A bank quotes an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?
1. A bank quotes an interest rate of 14% per annum with quarterly compounding. What is the 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
the 18-month zero rate? 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 a 3-month period 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
actually paid quarterly. How much interest will be paid each quarter on a $10,000 deposit?
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