Question

out
Miranda decided to buy a $50,000 term life insurance policy from Palmetto Insurance Company to cover
her until she is 55. She is currently 50 years old and in good health. The probability of death in a given
year is provided by the Social Security Actuarial Life Table.
= Age
50
51
52
53
54
P(Death at a Given Age) 0.0032 0.0035 0.0038 0.0041 0.0044
1. Fill in the expected cost to Palmetto Insurance Company for each year Miranda has the policy.
Age at
Death
Expected
Cost
50
Check
$
Z=
51
$
x
52
$
x
53
$
x
54
$
x
2. The insurance company wants to make a profit of $500. How much would they need to charge for the
policy? $
x
Finish

Answer 1

The expected cost to Palmetto Insurance Company for each year Miranda has the policy is illustrated.

How to illustrate the information?

Term policy amount = $50000

x (age) 50 51 52 53 54

p (death) 0.0032 0.0035 0.0038 0.0041 0.0044

1. Expected cost to Palmetto Insurance Company for each year Miranda has the policy

= P(death for a given year)*term policy amount

Thus, when x = 50

Expected cost = P(x) * 50000 = 0.0032*50000 = $160

Thus, when x = 50

Expected cost = P(x) * 50000 = 0.0032*50000 = $160

Thus, when x = 51

Expected cost = P(x) * 50000 = 0.0035*50000 = $175

Thus, when x = 52

Expected cost = P(x) * 50000 = 0.0038*50000 = $190

Thus, when x = 53

Expected cost = P(x) * 50000 = 0.0041*50000 = $205

Thus, when x = 54

Expected cost = P(x) * 50000 = 0.0044*50000 = $220

Thus, the table will become

x (age) 50 51 52 53 54

p (death) 0.0032 0.0035 0.0038 0.0041 0.0044

Expected cost 160 175 190 205 220

2) For company to make $500 profit

They should charge $500 more than their expected cost

= $(500 + 160 + 175 + 190 + 205 + 220)

= $1450

Thus, they need to charge $1450 overall or (1450/5 = $290 per year)

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