The ship insurance company issues life annuities. It prices its annuities using the following probabilities.

Survival probabilities

Year
1	0.99
2	0.66
3	0.43
4	0

The annuities pay $60 000 at the end of each year while the policyholder is alive. Ship insurance believes it can earn 4% p.a. interest on investments. It also has to provide for initial expenses of $50 at the date of issue.

(a) What is probability of a new policyholder being alive at the start of Year 3?

a.

0.3366

b.

0.6534

c.

0.01

d.

0.28

(b) What is a new policyholder's probability of dying in Year 3?

a.

0.3466

b.

0.3366

c.

0.3724

d.

0.6534

(c) Calculate the fair single premium value which is paid on the issue date of this policy. Round your answer to two decimal places.

a.

116713.92

b.

110113.53

c.

110163.53

d.

108398.14