Deitz J.E., Southam J.L. Contemporary Business Mathematics for Colleges
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It is common practice for a fire insurance policy to have an 80% coinsurance clause.
Under this clause, the full amount of the loss will be paid by the insurance company only
if the policy amount equals 80% of the property value.
234 Part 3 Accounting Applications
12.5 A precaution commonly taken by
insurance companies is to adjust the
amount of exposure that one company
assumes in a given area through a form
of coinsurance.If a major disaster in one
locale would jeopardize the ability of
an insurance company to continue
operations and meet its obligations,
the company should acknowledge
this fact and limit exposure to a
manageable amount through a
coinsurance arrangement with
another carrier.
to Determine the Owner’s Share of Property Loss Under
Coinsurance
1. Compute the amount of insurance required by multiplying the entire
value of the property by the percentage of coinsurance specified.
2. Compute the recovery amount, the maximum amount the insurance
company will pay, by using the formula
3. Compare the recovery amount with the amount of the insurance policy.
a. If the recovery amount is greater than the amount of the policy, the
insurance company will limit its payment to the amount of the policy.
b. If the recovery amount is less than the amount of the policy, the
insurance company will pay the recovery amount.
Note: The insurance company will never pay more than the amount of
the loss.
4. Determine the owner’s share of the property loss by subtracting the
amount the insurance company will pay from the loss amount.
Amount of insurance carried
Amount of insurance required
3 Loss 5 Recovery amount.
STEPS
EXAMPLE G
A building valued at $400,000 is insured for $200,000 under a policy with an 80%
coinsurance clause. The annual premium is $2,800. A fire causes $100,000 damage to the
building.
a. How much will the insurance company pay the insured?
$400,000 3 80% 5 $320,000 insurance required
b. How much must the owner pay if the building is repaired for $100,000?
$100,000 2 $62,500 5 $37,500 paid by owner
c. How much does the property owner pay that year for damages and insurance?
$37,500 damages 1 $2,800 premium 5 $40,300
d. How much would the insurance company pay if the fire caused $300,000 damage to the
building?
$187,500 recovery amount
The insurance company would pay $187,500 (because the recovery amount is within the
policy’s coverage).
$200,000
$320,000
3 $300,000 5
STEP 4
$200,000 amount of insurance carried
$320,000 amount of insurance required
3 $100,000 5 $62,500 insurance pays
STEPS 2 & 3
STEP 1
The policies most commonly issued by life insurance companies are term insurance,
straight life (sometimes called ordinary life), limited-payment life, endowment, and
annuity.
Term insurance is protection issued for a limited time. A certain premium is paid
every year during the specified time period, or term. The policy is payable only in case of
death of the insured during the term. Otherwise, neither the insured nor the specified
beneficiaries receive any payment, and the protection stops at the end of the term.
For straight (ordinary) life insurance coverage, a certain premium, or fee, is paid
every year until the death of the insured. The policy then becomes payable to the
beneficiary. A policy beneficiary can be a person, a company, or an organization.
Limited-payment life insurance (such as 20-payment life) requires the payment of a
specified premium each year for a certain number of years or until the death of the
insured, whichever comes first. Should the insured live longer than the specified number
of years, the policy requires no further payments for the remainder of the insured’s life
and is payable to the beneficiary on the death of the insured.
Endowment insurance provides insurance payable on the insured’s death if it occurs
within a specified period. If the insured is alive at the end of the specified period, an
endowment of the same amount as the policy is payable.
Annuity insurance pays a certain sum of money to the insured every year after the
insured reaches a specified age, until the insured’s death.
An additional death benefit (ADB), sometimes referred to as an accidental death
benefit, accompanies some policies. ADB allows the insured to purchase, at a low rate per
thousand dollars of coverage, additional insurance up to the full face value of the policy.
In case of death of the insured by accident, both the full value of the policy and the ADB
are paid to the beneficiaries. If death occurs other than by accident, the full value of the
policy is paid, but no ADB is paid.
Chapter 12 Insurance 235
EXAMPLE H
If the amount of insurance carried in example G had been $320,000, how much would
the insured have paid for damages and insurance that year?
$2,800 premium only (the 80% coinsurance requirement would have been met)
A building worth $100,000 is insured for $60,000 with an 80% coinsurance clause. A fire
causes $70,000 in damage.How much of the repair cost will the insurance company pay, and
how much will the insured pay?
