per annum with semi-annual compounding 415.2. Below are listed four bonds at various maturities from six months to two years. Along with the price of each bond is listed its coupon rate, the discount factor for its maturity, and the spot rate at each maturity: For example, the one-year spot rate, r(1.0), is about 2.85% based on a one-year discount factor, df(1.0), of 0.9271; and the six-month forward rate in six months, f(0.5,1.0), is equal to 3.72%. All rates are expressed per annum with semi-annual compounding. Which is nearest to the six month forward rate beginning in one-year, f(1.0, 1.5)? a. 2.80% b. 3.74% c. 4.91% d. 5.23% 415.3. The price of a four-year zero-coupon government bond is$86.00. The price of a similar five-year bond is \$79.51. If we assume all rates are expressed per annum with semi-annual compounding, which is nearest to the one-year implied forward rate from year four to year five; i.e., f(0.4, 0.5)?

a. 5.49%
b. 6.25%
c. 7.78%
d. 8.00%

Answers here: