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Problem Set 6

1. For each of the following situations, what amount would the insurance company pay?

a. Wind damage of $835; the insured has $500 deductible.

b. Theft of a stereo system worth $1,300; the insured has a $250 deductible.

c. Vandalism that does $425 of damage to a home; the insured has a $500 deductible.

Ans. a) Wind damage of $835.00 with deductible of $500.00. 835 - 500 = $335 b) Theft of stereo system worth $1,300 with deductible of $250.00. 1300 - 250 = $1050 c) Vandalism of $425.00 with deductible of $500.00. 425 - 500 = -75 = $0

2. Beverly and Kyle Nelson currently insure their cars with separate companies paying $650 and $575 a year. If they insure both cars with the same company, they would save 10 percent on the annual premiums. What would be the future value of the annual savings over ten years based on an annual interest rate of 6 percent?

Ans.

Total premiums $650 + $575 = $1225 New Premiums = $1225.00 - $122.50 = $1102.50

Savings $1225 x .10 = $122.50

Future value of $122.50 @ 6% for 10 yrs = 122.5 x 13.180 = $1,614.55

3. As of 2008, per capita spending on health care in the United States was about $8,000. If this amount increased by 5 percent a year, what would be the amount of per capita spending for health care in 10 years?

Ans.

$8,000 x 1.6289 (future value of a single amount, 5%, 10 yrs) = $13,031.20

4 Sarah’s comprehensive major medical health insurance plan at work has a deductible of $750. The policy pays 85 percent of any amount above the deductible. While on a hiking trip, she contracted a rare bacterial disease. Her medical costs for treatment, including medicines, tests, and a six-day hospital stay, totaled $8,893.

A friend told her that she would have paid less if she had a policy with a stop-loss feature that capped her out-of-pocket expenses at $3,000.

Was her friend correct? Show your computations. Then determine which policy would have cost Sarah less and by how much.

Ans.

Current policy less deductible: $8,893 – $750 = $8,143

If policy pays 85% then Sarah must pay 15%, so $8,143 x .15 = $1,221.45

Add the (deductible) $750 Total paid = $1,971.45.

Sarah’s friend was wrong

With stop-loss, Sarah would have paid the first $3,000 instead of the $1,971.45 she paid with her current policy. Her current policy costs less by $1,028.55 ($3,000 – $1,971.45).

5 The Kelleher family has health insurance coverage that pays 80 percent of out-of-hospital expenses after a $500 deductible per person. If one family member has doctor and prescription medication expenses of $1,100, what amount would the insurance company pay?

Ans.

Out-of-hospital related costs (prescription medication expenses) = $1100.00 Deductible = $500 Insurance Coverage = 80% So, $1100 – $500 = $600 .80 x 600 = $480 Insurance company pays $480