$100,000 3 80% 5 $80,000 insurance required
$70,000 2 $52,500 5 $17,500 insured pays
COMPLETE ASSIGNMENT 12.2.
$60,000
$80,000
3 $70,000 5 $52,500 insurance pays
✔
CONCEPT CHECK 12.4
Computing Life Insurance Premiums
Compute life insurance premiums.
5
Learning Objective
12.6 Businesses frequently use term
insurance to insure against losses that
would be incurred in the event of the
death of one or more of their “key”
executives.
© BRONWYN KIDD/PHOTODISC/GETTY IMAGES
Figure 12-1 shows typical annual, semiannual, and quarterly premiums (ages 25–28)
for straight life, 20-payment life, and 20-year endowment policies.
236 Part 3 Accounting Applications
Figure 12-1 Insurance Premium per $1,000
Straight Life 20-Payment Life 20-Year Endowment
Semi- Semi- Semi-
Age Annual annual Quarterly Annual annual Quarterly Annual annual Quarterly
25 $17.20 $ 8.94 $4.73 $31.20 $16.26 $8.26 $52.00 $27.04 $14.30
26 17.85 9.28 4.91 31.81 16.52 8.45 52.60 27.35 14.47
27 18.60 9.67 5.11 32.41 16.83 8.64 53.20 27.66 14.63
28 19.30 10.04 5.31 33.06 17.31 8.85 53.86 28.01 14.81
EXAMPLE I
Using the premiums shown in Figure 12-1, determine the yearly premiums for each of
the following $50,000 life insurance policies purchased at age 27.
T
ype of Insurance Method of Payment Premium Computation
Straight Life Annual $18.60 3 50 5 $930
20-Year Endowment Quarterly $14.63 3 4 3 50 5 $2,926
20-Payment Life Semiannual $16.83 3 2 3 50 5 $1,683
20-Year Endowment Semiannual $27.66 3 2 3 50 5 $2,766
Straight Life Quarterly $ 5.11 3 4 3 50 5 $1,022
(Use the premiums in Figure 12-1.)
a. If a person at age 28 purchases a straight life insurance policy having a face value of
$150,000 with quarterly premiums, what is the yearly premium?
$5.31 3 4 3 150 5 $3,186
b. If a person at age 25 purchases a 20-payment life insurance policy having a face value of
$100,000 with semiannual premiums, what is the yearly premium?
$16.26 3 2 3 100 5 $3,252
c. If a person at age 25 purchases a 20-year endowment insurance policy having a face value
of $75,000 with annual premiums, what is the yearly premium?
$52 3 75 5 $3,900
✔
CONCEPT CHECK 12.5
Computing Cash Surrender and Loan Values
Except for term insurance, insurance usually has a cash surrender value, which is the
amount of cash that the company will pay the insured on the surrender, or “cashing in,”
of the policy. The loan value of a policy is the amount that the insured may borrow on
the policy from the insurance company. Interest is charged on such loans. The values,
often quoted after the third year of the policy, are stated in the policy and increase every
year. Figure 12-2 shows typical cash surrender and loan values for policies issued at age
25 per $1,000 of life insurance.
6
Learning Objective
Compute cash surrender and loan
values.
Chapter 12 Insurance 237
12.7 Why would an insured take the
maximum loan instead of cash
surrender? Suppose that a person
bought a $20,000 straight life policy
10 years ago.The cash surrender or
loan value is $104 3 20 5 $2,080.The
insured borrows the full amount and
dies before repayment.The beneficiary
receives $20,000 2 $2,080,or
$17,920.If the insured had surrendered
the policy,no payment would have
been made upon death.
Figure 12-2 Insurance Values per $1,000
End of
Cash Surrender and Loan Values
Policy Year Straight Life 20-Payment Life 20-Year Endowment
3 $ 10 $ 43 $ 88
4 22 68 130
5 35 93 173
10 104 228 411
15 181 380 684
20 264 552 1,000
EXAMPLE J
Use the values shown in Figure 12-2 to determine the cash surrender or loan value for
each of the following policies.
