## Options Futures and Other Derivatives 10th Edition By JohnC. – Test Bank

**Hull: Options, Futures and Other Derivatives, Tenth Edition**

**Chapter 4: Interest Rates**

**Multiple Choice Test Bank: Questions with Answers**

- The compounding frequency for an interest rate defines
- The frequency with which interest is paid
- A unit of measurement for the interest rate
- The relationship between the annual interest rate and the monthly interest rate
- None of the above

Answer: B

The compounding frequency is a unit of measurement. The frequency with which interest is paid may be different from the compounding frequency used for quoting the rate.

- An interest rate is 6% per annum with annual compounding. What is the equivalent rate with continuous compounding?
- 5.79%
- 6.21%
- 5.83%
- 6.18%

Answer: C

The equivalent rate with continuous compounding is ln(1.06) = 0.0583 or 5.83%.

- An interest rate is 5% per annum with continuous compounding. What is the equivalent rate with semiannual compounding?
- 5.06%
- 5.03%
- 4.97%
- 4.94%

Answer: A

The equivalent rate with semiannual compounding is 2×(e^{0.05/2}−1) = 0.0506 or 5.06%.

- An interest rate is 12% per annum with semiannual compounding. What is the equivalent rate with quarterly compounding?
- 11.83%
- 11.66%
- 11.77%
- 11.92%

Answer: A

The equivalent rate per quarter is. The annualized rate with quarterly compounding is four times this or 11.83%.

- The two-year zero rate is 6% and the three-year zero rate is 6.5%. What is the forward rate for the third year? All rates are continuously compounded.
- 6.75%
- 7.0%
- 7.25%
- 7.5%

Answer: D

The forward rate for the third year is (3×0.065−2×0.06)/(3−2) = 0.075 or 7.5%.

- The six-month zero rate is 8% per annum with semiannual compounding. The price of a one-year bond that provides a coupon of 6% per annum semiannually is 97. What is the one-year continuously compounded zero rate?
- 8.02%
- 8.52%
- 9.02%
- 9.52%

Answer: C

If the rate is* **R** *we must have

or

so that *R *= ln(1/0.9137) = 0.0902 or 9.02%.