Ct1 X Assignment Solutions
Series X Solutions ActEd Study Materials: 2013 Examinations Subject CT1
Contents Series X Solutions If you think that any pages are missing from this pack, please contact ActEd’s admin team by email at ActEd@bpp.com. How to use the Series X Solutions Guidance on how and when to use the Series X Solutions is set out in the Study Guide for the 2013 exams.
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1 91 day discount 1 0.10 0.975 4 So:
1 v4
[1]
= 0.975 ﬁ (1 + i )

1 4
= 0.975
[1] [1]
ﬁ (1 + i ) = 0.9754 ﬁ i = 10.66% Note that if you use
91 91 1 or rather than in both calculations, you will get 365 365.25 4 exactly the same answer.
The Actuarial Education Company
© IFE: 2013 Examinations
Page 2
CT1: Assignment X1 Solutions
Solution X1.4
The annual rate of interest, i , is given by:
(1 + i ) = 1.032 = 1.0609 ﬁ i = 6.09%
The present value of the annuity is given by:
PV = 300a7 + 100v 7 a (4)
5
[1]
Now:
1 v 7 1 1.06097 5.90345 a7 d 1 1.06091
and: a (4)
5
1 v5 i (4)
1 1.06095 1 1.06095 4.29685 0.059557 4 1.0609¼ 1
So:
PV 300 5.90345 100 1.06097 4.29685
= 1771.04 + 284.07 = $2, 055.11 So the accumulated amount after 12 years is:
$2, 055.11 ¥ 1.060912 $4,178
[1]
[1]
[1]
Alternatively, this could be calculated as:
3007 (1 + i )5 + 100s (4) s
5
© IFE: 2013 Examinations
The Actuarial Education Company
CT1: Assignment X1 Solutions
Page 3
Solution X1.5
(i)
Level monthly annuity
Let X be the monthly amount paid, then the present value of the payments is: 1 1.0810 12 Xa (12) 12 X 83.4324 X i (12) 10 where i (12) 12 1.08 [1]
1 12

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