Amount Cash Surrender
Policy Year Type of Policy of Policy or Loan Value
10 Straight Life $ 75,000 75 3 $104 5 $ 7,800
5 20-Year Endowment $ 15,000 15 3 $173 5 $ 2,595
10 20-Payment Life $ 50,000 50 3 $228 5 $11,400
20 Straight Life $200,000 200 3 $264 5 $52,800
15 20-Year Endowment $ 50,000 50 3 $684 5 $34,200
Use the values shown in Figure 12-2 to determine the cash surrender or loan value for each
of the following policies.
a. Third policy year of a $50,000 20-year endowment policy
50 3 $88 5 $4,400
b. Twentieth policy year of a $100,000 straight life policy
100 3 $264 5 $26,400
c. Tenth policy year of a $25,000 20-payment life policy
25 3 $228 5 $5,700
✔
CONCEPT CHECK 12.6
Computing Medical Insurance Contributions
and Reimbursements
Compute medical insurance
contributions and reimbursements.
7
Learning Objective
Most large employers and many small employers subscribe to a group plan on behalf of
their employees. Group insurance plans provide medical insurance coverage to large
numbers of people at lower premium rates than individuals could obtain separately.
Employers generally pay all the premium for employees and a portion of the premium
for family members of employees. Many employers now use group plans known as a
health maintenance organization (HMO) or a preferred provider organization (PPO).
Many group plans include a provision for an annual deductible, which is the cost that
must be paid by the employee before any cost is paid by the insurance company. Group
medical plans also frequently provide for the payment by the insurance company of a
percent of costs over the deductible, usually 70% to 90%, with the remaining 30% to
10% paid by the insured.
238 Part 3 Accounting Applications
12.8 Premiums in the examples vary.
Explain to students that group medical
premiums are adjusted periodically,
based on actual medical costs and
payments made by the insuring
company.A few serious,long-term
illnesses by one or more employees
can cause premiums to be increased
significantly.
EXAMPLE K
Employer A selected a basic health care plan to cover employees who want to participate.
Monthly premiums are as follows: employee only, $350; employee with one dependent,
$450; and employee with multiple dependents, $530. Employees pay a portion of the
premium as follows: employee only, $0; employee with one dependent, $80; and
employee with multiple dependents, $120. How much does the employer pay during the
year for each category of employee?
Employee only: $350 3 12 5 $4,200
Employee with one dependent: ($450 2 $80) 3 12 5 $4,440
Employee with multiple dependents: ($530 2 $120) 3 12 5 $4,920
EXAMPLE L
Employer B selected a total care health plan to cover employees who want to participate.
Monthly premiums are as follows: employee only, $300; employee with one dependent,
$400; and employee with multiple dependents, $480. The employer pays most of the
premium, but employees pay a portion as follows: employee only, $30; employee with
one dependent, $80; and employee with multiple dependents, $120. What percent of the
premium will be paid by a single employee, an employee with one dependent, and an
employee with six dependents?
A single employee: $30 4 300 5 0.10, or 10%
An employee with 1 dependent: $80 4 400 5 0.20, or 20%
An employee with 6 dependents: $120 4 480 5 0.25, or 25%
EXAMPLE M
Employer C provides group health coverage that includes a $500 annual deductible per
family and payment of 70% of the medical charges exceeding the deductible. How
much would an employee with three dependents pay if her medical bills for the year
were $1,500?
$1,500 2 $500 deductible 5 $1,000
$1,000 3 30% paid by employee 5 $300
$500 deductible 1 $300 payments 5 $800 paid by the employee
© PHOTODISC/GETTY IMAGES
Chapter 12 Insurance 239
An employer provides group health coverage that includes a $300 annual deductible per
family and payment of 80% of costs over the deductible.
a. How much would an employee with two dependents pay if his medical bills for the year
were $460?
$460 2 $300 deductible 5 $160
$160 3 20% 5 $32
$300 deductible 1 $32 5 $332 paid by the employee
b. How much would that employee have paid if his total medical bills for the year had been $4,300?
$4,300 medical costs 2 $300 deductible 5 $4,000
$4,000 3 20% 5 $800
$300 deductible 1 $800 5 $1,100
c. How much of the $4,300 in medical bills would that employee have paid if his employer did
not provide medical insurance and he did not have other coverage?
$4,300
d. How much would the employer pay if the monthly premium for an employee with multiple
dependents was $480?
$480 3 12 5 $5,760
COMPLETE ASSIGNMENT 12.3.
