UNSW
ACTL1001 Actuarial Studies and Commerce
Solutions Tutorial Exercises 6
Exercise 1
Now the payments are monthly, so we need a per month interest
rate. The interest rate is 5% p.a. quarterly so the monthly rate is
i
where
(1 +
i
)
3
=
1 +
0
.
05
4
or
i
=
1 +
0
.
05
4
1
3

1
=
0
.
0041494
Present value is
1000¨
a
60
at rate
0
.
0041494
=
1000 (1
.
0041494)
1

(
1
1
.
0041494
)
60
0
.
0041494
=
1000
×
53
.
23732
=
53
,
237
.
32
Exercise 2
Present value is
100
,
000
v
5
at 6%
=
100
,
000
×
1
(1
.
06)
5
=
74
,
725
.
82
Exercise 3
Note: For Parts 13, one very important concept you will need
to understand is how to setup a table (eg in a spreadsheet format) listing
the cashflows, interest, PL and Asset values, and in particular the recur
sive/formula links between each item on the table. Please also find attached
a spreadsheet which demonstrates these relationships. You should ensure that
you can replicate this by hand as that is a great way of learning how each item
(eg premiums, claims, expenses, PL, interest etc) relate to each other at a
particular period and also between periods).
1
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1. Premium will be given by (using the principle of equivalence)
P
¨
a
5
= 100
,
000
v
5
+ 8
,
000 + 0
.
02
P
¨
a
n
+ 100¨
a
5
at 6%
so that
P
=
1
(1

0
.
02)
"
100
,
000
v
5
¨
a
5
+
8
,
000
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 One '09
 Nicole
 policy liabilities

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