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Business Math

Business Math. Chapter 18: Insurance. Insurance. Life Estimate insurance premiums using a rate table Apply the extended term non-forfeiture option Property Estimate insurance premiums using a rate table Find the refund for a cancelled policy Find the compensation for a coinsurance policy

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Business Math

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  1. Business Math Chapter 18: Insurance

  2. Insurance • Life • Estimate insurance premiums using a rate table • Apply the extended term non-forfeiture option • Property • Estimate insurance premiums using a rate table • Find the refund for a cancelled policy • Find the compensation for a coinsurance policy • Motor Vehicle • Find automobile insurance premiums using rate tables

  3. Key Terms • Insurance: a form of protection against unexpected financial loss • Comprehensive policy: insurance policy that protects the insured against several risks such as fire, flood and earthquake • Insured (policyholder): the individual, organization or business that carries the insurance or financial protection against loss • Insurer (underwriter): the insurance company that assures for a specific loss according to contract provisions

  4. Key Terms • Policy: the contract between the insurer and the insured • Premium: the amount paid by the insured for the protection provided by the policy • Face value: the maximum amount of insurance provided by the policy • Beneficiary: the individual, organization, or business to whom the proceeds of the policy are payable

  5. 18.1.1 Estimate life insurance premiums using a rate table • Life insurance pays a specified amount to the beneficiary and provides financial assistance to the surviving dependents of the insured person • A company may offer life insurance as a fringe benefit to its employees • Several types of policies exist; some even function as savings policies

  6. Types of life insurance policies • Term insurance: insurance purchased for a certain period of time. At the end of the time period, the policy has no cash value and the insurance ends. • Straight-life (ordinary life) insurance: insured pays premiums for entire life. At the death of the insured, the beneficiary receives the face value of the policy. If the policy is cancelled, the insured is paid the cash value of the policy.

  7. Table 18-1

  8. Estimate an annual life insurance premium using a table • Locate the estimated annual rate in Table 18-1 according to the type of policy, age and sex. • Divide the policy face value by $1,000 and multiply the quotient by the rate from step 1. Estimated annual premium = face value ÷ 1000 x rate.

  9. Look at this example • Estimate the annual premium of an insurance policy with a face value of $100,000 for a 30-year old male for (a) a 20-year fixed rate policy and (b) a straight life policy. • Estimated annual premium =$100,000 ÷ $1,000 x rate • Look at Table 18-1 for each rate and calculate the estimated annual premium. • (a) = $191 (b) $349

  10. Making insurance premium payments If premiums are not paid annually, but in smaller increments semi-annually, quarterly or monthly, this table shows premium rates for periods less than one year.

  11. Look at this example • Use Tables 18-1 and 18-2 to estimate the (a) semiannual, (b) quarterly and (c) monthly premiums for a $250,000 policy on a 40-year old female. • Annual premium = amount of coverage ÷ $1,000 x rate • $250 x 3.88 = $970 • The annual premium for this policy would be $970. (Go to next slide)

  12. Premium payments • Semiannual premium = $970 x 0.51 = $494.70 • Quarterly premium = $970 x 0.26 = $252.20 • Monthly premium = $970 x 0.0875 = $ 84.88 • In the semiannual payment structure, the insured would pay $989.40. • In the quarterly payment structure, the insured would pay $1,008.80 • In the monthly payment structure, the insured would pay $1,018.56

  13. Key Terms • Fixed payment insurance policy: gives a specific face value for the insured’s entire life, but payments are made only for a fixed period of time; at the end of the fixed time, the insured has paid-up insurance. • Fixed time endowment insurance policy:a combination of insurance and savings plan. • Universal life insurance policy: has flexible premium rates and death benefits depending on interest rates, mortality rates and insured’s age.

  14. 18.1.2 Apply the extended term non-forfeiture option • Most life insurance policies, except term life insurance, build up cash value. If a policy holder decides to cancel a policy or allow it to lapse, the insured normally has three choices called non-forfeiture options: • Cash value or surrender option • Paid-up insurance • Extended term insurance

  15. How to apply the extended term non-forfeiture option • Identify the cash value of the cancelled policy. • Estimate the annual premium for the term policy of the same value. (Use the 10 year fixed rates on Table 18-1) • Determine the amount of paid-up insurance = cash value of surrendered policy ÷ annual term of term policy

  16. Look at this example A 50-year old female started a $100,000 straight-life policy when she was 30. It has a cash value of $3,857 and she wants to convert it to an extended term for the same face value. Using the 20-year fixed rates, estimate how long her extended term insurance will last. (Go to next slide)

  17. How long will it last? • Estimated annual term premium: $3.51 per $1,000 • $100,000 ÷ $1000 = 100 units • $3.51 x 100 = $351 (annual term rate) • Cash value ÷ annual premium $3,857 ÷ $351 = 10.99 years • Her extended term insurance will last an estimated 10.99 years.

  18. 18.2 Property insurance Businesses and homeowners need property insurance to protect them from financial loss that could come from: • Fire • Storms • Burglary • Vandalism

  19. Annual Fire Insurance Rates per $100 of Face Value

  20. 18.2.1 Estimate property insurance premiums using a rate table • Insurance rates are expressed as an annual amount per $100 of coverage. • To find the annual premium, divide the amount of coverage by $100 and multiply by the rate in the table. (Do this for both building and contents.)

  21. Estimate the annual fire insurance premium using a table • Locate the annual rate for building (or contents) being insured according to the building’s area rank and its class. • Find the annual premium for both the building and contents. • Add the two premiums. Annual premium = face value x rate $100

  22. Look at this example The building owned and occupied by O’Toole Hardware is insured for $85,000. The contents are insured for $50,000. If it is a class B building located in area 2, find the annual premium for the building and contents. • Annual premium (for building) = $85,000 ÷ $100 x 0.54 = $459 • Annual premium (for contents) = $50,000 ÷ $100x 0.62 = $310 • The sum of the two premiums is $769.

