November 2005 Exam (Solutions)
6
Course FM November 2005 solution set page 1 of 6 1. D 2, 000, 000 .08 (25,000,000 .5 ( 2, 200, 000 750, 000)) 1,882, 000 .04 118, 000 .04 2, 950, 000 End of year value is given by 25, 000, 000 2, 000, 000 2, 950, 000 2, 200, 000 750, 000 27, 000, 000 27, 000, 000 25, 000, 000 X X X X 0.5 0.5 (1 ) (2,950,000 2, 200, 000 750,000) (1 ) 27, 000, 000 25,000,000 (1 ) 0 (1 ) 1 1.08 0.08 i i i i i i 2. C 8 8 8 8 10 800 5.989 10 100 Ia v a v with 8% i and coupon 10% 100 10 3. C 5 3 24 24 24 4 2 24 4 2 24 50 1 100 1 150 1 10, 000 50 1 1 21 3 10, 000 1 1 21 3 200 j j j j j s i s i s i s i i i s i i i ª º ¬ ¼ ª º ¬ ¼ 4. D 20 20 0.03 0.08 1 118.2 100 2 1.03 n n P Fra Cv a C § · § · ¨ ¸ ¨ ¸ © ¹ © ¹ Using the calculator, enter N = 20, %I = 3, PV = 118.20, PMT = 4 and then CPT FV to get 106. The text makes it clear that the redemption value does not have to equal the par (or face) value, but that it often does. 5. Not scored because some of the material asked was not on the syllabus.
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Transcript of November 2005 Exam (Solutions)
Course FM November 2005 solution set page 1 of 6
1. D2,000,000 .08 (25,000,000 .5 ( 2, 200,000 750,000))
1,882,000 .04118,000 .04
2,950,000End of year value is given by25,000,000 2,000,000 2,950,000 2, 200,000 750,000
27,000,00027,000,000 25,000,000
XX
XX
0.5
0.5
(1 ) (2,950,000 2,200,000 750,000) (1 )27,000,000 25,000,000 (1 ) 0 (1 )
1 1.080.08
i i
i iii
2. C8
88
8
10 8005.989
10 100
Ia v
a v
with 8%i andcoupon 10% 100 10
3. C5 3
24 24 24
4 2
24
4 2
24
50 1 100 1 150 1 10,000
50 1 1 2 1 3 10,000
1 1 2 1 3 200
j j j
j
j
s i s i s i
s i i i
s i i i
4. D
2020 0.03
0.08 1118.2 1002 1.03
nn
P Fra Cv
a C
Using the calculator, enter N = 20, %I = 3, PV = �–118.20, PMT = 4 and then CPT FV to get 106. The text makes it clear that the redemption value does not have to equal the par (or face)value, but that it often does.
5. Not scored because some of the material asked was not on the syllabus.
Course FM November 2005 solution set page 2 of 6
6. A5
5
4
45
4
0.09 (0.002)(5) (0.001)(25)7.5%0.09 (0.002)(4) (0.001)(16)8.20%(1.075) 1 4.7%(1.082)
iiii
j
7. DThere are only two real possibilities:
Two consecutive 3 year CDs: 12 120.05 0.0510,000 1 1
4 413,473.51
One 5 year CD and a 1 year CD: 20 40.0565 0.0410,000 1 1
4 413,775.75
13,775.75 is the greater. The annual effective rate is6
6
10,000 1 13,775.75
1 1.3775755.48%
i
i
i
8. BDivide the annuity into the first 10 and last 10 payments.The present value of the first 10 payments
present value
101.0511.07100 1.07 919.95
0.07 0.05
The present value of the last 10 payments911th payment is 100 1.05 0.95 147.38
10
10
0.95111.07present value 147.38 1.07 464.71
0.07 0.05 1.07
The total present value of all payments is 1385.
Course FM November 2005 solution set page 3 of 6
9. E150 1001000
0.05i i1000 0.05 150 0.05 100 0i i i i
2 1000 7.5, 8.7%i i .
10. CTo exactly match its liabilities, the company will purchase one 1-year bond and two 2-year bonds:
Cost = 21000 100021.1 1.12
= 909.09 + 1594.39 = 2503
11. BPrice of a bond: 20
20 3%1000 1.03 0.04 1148.77 loan principala
Loan principal and interest paid: 101148.77 1.05 1871.23
Accumulated bond payments: 20 2%1000 1 0.04 1971.89s
Net gain = 100.66
12. B
Use the formula for a perpetuity-immediate, 2
P Qi i
, to determine i = 4%. Then use the
annuity-immediate formula with Q = 15, n
Ia = 3250, i = 4%, n = 20, to obtain P = 116.
20 0.04 19 0.04
1303250 0.04
3250 15
116
ii
Pa v Ia
P
13. A(4)
4i
j
40
1 3
10,000 400 calculator: 40, 10,000, 400
2.52% per quarter
1.0252 0.833% per month
12 0.833% 9.996% 10.0%
ja N PV PMT
CPT i
Course FM November 2005 solution set page 4 of 6
14. B
21 6% 2120 0.08 5600
0.06
45.3236 5600123.56
sX
X
X
15. B
2 3 41 1 15000 1.05 13,152.5
1.0575 1.0625 1.065PV
16. CSolve the following: 20
20 0.035925(1 ) 45 1000i s . This gives i = 0.046. Times two is 9.2%.
17. DProfit on transaction has two pieces:(1) The profit on the short sale 25,000 X(2) Interest on the margin deposit of 40% 25,000 10,000 0.08 800Margin deposited is 40% 25,000 10,000 .So, yield rate = profit/margin deposited
25,000 80025%10,000
X
X 23,300
18. DTotal payment = 789 + 211 = 1000Principal in 18th payment = Principal in 8th payment (18 8) 1.07Principal in 18th payment = 211 10(1.07 ) = 415Interest in 18th payment = 1000 �– 415 = 585
19. EI. is true.II. is true.III is false because the interest rates on the risk-free yield curve are called spot rates.
Course FM November 2005 solution set page 5 of 6
20. D10
55 0.06 5 0.06
2.041 2 4.21 6.30 28.48 38.990.06 0.02
va v a
21. DI is false. To achieve immunization, the duration of the assets must equal the duration ofthe liabilities.II is true.III is true.
22. B
,
1 0.9524918 45 1100(0.9524) ,0.05
1.02 1 0.9524 1.222(0.9524) ,0.02 0.2222(0.9524) , 0.09 (0.9524) ,ln(0.09) ln(0.9524), ln(0.09) ( 0.04877), 49.37,
Years to maturity = 252
nn
nn
n n
n n
P Fra Cv
n n Nn
23. C
2525
25 25 9.077100( ) 100 100 15,9230.10
aX Da
i
Course FM November 2005 solution set page 6 of 6
24. C
120120
120
0.12850 1000 10004
850 30 1000
Using the calculator, enter850, 1000, 120, 30, and then to get 3.54% .
The answer is 3.54(4) 14.2% annual.
nn
i
n
P Fra Cv
a v
a v
PV FV N PMT CPT i
25. E17 15 12 20 18 15X v v v Y v v v