✔
CONCEPT CHECK 12.7
additional death
benefit (ADB)
annuity insurance
auto collision
insurance
auto comprehensive
insurance
auto liability and
property damage
insurance
beneficiary
cash surrender value
coinsurance clause
deductible clause
endowment insurance
group insurance
health maintenance
organization
(HMO)
high-risk driver
insured
limited-payment life
insurance
loan value
low-risk driver
no-fault insurance
preferred provider
organization (PPO)
premium
property insurance
recovery amount
short rates
straight (ordinary)
life insurance
term insurance
Chapter Terms for Review
Try Microsoft
®
Excel
Try working the problems using the Microsoft Excel templates found on your student
CD. Solutions for the problems are also shown on the CD.
240 Part 3 Accounting Applications
THE BOTTOM LINE
Summary of chapter learning objectives:
Learning Objective
12.1
Compute costs and savings for auto insurance.
Example
Drivers A and B live in a state in which no-fault insurance is mandatory.
Both drivers carry all three classifications of insurance. Driver A has a
deductible of $500; driver B has a deductible of $200. Driver A crashes
into driver B. Neither auto has any passengers. Car A has $1,800 in
damages; car B has $2,000 in damages. Driver A is not hurt; driver B
has $900 in medical bills.
1. How much does driver A’s insurance company pay?
2. How much does driver B’s insurance company pay?
Answers: 1. $3,300 2. $900 3. $1,800 4. $840 5. $187,500 6. $1,685.40
12.2
Compute auto insurance premium rates for high- and
low-risk drivers.
3. Juan has an excellent driving record and receives a 20% discount on
his annual premium. Dave has a record of numerous tickets and must
pay 2 times the normal annual premium rate. If the normal premium
for each driver is $1,500, how much more does Dave pay for his
insurance than Juan pays?
12.4
Compute coinsurance on property losses.
5. A building worth $400,000 is insured for $300,000 with an 80%
coinsurance clause. Fire causes $200,000 in damage. How much does
the insurance company pay?
12.3
Compute short-rate refunds.
4. XYZ company purchased a delivery truck and paid an annual
insurance premium of $3,600. XYZ company sold the truck at the
end of 8 months and canceled the policy. The insurance company
charges a 10% penalty for short-rate refunds. What was the amount
of the short-rate refund to XYZ company?
12.5
Compute life insurance premiums.
6. Premiums per $1,000 of straight life insurance at the age of 25
are as follows: annual, $17.20; semiannual, $8.94; and quarterly,
$4.73. What will be the cumulative yearly premiums for the fol-
lowing three policies: $50,000, annual; $25,000, semiannual; and
$20,000, quarterly?
Chapter 12 Insurance 241
Learning Objective
12.6
Compute cash surrender and loan values.
Example
7. If cash surrender values for year 15 of a policy are $200 per
thousand dollars of coverage for straight life and $380 per
thousand dollars of coverage for 20-payment life, what is the total
cash surrender value of these two policies: $50,000 straight life and
$50,000 20-payment life?
Answers: 7. $29,000 8a. $780 8b. $804
12.7
Compute medical insurance contributions and
reimbursements.
8a. An employer provides group health coverage that includes a $200
annual deductible per family and payment of 80% of costs over
deductible. How much would an employee with four dependents
pay if his medical bills for the year were as follows: self, $240;
dependent 1, $170; dependent 2, $30; dependent 3, $460; and
dependent 4, $2,200?
b. How much would the employee pay if the annual deductible were
$50 per person?
1 Drivers Jim Olson and Joshua Stein live in a state having no-fault auto insurance. Joshua causes an
accident by hitting Jim’s car. Joshua isn’t hurt. Jim spends 3 days in the hospital at a cost of $5,300.
Compute the amount that each driver’s insurance company pays toward medical expenses.
2 IXP insured an office building for $290,000 for 1 year at a premium rate of $7.20 per thousand. At the end of
9 months, IXP sold the building and canceled the policy. If the insurance company has a short-rate refund
policy that includes a 10% penalty, how much refund did IXP receive?
3 Driver Devon Cooper has a poor driving record and pays double the usual premium as a high-risk driver. The
regular premium would be $490 for a year. If Devon must pay the high-risk premium every year for 5 years,
how much more will he pay for insurance premiums than a low-risk driver receiving a 10% discount over the
same 5-year period?
