1. Chapter 27 Levelling the Net Single Premium

2. 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.

3. 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.

4. 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.

5. 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.

6. 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.

7. 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.

8. 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)

9. Example: Calculating the net level premium(NLP) for Mr. Worth
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)

10. 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).

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

12. 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.

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

14. 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=

15. Third Step: NLP=NSP/ LAD NLP=$209.185/20.563 =$10.172

16. 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+$822.53=$ (Table 6 & Table 7 chapter26)

17. First Step: NSP calculation (Table6 & 7, Slide 63, Chapter26)
NSP to pay death benefit
8.183
Year
Age
Probability of surviving
Death Benefit
PVF
Yearly NSP 5 35
9,491,711/9579,998
1000
0.822
Plus: NSP death benefit
8.183
NSP for five year endowment
NSP= death benefit+ survivor benefit=$8.183+$ =$

18. Second step: calculate the LAD
TLAD= (Table2, slide 11 )

19. Third Step: NLP= NSP/LAD= $822.535/4.615=$178.23