Applied Mathematical Sciences, Vol. 9, 2015, no. 39, 1899-1909 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.411930 Optimization of Integration Model in Family Takaful Puspa Liza Ghazali Faculty of Economics and Management Sciences Nor Mazlina Abu Bakar Faculty of Economics and Management Sciences Izah Mohd Tahir Faculty of Economics and Management Sciences Maslina Haron Faculty of Economics and Management Sciences Wan Zulqurnain Wan Ismail Faculty of Economics and Management Sciences Mustafa Mamat Faculty of Informatics and Computing
1900 Puspa Liza Ghazali et al. Copyright 2014 Puspa Liza Ghazali, Nor Mazlina Abu Bakar, Izah Mohd Tahir, Maslina Haron, Wan Zulqurnain Wan Ismail and Mustafa Mamat. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract The partition of premium life tables of the monthly payment defines the ratio of the riders. The overall monthly fee for the Integration model is RM50 and the overall total is divided into different portions; savings, pension, death coverage, death benefit, hospital bills, loss of ability to work or critical illnesses. This new plan offers complete riders for two people in one product plan; participant and a child. The overall total of the portions in riders are 54. Therefore, each partition out of RM5 is RM0.0926. The model offers buying multiple units for the product business. If the participant buys more than 1 unit, the value of premium, riders, surrender value and maturity value will be multiplied by the numbers of units bought by the participant. Keywords: Premium tables life, pension, death coverage, death benefit, hospital bills, loss of ability to work and critical illnesses 1 Introduction The two main business models use in the Takaful industry are the Mudharabah and the Wakalah models (Zainol, 2005). The Mudharabah model is commonly used in Malaysia and involves the takaful operator managing the operation in return for a share of the surplus on underwriting and a share of profit from investments. The Wakalah model is more prevalent in the Middle East region. In this model, the Takaful operator acts as an agent for the participants and manages the takaful/ retakaful fund in return for a defined fee. Contributions are made into the risk pool. From this pool, direct, indirect expenses and claims are paid. If there is a surplus shared amongst participants. Deficits are also made up with additional contributions from participants or with an interest free loan from the operator. Money is invested into Syariah approved investment vehicles such as property, sukkuk bonds, or equities. Accounting practices in the takaful model are slightly different. Pay out of the fund s excess to participants at the end of the contract is linked to when the donation was made. A donation that was three months late receives only three-quarter of the excess. Treatment of the operator s management expense is also the key. This expense is treated separately from other costs such as payment of claims, retakaful, and reserves (Stagg-Macey, 2007). As mentioned in Ali (1991), there are two differences between conventional and takaful insurances which involve the investments of the assets and the treatment of expenses and surplus. In Takaful insurance all the investments are made in halal (permissible) assets and the treatment of the trading also are made in halal practices. The takaful operator s fund is based on two models of family takaful so-called Mudharabah and Wakala Models (Ali, 2006).
