2024年4月25日发(作者:)
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?
(a) The rate with continuous compounding is
014
4ln
1
01376
4
or 13.76% per annum.
(b) The rate with annual compounding is
014
1
101475
4
4
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
44104
9674
10521052
2
1052
3
If the 18-month zero rate is
R
, we must have
44104
9674
105105
2
(1R2)
3
which gives
R1042
%.
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.
(a) With annual compounding the return is
1100
101
1000
or 10% per annum.
(b) With semi-annual compounding the return is
R
where
R
1000
1
1100
2
2
i.e.,
R
1110488
2
so that
R00976
. The percentage return is therefore 9.76% per annum.
(c) With monthly compounding the return is
R
where
1
R
1000
1
1100
12
12
i.e.
R
12
1
11100797
12
so that
R00957
. The percentage return is therefore 9.57% per annum.
(d) With continuous compounding the return is
R
where:
1000e
R
1100
i.e.,
e
R
11
so that
Rln1100953
. The percentage return is therefore 9.53% per annum.
Problem 4.5.
Suppose that zero interest rates with continuous compounding are as follows:
Maturity (months) Rate (% per annum)
3 8.0
6 8.2
9 8.4
12 8.5
15 8.6
18 8.7
Calculate forward interest rates for the second, third, fourth, fifth, and sixth quarters.
The forward rates with continuous compounding are as follows to
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