Question

Mr. Wong has just turned 30 today. He approaches Nopay Assurance Limited to buy a $1,000,000 WHOLE life insurance protection. The mortality table appropriate for an average male of Mr. Wong's age and health conditions is given below.

age	30	50	70	90	110
number of person alive at age	1000	900	500	100	0

The insurance premiums are paid at the beginning of each period and death benefit is paid at the end of the period of death. The current interest rate is so low that it can be assumed to be 4% per year. Ignore the cost loadings and the profit margin of Nopay Assurance.

(a) If Mr. Wong wants to make one and only one premium payment at Age 30, what is the single premium payment?

(b) Determine the level premiums for Mr. Wong's whole life policy. There are FOUR level premiums.

(c) Determine the cash value at each age of Mr. Wong.

Answer 1

(a) If Mr. Wong wants to make one and only one premium payment at Age 30, what is the single premium payment ?

Answer : The details are as follows:

1) Age of Mr. Wong - 30

2) Mr. Wong approaches Nopay Assurance Limited to buy a $1,000,000 WHOLE life insurance protection.

3) The insurance premiums are paid at the beginning of each period

4) The death benefit is paid at the end of the period of death.

5) The current interest rate 4% per year.

6) The cost loadings and the profit margin of Nopay Assurance - Nil.

7) The calculation of single premium payment is given below:

=10^6/(1+4%)^0*100/1000+10^6/(1+4%)^20*900/1000*400/900+10^6/(1+4%)^40*500/1000*400/500+10^6/(1+4%)^60*100/1000*100/900

= $366,926.6230

Note : i) 10^6 = $1,000,000

Hence, If Mr. Wong wants to make one and only one premium payment at Age 30, the single premium payment works out to $366,926.6230.

(b) Determine the level premiums for Mr. Wong's whole life policy. There are FOUR level premiums.

Answer: Since Mr. Wong wants to make one and only one premium payment at Age 30, the FOUR level premiums for Mr. Thrift's whole life policy are as follows:

1) 10^6/(1+4%)^0*100/1000 = $100,000.0000

2) 10^6/(1+4%)^20*900/1000*400/900 = $182,554.7785

3) 10^6/(1+4%)^40*500/1000*400/500 = $83,315.6179

4) 10^6/(1+4%)^60*100/1000*100/900 = $1,056.2266

Note : i) 10^6 = $1,000,000

Hence, the FOUR level premiums for Mr. Wong's whole life policy are $100,000.0000, $182,554.7785, $83,315.6179, $1,056.2266.