Optimization of integration model in family takaful 1901 2 The Concept of Integration Model This new model offers complete riders for two people in one product plan; participant and a child. The monthly premium is reasonable to all categories income earners. The model offers buying multiple units for the product business. If the participant buys more than 1 unit, the value of premium, riders, surrender value and maturity value have to be multiplied by the number of units bought by the participant. In regards to the Muslim people, they need a new insurance or takaful which can coverage most of their risk. In this method, client proposal needs to add more riders as shown in the Table 2(a). Table 2(a): Client Proposal of Integration Model NUMBERS THINGS VALUES 1 Monthly payment RMY 2 Female un smoker K year old 3 Period Term N year 4 Interest Rate R per year 5 Monthly saving RMp 6 Tabarru Account RMj 7 Surrender Values RMt 8 Death Coverage RM10x 9 Khiarat RM2x 10 Loss of ability to work/ RM10x 40 critical illnesses 11 Hospital Bills RM5x 12 Pension 0.3x Client proposal needs many riders such as death coverage, death benefit, khiarat, loss of ability to work or 40 critical illnesses, hospital bills and pension (Puspa, 2010). After discussion with many Muslim people, it was found that they need a detailed client premium life table to avoid uncertainty in their business as shown in Table 2.2(b). Q 1 is the year, Q 2 is the age, Q 3 is the layout payment, Q 4 is the tabarru account, Q 5 is the personal account, Q 6 is the surrender value, Q 7 is the khiarat, Q 8 is the loss of ability to work or 40 critical illnesses, Q 9 is the death coverage, Q 10 is the hospital bills, Q 11 is the pension and Q 12 is the death benefit. Table 2(b): Client Quotation for i= 1, 2, 3,,17 (Mudharabah Model) Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 Q 7 Q 8 Q 9 Q 10 Q 11 Q 12 n i k i 1 2iy i (12y w) p i t i 2x 10x 10x 5x 0.3x
1902 Puspa Liza Ghazali et al. Table 2(b) is used for Mudharabah model because the Wakala fees is not include in the table above. Table 2(c): Client Quotation for i= 1, 2, 3,,17 (Wakala Model) Q 1 Q 2 Q 3 Q 4 Q 5 Q 6 Q 7 Q 8 Q 9 Q 10 Q 11 Q 12 Q 13 n i k i 1 2iy i(12y w) p i t i 2 x 10x 10x 5x 0.3x Table 2(c) is used for Wakala model because it has the Wakala fees shown as Q 13. From Table 2(b) and Table 2(c), the value of Q 7 to Q 11 are in ratio items where if the value of x is RM1000 so that the value of hospital bills is RM5000. The detail partition of the ration is given below. 3 Partition in Integration Model of Premium Life Table for Monthly Payment According to the Riders Ratio The researcher wants to construct the Integration model of premium life tables which follow the basic models in family takaful (Mudharabah and Wakala). The premium table life shows the partition of the monthly payment which as in Table 3.1(a) to define the ratio of the riders. Table 3.1(a) is to elaborate the partition of the monthly payment according to riders` ratio. Overall the monthly payment is RM50. Therefore, the overall total is divided into different portions; savings, pension, death coverage, death benefit, hospital bills, loss of ability to work or critical illnesses (Puspa, 2010). This new plan offers complete riders for two people in one product plan; participant and a child. According to the partition in Takaful Ikhlas quotation (2008), RM0.11 is for one unit (RM1000 = 1 unit). Based on Table 3.1(a), the overall total of the portions mentioned is 54. Therefore, each partition out of RM5 is RM0.0926. Table 3(a): Partition of Riders of the Tabarru Account in Integration Model Tabbarru Account Partition Ratio of Tabbarru Account (54X) Partition of the Premium Payment (RM5.00) Q 7 (Khiarat) (2X) 2X (2 People) = 4X RM0.0926(4) =RM0.3704 (Child and Participant) Q 8 (Loss of ability to work/ critical illnesses) (10X) 10X ( 2People) = 20X RM0.0926(20) = RM1.852 (Child and Participant) Q 9 (Death Coverage) (10X) 10X (1Person) = 10X RM0.0926(10) =RM0.926 (Death Child) Q 10 (Hospital Bill) (5X) 5X (2 People) = 10X RM0.0926(5) = RM0.926 (Child and Participant) Q 12 (Death Benefit) (10X) 10X (1 Person) = 10X RM0.0926(10) RM0.926 (Death Participant)