4 Insurance company A has a standard 90% coinsurance clause for all fire insurance coverage. Insurance
company B has a standard 75% coinsurance clause for all fire insurance coverage. A building is valued at
$195,000. How much more insurance coverage would insurance company A require than insurance company
B for full coinsurance coverage?
5 The Morgan Company warehouse was valued at $425,000. The building was insured for $170,000. The
policy contained an 80% coinsurance clause. A fire caused $60,000 in damages. Compute the amount of the
fire damage The Morgan Company had to pay.
6 Mike Jankowski, age 27, purchased a $35,000, 20-payment life policy with premiums payable annually. John
Jamison, also age 27, purchased a $35,000 straight life policy with premiums payable semiannually. Both
Mike and John lived 40 more years. How much more in premiums did John pay the insurance company
during his lifetime than Mike paid during his? (Use values from Figure 12-1.)
7 Sally Munson, age 25, purchased a $35,000, 20-payment life policy. Five years later she needed cash.
Compute the maximum amount she could borrow on the policy. (Use values from Figure 12-2.)
8 An employer provides group health coverage that includes a $600 annual deductible per family and payment
of 80% of costs exceeding the deductible amount. An employee with no dependents incurs $4,800 in medical
expenses during the year. How much of the medical costs must the employee pay?
SELF-CHECK
Review Problems for Chapter 12
242 Part 3 Accounting Applications
Answers to the Self-Check can be found in Appendix B at the back of the text.
Chapter 12 Insurance 243
Assignment 12.1: Auto Insurance
Name
Date Score
A (50 points) Solve the following problems. (5 points for each correct answer)
1. Mary Johnson had full insurance coverage. Her liability and property damage coverage was $100,000 per
accident. Her collision insurance had a $500 deductible clause. She struck two cars. Damages to the cars
were $640 and $320. Damage to her own car was $470. Her annual insurance premium was $1,180.
a. What are the total costs to the insurance company for Mary’s accident?
b. If this was the only accident that Mary had this year, did the insurance company profit after paying for Mary’s
accident?
c. What are Mary’s total costs this year for insurance and the accident?
d. What would Mary’s total costs for the accident have been without insurance?
2. Renaldo Garcia paid an annual premium of $3,200 for auto collision insurance with a $500 deductible
clause. His steering went out and he hit a tree, causing $4,000 damage to his car. How much did he save
this year by having insurance?
3. Sean O’Day received his driver’s license 1 year ago. He has had three citations for speeding, but no acci-
dents. His insurance premium last year was $1,800. This year his premium will be 100% higher because of
his driving record.
a. What will be the amount of his premium this year?
b. Four months into the next year, Sean has continued his unsafe driving habits. The insurance company is canceling
his policy. What will be the amount of the refund?
c. Sean O’Day has found an insurance company that will insure him as a high-risk driver at triple the standard
annual rate of $1,600. What will be his average monthly insurance premium for the first 28 months of his driving
career? (Round your answer to the nearest dollar.)
d. If Sean had been a careful driver and kept the amount of his premium unchanged, how much would he have saved
in these first 28 months? (Round your computations to the nearest dollar.)
$3,600
$7,800 4 28 5 $278.57 5 $279.00 rounded average monthly premium
$1,800 1 $1,200 1 $4,800 5 $7,800 for 28 months
This 12 months: $1,600 3 3 5 $4,800
Next 4 months: $3,600 2 $2,400 refund 5 $1,200
First 12 months: $1,800
$279
8/12 3 $3,600 5 $2,400
$2,400
$1,800 3 100% 5 $1,800; $1,800 1 $1,800 5 $3,600
$3,600
$4,000 damages 2 $3,700 paid 5 $300 saved
$3,200 premium 1 $500 deductible 5 $3,700 total payments
$300
$640 1 $320 1 $470 5 $1,430 damage to all three cars
$1,430
$1,180 premium 1 $470 damage to her car 5 $1,650
$1,650
$1,180 premium 2 $960 cost of accident 5 $220
$220
$640 1 $320 5 $960 damage to other cars; her car damage was less than deductible
$960
1
Learning Objectives
2
$1,800 original premium 3 years (28 months) 5 $4,200
$7,800 2 $4,200 5 $3,600 savings
2
1
3