1. A bank quotes an interest rate of 14% per annum with quarterly compounding. What isthe equivalent rate with (a) continuous compounding and (b) annual compounding?

2. What is meant by LIBOR and LIBID. Which is higher?

3. The 6-month and 1-year zero rates are both 10% per annum. For a bond that has a life of

18 months and pays a coupon of 8% per annum (with semiannual payments and one

having just been made), the yield is 10.4% per annum. What is the bond's price? What are

the 18-month zero rates? All rates are quoted with semiannual compounding.

4. An investor receives $1,100 in one year in return for an investment of $1,000 now.

Calculate the percentage return per annum with:

(a) Annual compounding

(b) Semiannual compounding

Interest Rates 97

(c) Monthly compounding

(d) Continuous compounding.

5. Suppose that 6-month, 12-month, 18-month, 24-month, and 30-month zero rates are,

respectively, 4%, 4.2%, 4.4%, 4.6%, and 4.8% per annum, with continuous compounding.

Estimate the cash price of a bond with a face value of 100 that will mature in

30 months and pays a coupon of 4% per annum semiannually.

6. Assuming that zero rates are as in Problem 4.5, what is the value of an FRA that enables

the holder to earn 9.5% for 3 months starting in 1 year on a principal of

$1,000,000? The interest rate is expressed with quarterly compounding.

7. The term structure of interest rates is upward-sloping. Put the following in order of

magnitude:

(a) The 5-year zero rate

(b) The yield on a 5-year coupon-bearing bond

(c) The forward rate corresponding to the period between 4.75 and 5 years in the future.

What is the answer when the term structure of interest rates is downward-sloping?

8.What does duration tell you about the sensitivity of a bond portfolio to interest rates.

What are the limitations of the duration measure?

9. What rate of interest with continuous compounding is equivalent to 15% per annum with

monthly compounding?

10. A deposit account pays 12% per annum with continuous compounding, but interest is

paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?