Chapter 10-Net Premiums Flashcards
What factors are used in the calculation of the net premium?
- Rate of Mortality
- Rate of Interest
What is loading?
The amount added to the net premium to provide a margin for expenses, contingencies, and profit
What are some characteristics of the net single premium?
- The present value of future benefits
- The present value of all benefits expected to be paid
- It is assumed that all claims are paid at the end of each policy year
- Interest earnings are included in the calculation
(Insurer’s expenses are not included in the calculation)
(No assumption is made as to how policy owners will pay premiums)
Why would the net single premium for a five year policy at a certain age not equal the sum of the net single premium for five consecutive one year term policy at the same ages?
- The discounted value of the total claims to be paid differs
- The number of persons over whom the net present value of future claims is spread differs
(The total number of claims paid would be the same)
How is the net single premium calculated?
- Face Amount (presumably $1,000)
- Multiplied by
- Mortality Rate (the number dying divided by the number alive at the beginning of the period)
- Multiplied by
- Present Value Factor (relevant discounting period)
- Total the results (expected present value) from each relevant year for the net single premium
What is the equivalent of the net single premium for a whole life policy issued at a certain age?
A term policy the runs from that particular age to the end of the mortality table (where everyone is presumed to be dead)
What combination creates an endowment policy?
- Term Insurance
- Pure Endowment
(net single premium calculations start the same as term until endowment when the final calculation is the same as a whole life where the mortality table ends but in a shorter time frame)
What type of policy is equivalent to the net single premium for a straight life annuity with no refund or guarantee feature?
A series of pure endowments
Nothing is paid in the event of death
What factors create a price difference between the net single premium for an immediate annuity at an older age and the net single premium for a deferred non refund annuity at a younger age that would start at the same time?
- Benefit payments are discounted for a longer period with the deferred non refund method
- A smaller percentage of purchasers will collect their benefit under the deferred nonrefund method
(mortality rates do not affect the annuity prices)
How is the net single premium for a deferred nonrefund annuity calculated?
- The number of people alive at the payout period, divided by the number of people alive at the beginning period
- Multiply that number by the annuity benefit amount
- Multiply that number by the interest rate using the discounted value of 1 at the year of payout
What would be needed to make a net level premium equivalent to a net single premium?
- Lost premium revenue due to death of insureds during premium paying period
- Lost investment earnings due to the smaller amount available for investing
How is the net level annual premium calculated?
Divide the net single premium by the present value of a life annuity due of $1 for the premium paying period
How is the present value of a multiple year life annuity due of $1 calculated?
- YEAR 1: The number alive at the beginning divided by that same number (because payment starts at the beginning of the period when due). Multiply $1 by 1 (when due). Multiply the two numbers.
- YEAR 2: The number alive at year 2 divided by the number alive at year 1. Multiply $1 by interest rate factor for year 1 (when due). Multiply the two numbers.
- OTHER YEARS: Repeat the year 2 process for each additional year
- Add the results for the answer
(When The annuity is not due the interest rate factor starts off discounted instead of 1)
Why would the net level premium for an ordinary life policy be lower than a limited pay policy?
The premium paying period is longer for the ordinary life policy
(When the present value is divided into the net single premium, it produces a lower net level premium for the ordinary policy)
Why would the sum of 10 net annual level premiums exceed the net single premium for a 10 Payment life policy?
- Loss of interest income for the insurer
- Loss of premium income for the insurer
(premium collection expenses are not included in net premiums)