Optimization of integration model in family takaful 1903 According to the Am Assurance pension scheme quotation (2008), the monthly payment is RM125 for 21 years. The participant will earn RM500 per month after retirement for the whole life. In the Integration model, the monthly payment of the pension scheme is RM15 and the child will earn RM300 for 10 years if the participant dies. If the participant dies when the child s age is below 11 years old, the value of the pension is depending on the age of the child. For example if the participant dies when a child age 6 years old, so the child will earn RM200 for 15 years until the child will reach 21 years old. It means that the longer a child will have for pension, the less a child will earn for pension per month. The overall total of monthly premium payment in Mudharabah model is shown in Table 3.1(b) and Wakala model in 3.1(c). Partition ratio is very important to know the correct distribution of the ratio of premiums paid by the participant. Table 3(b): Partition of Monthly Premium Payment in Mudharabah Model Overall Total of Monthly Premium Payment Personal Investment Account Partition of the Pension Scheme Payment Partition of the riders RM50 RM30 RM15 RM5 Table 3(c): Partition of Monthly Premium Payment in Wakala Model Overall Total of Monthly Premium Payment Personal Investment Account Partition of the Pension Scheme Payment Partition of the riders Wakala Fee RM50 RM25 RM15 RM5 RM5 4 Mudharabah of Integration Model The proposal is used in the premium life tables for Mudharabah models of Integration model shown as follow. Below are the symbols of the elements use in the Mudharabah model. Mudharabah of Integration model has four types of model but in this section only static premium and static benefit are shown while the rest will be discussed in numerical result. Mudharabah of Integration model uses the proposal below for constructing the premium life table (Puspa et al., 2012a). Monthly payment = RM50.00 (1 unit) Term = 17 years Interest rate = 5% per year ( i ) Tabbarru Account = RM20.00
1904 Puspa Liza Ghazali et al. 4.1 Static Premium and Static Benefit of Life Table Below are the symbols of elements in mudharabah model where the static premium of life table (Q3, Q4 and Q5) and static benefit (Q6 to Q13) shown in the Table 4.1(a). 1. Q1 is year 8. Q8 is total surrender value 2. Q2 is age 9. Q9 is khiarat 3. Q3 is layout payment 10. Q10 is Loss of ability to work /40 critical illnessess 4. Q4 is tabarru account 11. Q11 is death coverage 5. Q5 is personal account 12. Q12 is hospital bills 6. Q6 is monthly profit 13. Q13 is pension 7. Q7 is yearly profit 14. Q14 is death benefit Table 4.1(a): Static Premium and Static Benefit of Mudharabah Integration Model Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 1 1 600 240 360 8 18 386 2000 10000 10000 5000 300 (P 1 ) (T 1 ) 2 2 1200 480 720 57 36 813 2000 10000 10000 5000 300 (P 2 ) (T 2 ) 3 3 1800 720 1080 110 54 1244 2000 10000 10000 5000 300 (P 3 ) (T 3 ) 4 4 2400 960 1440 164 72 1676 2000 10000 10000 5000 300 (P 4 ) (T 4 ) 5 5 3000 1200 1800 218 90 2108 2000 10000 10000 5000 300 (P 5 ) (T 5 ) 6 6 3600 1440 2160 272 108 2540 2000 10000 10000 5000 300 (P 6 ) (T 6 ) 7 7 4200 1680 2520 326 126 2972 2000 10000 10000 5000 300 (P 7 ) (T 7 ) 8 8 4800 1920 2880 380 144 3404 2000 10000 10000 5000 300 (P 8 ) (T 8 ) 9 9 5400 2160 3240 434 162 3836 2000 10000 10000 5000 300 (P 9 ) (T 9 ) 10 10 6000 2400 3600 488 180 4286 2000 10000 10000 5000 300 (P 10 ) (T 10 ) 11 11 6600 2640 3960 542 198 4700 2000 10000 10000 5000 300 (P 11 ) (T 11 ) 12 12 7200 2880 4320 596 216 5132 2000 10000 10000 5000 300 (P 12 ) (T 12 ) 13 13 7800 3120 4680 650 234 5564 2000 10000 10000 5000 300 (P 13 ) (T 13 ) 14 14 8400 3360 5040 704 252 5996 2000 10000 10000 5000 300 (P 14 ) (T 14 ) 15 15 9000 3600 5400 756 270 6426 2000 10000 10000 5000 300 (P 15 ) (T 15 ) 16 16 9600 3840 5740 812 288 6840 2000 10000 10000 5000 300 (P 16 ) (T 16 ) 17 17 10200 4080 6120 (P 17 ) 863 306 7289 (T 17 ) 2000 10000 10000 5000 300 The derivation of Q6 to Q8 in the Table 4.1(a) is shown below.
