This document contains 15 multiple choice questions regarding theory of interest, duration, convexity, immunization, and term structure of interest rates. The questions cover topics such as using duration to estimate bond prices given yield changes, calculating duration for various bonds, immunizing a portfolio, and determining spot and forward interest rates from given bond price and yield data.

1. Homework 7
Theory of Interest
Duration/Convexity/Immunization/Term Structure of Interest Rates
1. The current price of a bond is $114.72 and the current yield is 6.00%. The
modified duration of the bond is 7.02. Use the modified duration to estimate the
price of the bond if the yield increases to 6.10%.
A.114 B.120 C.210 D.220 E.300
2. A two-year bond has 8% annual coupons payable semiannually. The bond’s yield
is 10% compounded semiannually. Calculate the modified duration of the bond.
A.0.8 B.1.0 C.1.5 D.1.8 E.2.0
3. A 22-year bond pays 7% annual coupons and has a current price of $81.12. The
annual effective yield on the bond is 9%. The Macaulay duration of the bond is
10.774. Estimate the new price if the yield falls to 8.95%.
A.76 B.78 C.80 D.82 E.84
4. A 15-year mortgage is repaid with level monthly payments. The yield is 12%
compounded monthly. Calculate the Macaulay duration of the mortgage.
A.3.2 B.5.4 C.7.1 D.9.7 E.10.3
5. A 20-year bond yielding 9% has a price of $127.79. If the bond’s yield falls to
8.75%, then the price of the bond will increase to $130.65. If bond’s yield
increases to 9.25%, then the price of the bond will fall to $125.02. Calculate the
effective duration of the bond.
A.8.6 B.8.7 C.8.8 D.8.9 E.9.0
6. A five-year bond with a coupon of 6.7% pays coupons semiannually. It is
currently yielding 6.4%. Its current price is $101.2666. If the bond’s yield
increases by 10 basis points, then its price falls to $100.8422. If the bond’s yield
falls by 10 basis points, then its price rises to $101.6931. Calculate the effective
convexity of the bond.
A.15.67 B.17.75 C.18.52 D.19.32 E.20.74
7. The modified duration of an 8-year bond is 5.35 and its convexity is 39.19.
Estimate the percentage change in the price of the bond if its yield increases by 63
basis points.
A. -3.29% B.-1.09% C.1.09% D.3.29% E.5.14%

2. 8. An insurance company has committed to make a payment of $100,000 in 5 years.
The insurance company can fund this liability only through the purchase of 4-year
zero-coupon bonds and 10-year zero-coupon bonds. The annual effective yield for
all assets and liabilities is 12%. Determine how much the bank should invest in
the 4-year zero-coupon bond in order to immunize its position.
A.26401 B.26933 C.47286 D.47813 E.48005
9. You are given the following information with respect to a callable bond:
Time Expected Cash Flows at a 7% Annual Yield
1 8.00
2 7.90
3 107.80
Annual Yield Bond Price
6% 104.33
7% 102.37
8% 99.76
The current yield is 7%.
Calculate the ratio of the modified duration to the effective duration of this bond.
A.1.01 B.1.17 C.1.32 D.1.38 E.1.50
10. The current price of a bond is 100. The derivative of the price with respect to the
yield to maturity is -700. The yield to maturity is 8%.
Calculate the Macaulay duration.
A.8 B.9 C.10 D.11 E.12
11. Given the following annual effective spot rates, find the present value of a 3-year
bond paying 15% annual coupons and having a par value of $100.
Time Annual effective spot
1 7.000%
2 6.000%
3 8.000%
A.100 B.110 C.120 D.130 E.140
12. Given the following yields and coupons for bonds with $100 of par value,
determine the 2-year annual effective spot rate.
Maturity Annual coupon Annual effective yield
1 10.000% 8.000%
2 4.000% 8.979%
3 20.000% 9.782%
A.7% B.8% C.9% D.10% E.11%

3. 13. Given the following table of forward rates, find the present value of a 3-year bond
paying 15% annual coupons and having a par value of $100.
t ft
0 7.000%
1 5.009%
2 12.114%
A.118.66 B.120.24 C.132.86 D.144.12 E.151.97
14. The table below provides the prices of 5 zero-coupon bonds:
Maturity Price per $100 of par
1 97.0874
2 90.7029
3 81.6298
4 73.5030
5 64.2529
Determine the value of f 3 , the annual effective forward rate applicable from time
3 to time 4.
A.7% B.8% C.9% D.10% E.11%
15. The following spot rates are expressed as rates compounded twice per year:
s0.5  12.00%
(2)
s1.0  13.50%
(2)
s1.5  14.66%
(2)
s2.0  16.00%
(2)
Calculate the 1-year implied forward rate for the second year, expressed as a rate
that is effective over six months.
A.7% B.8% C.9% D.10% E.11%