Chapter 27

Levelling the Net Single Premium

AGENDA

• Review the assumptions used in calculating the net single premium.

• Describe the meaning of present value of future benefits

Explain the mathematics involved in leveling the net single premium for life insurance.

What is the reason behind Leveling the premium?

• It is not affordable for most people to pay one premium at the inception of the contract.

Example: paying a lump sum $20,918 to purchase $100,000 of whole life insurance.

• Instead of paying one large amount, people may prefer purchasing life insurance by paying equal periodic instalments-level premium.

• Using the level-premium method, the insured is overpaid( overinsured) the is early years of the contract an underpaid(underinsured) in the late years of the policy.

Level premium- A solution to dual problem

First problem: Affordability of premium payments as a result of increasing age and the need for owning the life insurance if he/she is in the good heath condition.Second problem: Adverse selection problem which cause the less healthy people stay in the pool while the more healthy people will select themselves out.

NSP Assumptions: Revisited

• In order to have the net single premium equal the present value of the future benefits , the following assumptions are made:

Assump.1: NSP premium is paid in full at the beginning of the contract term.

Assump.2: All death claims are paid at the end of policy year. Assump.3: The actual mortality rate(Probability of dying is

calculated by using the CSO1980 table) Assump.4:Net single premium is the amount that is paid only

for mortality costs; no additional amounts are included for operating expenses additions to surplus , or taxes.

Do life insurance companies operate within these restrictive assumptions?

• Life insurance companies pay claims and receive premiums throughout the calendar year.

• Also , they don’t adhere exclusively to the 1980 CSO Mortality

Table and various mortality tables are uses to calculate rates.

Leveling Term Life Insurance Contract

• Paying one time premium is not affordable for many people and they seek to pay the premiums in equal annual instalments.

• In order to find the level premium payment we use the following formula:

NLP= NSP /PVTLAD (formula 3)

or NSP=NLP ×PVTLAD NLP = net level premium NSP = net single premium PVTLAD= present value temporary life annuity due factor (must be

calculated)

Example: Calculating the net level premium(NLP) for Mr. Worth. He wants to buy a 5-year term life insurance at age 30, $1000 face

amount, 4 percent interest rate.

First step : calculate the NSP for a 5-yeat tem life insurance ( previous chapter, slide 58, Table 4)

Second step: Calculate Present Value Temporary Life Annuity Due (PVTLAD)

NOTE: For leveling the term life insurance we must calculate PVTLAD(it is called temporary because the number is not calculated for the whole life of the individual).

Third step : calculate NLP using the formula NLP= NSP/ PVTLAD NLP= 8.183/ 4.615 = 1.774

Leveling the Whole Life Insurance

• Leveling the premium for the whole life insurance is similar to leveling the premium for the term policy.

• The main difference between leveling the whole life insurance is using Life Annuity Due (LAD) instead of Present Value Temporary Life Annuity Due( PVTLAD).

Example: Suppose we want to calculate the level premium for whole life

insurance for Mr Worth at age 30 with 4 percent interest rate. -Because it is a whole life insurance you should find LAD for 70

years.

First Step: Calculation of NSP for a whole life insurance (Chapter(previous chapter, slide 61, table 5)

•

Second step: The sum of the 70 calculations starting at age 30 and ending at age 99 provides the LAD required for leveling the whole life contract.

LAD= 20.563

Third Step:

NLP=NSP/ LADNLP=$209.185/20.563 =$10.172

Leveling the Endowment Life Insurance

• For leveling premium for endowment life insurance first you have to calculate the NSP for endowment life insurance.

• Important: TLAD that is used to level the term life insurance is the same

TLAD required to level the endowment life insurance. Example: Calculate the level premium for 5-year endowment

life insurance for MR Worth(age30,4%interest rate).

NSP= death benefit+ survivor benefit=$8.183+$822.53=$814.35 (Table 6 & Table 7 chapter26)

First Step: NSP calculation (Table6 & 7, Slide 63, Chapter26)

NSP= death benefit+ survivor benefit=$8.183+$814.352=$822.535

NSP to pay death benefit 8.183

Year Age Probability of survivingDeath

Benefit PVF Yearly NSP

5 35 9,491,711/9579,998 1000 0.822 814.352 Plus: NSP death benefit 8.183

NSP for five year endowment 822.535

Second step: calculate the LAD

TLAD= 4.615 (Table2, slide 11 )

Third Step:

NLP= NSP/LAD= $822.535/4.615=$178.23