Optimization of integration model in family takaful 1905 1. 360 + ( 30*5/100 * (66 + 0 )) * 1/12 ) + ( 360 * 5/100 ) = 360 + 8 +18 = 386 2. 720 + ( 30* 5/100 * ( 66 + 386 )) + (720 * 5/100) = 720 + 57 + 36 = 813 3. 1080 + ( 30 * 5/100 * ( 66 + 813 ) ) + ( 1080 * 5/100 ) = 1080 + 110 + 54 = 1244 4. 1440 + (30 * 5/100 * ( 66 + 1244)) + ( 1440 * 5/100 ) = 1440 + 164 +72 = 1676 5. 1800 + (30 * 5/100 * ( 66 + 1676 )) + (1800 * 5/100 ) = 1800 + 218 + 90 = 2108. ------------------------------------------------------------------------------------------------- P n + (P * i/100 * (66 + T n-1 )) + ( P n * 5/100) Pi 66 T 1 Pn 1 0. 05 100 12 n = where P is the personal account, and n =1,2,3, The general formula of Table 4.1(a) in shown in the Table 4.1(b) below: Table 4.1(b): General Formula of Static Premium and Static Benefit of of Mudharabah Integration Model Symbols of elements Formula of elements Q3 Q4 Q5 Q6 to Q8 Q9 Q10 Q11 Q12 Q13 600n 0.4 (600n) 0.6 (600n) P n Pi 66 T 100 12 n1 1 0. 05 Where P is the personal account, and n =1,2,3, 2x 10x 10x 5x 0.3x 5 Wakala Integration Model The proposal used in the premium life tables for Wakala models of Integration model is shown as follow. Below are the symbols of the elements used in the Wakala model. Wakala integration model has four types of model but in this section only static premium and static benefit are shown while the rest will be discussed in numerical result. Wakala integration model uses the proposal below for constructing the premium life table (Puspa et al., 2012a). Monthly payment = RM50.00 (1 Unit) Term = 17 years Interest Rate = 5% per year (i) Wakala Fee = RM5.00 Tabbarru Account = RM20.00 Saving Account = RM25.00 5.1 Static Premium and Static Benefit of Wakala Integration Model Below are the symbols of elements in Wakala integration model where the static premium of life table (Q3 to Q6) and static benefit (Q7 to Q14) are shown in the Table 5.1(a).
1906 Puspa Liza Ghazali et al. 1. Q1 is year 9. Q9 is total surrender value 2. Q2 is age 10. Q10 is khiarat 3. Q3 is layout payment 11. Q11 is Loss of ability to work/40 critical illnesses 4. Q4 is tabarru account 12. Q12 is death coverage 5. Q5 is wakala fees 13. Q13 is hospital bills 6. Q6 is personal account 14. Q14 is pension 7. Q7 is monthly profit 15. Q15 is death benefit 8. Q8 is yearly profit Table 5.1(a): Static Premium and Static Benefit of Wakala Integration Model Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 1 1 600 240 60 (P 1 ) 7 15 (P 1 ) 2000 10000 10000 5000 300 300 322 2 2 1200 480 120 (P 2 ) 40 30 (P 2 ) 2000 10000 10000 5000 300 600 670 3 3 1800 720 180 (P 3 ) 77 45 (P 3 ) 2000 10000 10000 5000 300 900 1022 4 4 2400 960 240 (P 4 ) 113 60 (P 5 ) 2000 10000 10000 5000 300 1200 1373 5 5 3000 1200 300 (P 5 ) 150 75 (P 5 ) 2000 10000 10000 5000 300 1500 1725 6 6 3600 1440 360 (P 6 ) 187 90 (P 6 ) 2000 10000 10000 5000 300 1800 2077 7 7 4200 1680 420 (P 7 ) 223 105 (P 7 ) 2000 10000 10000 5000 300 2100 2428 8 8 4800 1920 480 (P 8 ) 260 120 (P 8 ) 2000 10000 10000 5000 300 2400 2780 9 9 5400 2160 540 (P 9 ) 296 135 (P 9 ) 2000 10000 10000 5000 300 2700 3131 10 10 6000 2400 600 (P 10 ) 333 150 (P 10 ) 2000 10000 10000 5000 300 3000 3483 11 11 6600 2640 660 (P 