  23. 18.2.2 Find the refund for a cancelled policy • A business or individual may need insurance for less than one year or they may need to cancel a policy before it has expired. • A short-term policy is an insurance policy for less than one year. • A short-rate premium is the premium for a short-term policy.

  24. Short-rate property insurance schedule

  25. Find a refund for a cancelled policy • Identify the annual premium • Identify the time the policy is in force • Use Table 18-4 to find the short rate for the time the policy is in force. • Find the short-rate premium= annual premium x short rate • Find the refund = annual premium –short rate premium

  26. Look at this example Sheldon Dan paid an annual premium of $5,285 for the building and contents for his business. He sold his business 7 months after the policy was in force and cancelled the policy. What was his refund? • Annual premium = $5,285 • Time policy is in force = 7 months • Short-rate percent = 75% ( go to next slide)

  27. Sheldon’s refund • Annual premium x short-rate percent = $5,285 x 0.75 = $3,963.75 • Refund is = annual premium – short-rate premium • Refund :$5,285 - $3,963.75 = $1,321.25 • Sheldon’s refund is $1,321.25

  28. 18.2.3 Find the compensation with a coinsurance clause • A coinsurance clause states that property must be insured for at least 50% of the replacement cost for full compensation for a loss. • Businesses take out this kind of policy to save money on premiums since a fire, for example, rarely destroys a whole building or all of its contents.

  29. Find the compensation with a coinsurance clause • Find the face value required by the 80% coinsurance clause for full compensation: multiply 0.8 by the replacement value of the property. • Find the compensation for the loss if the insurance is less than 80% of the replacement value. (go to next slide)

  30. Compensation formula Compensation (up to amount of loss) = amount of loss (up to face value) x face value of the policy 80% of replacement value

  31. Look at this example Budget Construction owns a building with a replacement value of $200,000. It has fire insurance policy with an 80% coinsurance clause, and a face value of $130,000. There is a fire and the building damage is figured to be $50,000. What will the insurance company pay as a compensation? • Compensation = loss xface value of the policy 80% of the replacement value

  32. Budget’s compensation • Compensation = $50,000 x $130,000 $160,000 • = $40,625 • Budget receives $40,625 compensation for its loss of $50,000.

  33. 18.3.1 Motor Vehicle Insurance • Major expense item for individuals and businesses because of high risk of personal injury or death, and damage to property. • Insurance can cover risks such as liability for personal injury and property damage, damage to or loss of the insured vehicle; damage or loss to an insured vehicle due to collisions, theft, fire, floods, or storms.

  34. Key Terms • Liability insurance: protection for the owner of a vehicle if an accident causes personal injury or property damage and is the fault of the driver of the insured vehicle. • Comprehensive insurance: protection for the owner of the vehicle for damage caused by a non-accident incident, such as fire, water, theft or vandalism.

  35. Key Terms • Collision insurance: protection for the owner of a vehicle for damages to the insured’s vehicle for an accident that is the insured driver’s fault. • No-fault insurance: protection for the owner of a vehicle for damage to the insured vehicle when the amount of damage falls within the no-fault limits imposed by state law.

  36. Key Terms • Uninsured-motorist coverage: protection for the owner of a vehicle when damages are incurred in an accident that is not the owner’s fault, but the other driver has no insurance. This coverage only applies to the owner’s vehicle. • Territory: the primary location where the vehicle is driven. • Driver class: the class for the primary driver based on factors such as age, sex, marital status and driving history.

  37. Key Terms • Bodily injury: personal injury sustained in an accident. • Property damage: damage to the property of others in an accident.

  38. Factors affecting the cost of automobile insurance • Location of the vehicle (city, town, rural area) • Total distance traveled per year • Distance traveled to work each day • Types of use (personal, commuting, business) • Academic record of the driver (for those still in school) • Driving record and training of the insured drivers • Age, sex and marital status of insured driver • Type and age of the vehicle. • Amount of coverage desired

  39. Annual Automobile Liability Insurance Premiums

  40. Annual Automobile Comprehensive and Collision Insurance

  41. Key Terms • Deductible: the amount an insured pays for damages to the insured vehicle before the insurance company pays for damages in excess of the deductible amount. • The book value: the value of a particular year, make and model of a vehicle is published for car dealers and insurance companies. If the damages resulting from an accident exceed the book value, the insurance company will only pay the book value and the automobile is said to be totaled.

  42. Find an annual automobile insurance premium using table values • Locate the bodily injury premium according to territory, driver class, and per person/per accident bodily injury coverage. • Locate the property damage premium according to territory, driver class, and property damage coverage. • Locate the comprehensive premium according to model class, vehicle age, territory and deductible.

  43. Insurance premium calculation (continued) 4. Locate the collision premium according to model class, vehicle age, territory and deductible. 5. Add the premiums from steps 1-4. Total annual premium = bodily injury premium + property damage premium +comprehensive premium + collision premium.

  44. Look at this example • Use Tables 18- 5 and 18-6 to find the annual premium for an automobile liability insurance policy in which the insured lives in territory 1, is class A, and wishes to have 50/100/10 coverage. • The automobile is a three-year old, model class 2 vehicle and both comprehensive and collision are carried with a $250 deductible. (continue on following slide)

  45. The annual premium • Bodily injury premium: $230 • Property damage premium: $105 • Comprehensive premium: $112 • Collision premium: $168 • Total: $615 • The total annual premium is $615.

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