AS 5103 Study Guide - Quiz Guide: Equivalence Principle, Term Life Insurance, Life Insurance

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Published on 23 Nov 2019
Course
Professor
TEMPLE UNIVERSITY
FOX SCHOOL OF BUSINESS
AS 3502 / AS 5103 Actuarial Modeling II
AMLCR Chapter 7 and review Problem Set
DR. KRUPA S. VISWANATHAN
1. A fully continuous 25-year term insurance with a benefit of b was sold to (30) with
level annual gross premiums of 2,750. You are told E[
!
"
#
] = -4,250.
You are given
$%"&'(
= 0.0175 for t > 0 and
d
= 0.01.
(a) Calculate the gross premium reserve at time 10 using the prospective method.
(b) Calculate the gross premium reserve at time 10 using the retrospective method.
2. A fully continuous 30-year endowment insurance with a benefit of 7,500 was sold
to (25). You are given
$)*
&
'
( = 0.05 for t > 0 and
d
= 0.045.
Calculate the net premium reserve at time t = 15.
3. A 20-year pure endowment with a benefit of 40,000 was sold to (55). The
policyholder pays for this policy with level annual gross premiums payable
continuously for the first 5 policy years. You are given the following expenses
that are incurred continuously over the year:
Percent of
Premium
First Year
18%
Renewal Years
11%
There is a policy fee of 125 incurred at issue.
You are given
$**
&
'
(
+
,
-.-/####- 0 ' 1 2
-.-3############' 4 2
and
d
= 0.02.
Premiums are calculated using the equivalence principle.
(a) Calculate the gross premium.
(b) Determine the gross premium reserve at time t = 10.
4. A 15-year term life insurance with a benefit of 60,000 was issued to Owen (30),
with the death benefit paid at the moment of death. Owen pays for this policy with
a net single premium.
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(i) d = 0.03
(ii) T(30) follows an exponential distribution with
$%"
&
'
(
#
= 0.05 for t > 0.
(a) Calculate the net single premium for this insurance.
(b) Determine the net premium reserve at time t = 7.
5. A 20-year deferred, continuous life annuity that makes payments at a rate of
55,000 per year was sold to (45). Continuous level net premium payments are
payable for the first 3 policy years.
You are given the following: = 0.05 and
$5*
&
'
( = 0.035 for t > 0.
(a) Calculate the net premium.
(b) Calculate the net premium reserve at time t = 21.
6. A fully continuous whole life insurance with a benefit of 50,000 was sold to (60).
(ii) Mortality follows
67+/2
&
/--8 9
(
#####:;<#- 1 9 0 /--
(iii) The force of interest is 1%.
Calculate the net premium reserve at time t = 15.
7. A fully discrete 10-year endowment insurance with a benefit of 2,500 was sold to
(50). Mortality follows the Illustrative Life Table with i = 0.06.
Level net premiums will be paid. Calculate the net premium reserve at time 5.
8. When Roy was 25 years old, he purchased a fully discrete whole life insurance
with a benefit of 30,000. Net premiums are payable for the first three policy
years.
You are given d = 0.05 and
$)*
&
'
( = 0.025 for t > 0.
(a) Calculate the amount of the net premium.
(b) Determine the amount of the net premium reserve at time 2 using the prospective
approach and using the recursive approach.
9. For a fully discrete 3-year term insurance on (40) with a benefit of 10,000, you
are given the following:
=5"
= 0.05,
=5>
= 0.06 and
=5)
= 0.08 and d = 0.05.
Level net premiums will be paid for the term of the policy.
Calculate the variance of the prospective loss at time 0.
δ
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10. A 20-year deferred, life annuity-due with an annual benefit of 30,000 was sold to
(32). The policyholder pays for this policy with level gross premiums during the
deferral period. The gross premium is 120% of the net premium.
Mortality follows the Illustrative Life Table with i = 0.06.
(a) Calculate the gross premium.
(b) Determine the gross premium reserve at time 10.
11. A semi-continuous whole life policy with a benefit of 55,000 was sold to (41).
Level net premiums are payable for the first 9 policy years.
You are given
d
= 0.04 and
$5>
&
'
( = 0.03 for t > 0.
(a) Calculate the net premium.
(b) Determine the net premium reserve at t = 5.
12. A fully discrete whole life policy with a benefit of 24,000 was sold to (24). The
policyholder’s mortality follows the Illustrative Life Table with i = 0.06. The
policyholder pays gross annual premiums of 130.
Calculate the amount of the gross premium reserve at t = 1 using the prospective
approach and using the recursive approach.
13. A fully continuous 15-year endowment insurance with a death benefit of 8,000
and a pure endowment benefit of 9,000 was sold to (35). You are given
$%*
&
'
( = 0.025 for t > 0 and
d
= 0.05.
Calculate the amount of the net premium reserve at time t = 10.
14. Chloe (45)'s future lifetime follows an exponential distribution with
$55
&
'
(
+ $
for
t > 0. You are given
?
@
5*
= 25 and
A
= 0.021.
She purchases a 15-year deferred, continuous life annuity paying at an annual
rate of 56,000. She will be paying for this product with continuous level gross
premiums of 80,000 during the deferral period.
Determine
B
"
#
.
15. A fully continuous whole life policy with a benefit of 25,000 was sold to (40),
whose future lifetime follows an exponential distribution with
$5"
&
'
(
+ $
, for t > 0.
You are given
C
D
5"
= 0.40 and = 0.06. Level net premiums are payable for the
first 20 policy years.
(a) Calculate the net premium reserve at time 10.
(b) Calculate the net premium reserve at time 20.
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