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CHAPTER 4

Interest Rates


Practice Questions

Problem 4.1.

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

  1. The rate with continuous compounding is

or 13.76% per annum.

  1. The rate with annual compounding is

or 14.75% per annum.

Problem 4.2.

What is meant by LIBOR and LIBID. Which is higher?
LIBOR is the London InterBank Offered Rate. It is calculated daily by the British Bankers Association and is the rate a AA-rated bank requires on deposits it places with other banks. LIBID is the London InterBank Bid rate. It is the rate a bank is prepared to pay on deposits from other AA-rated banks. LIBOR is greater than LIBID.

Problem 4.3.

The six-month and one-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 is the 18-month zero rate? All rates are quoted with semiannual compounding.
Suppose the bond has a face value of $100. Its price is obtained by discounting the cash flows at 10.4%. The price is

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If the 18-month zero rate is, we must have

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which gives %.

Problem 4.4.

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, c) monthly compounding and d) continuous compounding.

  1. With annual compounding the return is

or 10% per annum.

  1. With semi-annual compounding the return is where

i.e.,

so that