MATH 471: Actuarial Theory I
Midterm #2
November 11, 2009
There are 7 problems on this midterm for a total of 60 points. Put your name
and lecture section time on the cover of the exam booklet. Make sure that all
your work is shown in the exam booklet. It is possible to earn partial credit
by showing all your work. Keep at least five decimal places during each of
your calculations. Refer to the accompanying tables when necessary.
Good luck!
1. For a continuous whole life annuity of 1 per year on (x):
(i)
δ
t
= 0.05 for 0
< t
≤
15,
δ
t
= 0.06 for 15
< t
(ii)
μ
x
(
t
) = 0.02 for 0
< t
≤
15,
μ
x
(
t
) = 0.04 for 15
< t
Calculate the single benefit premium. (8 points)
2. Let
Z
be the present value random variable for a whole life insurance on
(x) with a benefit of 10,000 payable at the moment of death.
Assume
μ
x
(
t
) = 0.03 and
δ
t
= 0.06 for
t
≥
0.
(a) Determine the cumulative distribution function of
Z
. (5 points)
(b) Calculate the 65th percentile of the distribution of
Z
. (4 points)
3. Suppose
Z
is the present value random variable for a 2year pure endow
ment insurance of 1 on (x). You are given:
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Staff
 Math, Actuarial Science, Normal Distribution, value random variable

Click to edit the document details