Ct1 X Assignment Solutions

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CT1 – P XS – 13
Series X Solutions ActEd Study Materials: 2013 Examinations Subject CT1
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Using the simple discount formula of (1 - nd ) to get the discount factor:
 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 ) = 0.975-4 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  1.06097    5.90345 a7  d 1  1.06091

and: a (4) 
5

1  v5 i (4)



1  1.06095 1  1.06095   4.29685 0.059557 4 1.0609¼  1  

So:
PV  300  5.90345  100  1.06097  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:
3007 (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  1.0810  12 Xa (12)  12 X    83.4324 X  i (12)  10   where i (12)  12 1.08 [1]



1 12