11 ) 370 165 (P 11 ) 2000 10000 10000 5000 300 3300 3835 12 12 7200 2880 720 (P 12 ) 406 180 (P 12 ) 2000 10000 10000 5000 300 3600 4186 13 13 7800 3120 780 (P 13 ) 443 195 (P 13 ) 2000 10000 10000 5000 300 3900 4538 14 14 8400 3360 840 (P 14 ) 480 210 (P 14 ) 2000 10000 10000 5000 300 4200 4890 15 15 9000 3600 900 (P 15 ) 516 225 (P 15 ) 2000 10000 10000 5000 300 4500 5241 16 16 9600 3840 960 (P 16 ) 553 240 (P 16 ) 2000 10000 10000 5000 300 4800 5593 17 17 10200 4080 1020 (P 17 ) 5100 589 255 (P 17 ) 5944 2000 10000 10000 5000 300 The derivation of Q7 to Q9 in the Table 5.1(a) is shown as below: 1. 300 + (25 * 5/100 * (66 + 0)) + (300 * 5/100) = 300 + 7 + 15 = 322 2. 600 + (25 * 5/100 * (66 + 322)) + (600 * 5/100) = 600 + 40 + 30 = 670
Optimization of integration model in family takaful 1907 3. 900 + (25 * 5/100 * (66 + 670)) + (900 * 5/100) = 900 + 77 + 45 = 1022 4. 1200 + (25 * 5/100 * (66 + 1022)) + (1200 * 5/100) = 1200 + 113 + 60 = 1373 5. 1500 + (25 * 5/100 * (66 + 1373)) + (1500 * 5/100) = 1500 + 150 + 75 = 1725 -------------------------------------------------------------------------------------------------- P n + [P * i/100 * (66 + T n-1 )] + ( P n * 5/100) Pi 66 Tn 1 = Pn 1 0. 05 where P is the personal account, and n =1,2,3, 100 12 The general formula of Table 5.1(a) shown in the Table 5.1(b) is as follows. Table 5.1(b): General Formula of Static Premium and Static Benefit of Wakala Integration Model Symbols of elements Formula of elements Q3 Q4 Q5 Q6 Q7 to Q9 Q10 Q11 Q12 Q13 Q14 600n 0.4n. (600n) 0.1n. (600n) 0.5n. (600n) P n Pi 66 T 100 12 n1 1 0. 05 Where P is the personal account, and n =1,2,3, 2x 10x 10x 5x 0.3x 6 Discussion The present premium life table in family takaful or life insurance uses only one method especially in maturity value but in new idea of model in premium table the alternatives table which shows the increase of customer price index (Bureau of Labor Statistics, 2010) will affect the premium payment and also the lump sum of maturity value must be given (Puspa et. al., 2012c).The value of RM10,000 is not the same after 10 years and it has to find the solution in the maturity value. Education plan takaful pays higher education fees for the children in the future. However, if they received RM15,000 from takaful or insurance company after invested for 17 years, can the amount of maturity value pay for the education fees? The value of RM15,000 in 17 years in the is the same value of RM5,000 in the present day. This means that the parent only might just be able to pay the registration fee (Puspa et al., 2012b). This new plan offers complete riders for two people in one product plan; participant and a child. The monthly premium is reasonable to all categories income earners. The plan offers buying multiple by units for the product business. If the participant buys more than 1 unit, the value of premium, riders, surrender value and maturity value will have to be multiplied by the numbers of units bought by the participant. The plan also gives the customer choice to choose the suitable premium life table for them which have four types of model (show in numerical result) whether in Mudharabah or Wakala model (Puspa et al., 2012c). The new product in premium life table will give the better perception of family takaful business because the plan offers
