Lecture 18 CHAPTER 7 Annual Premiums Of Life

It is possible to buy either a life insurance policy or an annuity by

Ordinary Whole Life (Straight Life Policy) Let Px indicates the net annual premium for

and hence Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and

EXAMPLE page 235 Calculate the net annual premium for a L. E 10000 ordinary

EXAMPLE page 235 Find the net annual premium for a LE 70000 whole life

Let P represents the net annual premium. Then using the fundamental equation, we obtain

(Limited Life Policy) Let, t. Px denotes the annual premium for a limited payment

EXAMPLE page 237 Find the net annual premium for a L. E 90000 20

Solving for P, we obtain Instructor: Dr. Lobna M Farid, Copy rights for Dr.

EXAMPLE page 238 Compute the net annual premium for a L. E 30000 paid

Solving for p, we have Instructor: Dr. Lobna M Farid, Copy rights for Dr.

Term Insurance a) Premium payment period coincides with the term insurance period. (t =

This value will equal the present value of the death benefits provided by the

EXAMPLE page 240 Compute the net annual premium for a 5 -year, L. E

SOLUTION S = 150000 x = 50 t=n=5 term insurance the net annual premium

EXAMPLE page 240 Find the net annual premium for a L. E 50000 20

x = 35 t = n = 20 term insurance the net annual premium

b) Premium Payment Period Less Than The Term Insurance Period. (t < n) Let

EXAMPLE page 242 Find the net annual premium for a 15 -year, L. E

represent the net annual premium, and using the fundamental Let equation, we obtain Solving

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Lecture 18 CHAPTER 7 Annual Premiums Of Life Insurance policies Net Annual Premiums Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 1

It is possible to buy either a life insurance policy or an annuity by paying a single premium, but the amount of a single premium is too large for most people. Instead, individuals usually pay an annual premium to the insurance company to receive the policy benefits. Under annual premium plan, premiums are paid in annual installments prior to the data benefits begin. Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 2

Ordinary Whole Life (Straight Life Policy) Let Px indicates the net annual premium for a straight life policy issued at age x. The present value of a whole life annual due to L. E 1 is therefore the present life value of the premiums is This value will equal the present value of the death benefits provided by the. policy, which are the same as for a single premium whole life of Setting the equation of value, in which the present value of the premiums equal to the present value of the death benefits, we obtain the form of Px as follows Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 3

and hence Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 4

EXAMPLE page 235 Calculate the net annual premium for a L. E 10000 ordinary life policy issued at age 45. SOLUTION x = 45 n=∞ S = 10000 Ordinary life policy the net annual premium =? Let P represents the net annual premium, we have Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 5

EXAMPLE page 235 Find the net annual premium for a LE 70000 whole life insurance policy issued to an applicant aged 30. SOLUTION x = 30 n=∞ S = 70000 Whole life policy the net annual premium ? Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 6

Let P represents the net annual premium. Then using the fundamental equation, we obtain Solving for P, we have Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 7

(Limited Life Policy) Let, t. Px denotes the annual premium for a limited payment life policy, with a premium payment period of t-years. At- payment life policy is one that provides protection for the lifetime of the insured although premiums are paid for only t years. Since life time protection is provided in straight and a limited payment life, then the present value of the benefits is the same as for ordinary life policy, The present value for a t-year temporary life annuity due of L. E 1 is the present value of the premiums will be Setting the equation of value, in Which the present value of the premiums equal to the present value benefits, we have Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 8

and hence Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 9

EXAMPLE page 237 Find the net annual premium for a L. E 90000 20 pay whole life insurance policy issued to a man age 40. SOLUTION x = 40 n=∞ S = 90000 t = 20 Limited life policy The net annual premium - Premium are payable for 20 years, but the insurance coverage is whole life, we have 10 Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University

Solving for P, we obtain Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 11

EXAMPLE page 238 Compute the net annual premium for a L. E 30000 paid -up - at age 65 policy issued a 25 year-old man. SOLUTION x = 25 n=∞ S = 30000 t = 40 Limited life policy the net annual premium ? Premium are payable for 40 years (from age 25 until age 65), but the insurance coverage is whole life, we find Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 12

Solving for p, we have Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 13

Term Insurance a) Premium payment period coincides with the term insurance period. (t = n) Let. denotes the net annual premium for term life policy for n-year issued at age coincides with the term insurance period. The present value for a (t = n) year temporary life annuity due of L. E 1 is , the present value of the premiums will be Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 14

This value will equal the present value of the death benefits provided by the policy, which are the same as for a single premium term insurance of. Setting the equation of value, in which the present value of the premiums equal to the present value of the benefits, we obtain Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 15

EXAMPLE page 240 Compute the net annual premium for a 5 -year, L. E 150000 term policy for a man aged 50. Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 16

SOLUTION S = 150000 x = 50 t=n=5 term insurance the net annual premium ? Let P represents the net annual premium Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 17

EXAMPLE page 240 Find the net annual premium for a L. E 50000 20 -year term insurance policy issued to a man aged 35. Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 18

x = 35 t = n = 20 term insurance the net annual premium =? SOLUTION S = 50000 Solving for P, we have Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 19

b) Premium Payment Period Less Than The Term Insurance Period. (t < n) Let indicate the annual premium payable for t years (t < n) to provide on n-year term insurance issued at age x. The present value for a t-year temporary life annuity due of LE 1 is , the present value of the premiums will be This value will Equal the present value of the death benefits provided by the policy, which are the same as for a single premium term insurance of Setting the equation of value, in which the present value of the premiums equal to the present value of the benefits, we have Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 20

and hence Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 21

EXAMPLE page 242 Find the net annual premium for a 15 -year, L. E 120000 term policy issued to a man aged 40 if 1) premiums are payable for 5 years, 2) premiums are payable to age 50. SOLUTION x = 40 n = 15 S = 120000 t=5 For Term insurance, the net single premium =? Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University 22

represent the net annual premium, and using the fundamental Let equation, we obtain Solving for x = 40 n = 15 S = 120000 t = 10 Term insurance the net annual premium = ? Let represent the net annual premium, 23 Instructor: Dr. Lobna M Farid, Copy rights for Dr. Ibrahim Morgan and Dr. Raafat A. Ibrahim, " Life Insurance", Faculty of Commerce, Cairo University

Thank You 24