1908 Puspa Liza Ghazali et al. affordable price for all categories of income earners and it also includes almost complete riders price to all income earner. 7 Conclusion The significant weakness in Mudharabah and Wakala model is if a participant dies when the premiums is approaching maturity, the child will not get the full amount of the insured death. The child should get more for the insured death since the participant has paid premiums and investment and it is approaching the maximum limit. (Puspa and Ismail, 2011) Many Takaful Companies in Malaysia still use the concept of profit sharing which give the advantage to the participant but this model does not offer integrated riders to their clients (Puspa and Ismail, 2012). Therefore, it means the more riders in their premium; the more money will be needed to buy the premium. Therefore, the detailed introduction to new model which is cheap, integrated riders and also affordable to all income earners is required. The Model is called Integration model. References [1] K.M.M. Ali, Insurance in Islam: Some Aspects of Islamic Insurance, Dhaka: Islamic Economics Research Bureau, 1991. [2] K.M.M. Ali, Basis and Models of Takaful: The need for Ijtihad, ICMIF Takaful, 2006. [3] Am Assurance, Am Assurance Pension Scheme Quotation. Kuala Lumpur: Am Assurance, 2008. [4] P.L. Ghazali, Comparison in formulation between life insurance and family takaful, Master Thesis, Kuala Terengganu: UMT Press, 2010. [5] P.L. Ghazali, M. Ismail, M. Mustafa, and W.A. Wan Muhamad Amir, Mathematical Modeling in Family Takaful. Journal of Applied Science, 11 (2011) 3381 3388. http://dx.doi.org/10.3923/jas.2011.3381.3388 [6] P.L. Ghazali and M. Ismail, Perbezaan Model Matematik dalam Insurans Nyawa dan Takaful Keluarga Kini. Kesturi, 2 (2011), 34 51. [7] P.L. Ghazali and M. Ismail, Pengabungan Model Insurans Takaful Berkebajikan Dalam Jadual Hayat, Kesturi, 1 (2012). [8] P.L. Ghazali, M. Ismail, M. Mustafa and W.A. Wan Muhamad Amir. W. A. and M. Mustafa, Integration Model of Education Plan Takaful: A Case Study for Terengganu,
Optimization of integration model in family takaful 1909 Kelantan and Perlis States in Malaysia, Far East Journal of Mathematical Sciences (FJMS). Allahabad, India: Puspha Publishing House, 65(1) (2012) Issue of the FJMS, 97-117. [9] P.L. Ghazali, M. Ismail, M. Mustafa and W.A. Wan Muhamad Amir, Comparison between Existing Model and Integration Model in Family Takaful. Journal of Applied Science Research. Jordan: American-Eurasian Network for Scientific Information (AENSI), 2012. [10] P.L. Ghazali, M. Ismail, M. Mustafa and W.A. Wan Muhamad Amir, Integration Model of Premium Life Tables of Family Takaful. Journal of Applied Science Research. Jordan: American-Eurasian Network for Scientific Information (AENSI), 2012. [11] C. Stagg-Macey, An overview of Islamic insurance. Kuala Lumpur: ICMIF Takaful, 2007. [12] Takaful Ikhlas, Education Plan Quatation. Kuala Lumpur: Syarikat Takaful Ikhlas, 2008. [13] A.M.K. Zainol. The Islamic Way of Insurance. Contingencies January/February (2005), 33 38. Received: November 23, 2014; Published: March 10, 2015