Available online at https://journal.
com/index.
php/ijqrm/index International Journal of Quantitative Research and Modeling e-ISSN 2721-477X p-ISSN 2722-5046 Vol.
No.
3, pp.
377-390, 2025
A Comparative Study of Projected Unit Credit and Attained Age Normal Methods for Actuarial Liability Estimation: A Case Study of PT Taspen Amalia Aura Muqtashida1*.
Suryaningrum Virgia Melania2 Department of Mathematics.
Faculty of Mathematics and Natural Science.
Universitas Padjadjaran.
Jl.
Raya Bandung Sumedang KM 21 Jatinangor Sumedang 45363 Corresponding author email: amalia@gmail.
Abstract The selection of an appropriate actuarial liability calculation method will help PT Taspen (Perser.
to ensure the adequacy o f pension funds that must be prepared, optimize pension fund management, and reduce the risk of future underfunding.
This study aims to analyze the comparison between the Projected Unit Credit and Attained Age Normal methods in the context of estimating actuarial liabilities at PT Taspen (Perser.
, and evaluate how the differences in these methods affect pension fund planning and Through this analysis, it is expected to find a method that is more suitable for the characteristics of pension participants and the long-term needs of PT Taspen (Perser.
in ensuring the sustainability of an efficient pension program.
Comparative descriptive research was conducted in this study to describe the comparison of the results of estimating actuarial liabilities from two methods: Projected Unit Value (PUC) and Attained Age Normal (AAN) and assess their impact on funding In total, the value of actuarial liabilities generated by the PUC method is slightly higher at IDR421,875,241,393.
compared to the AAN method of IDR420,746,185,877.
This difference shows that the method used in the calculation greatly affects the amount of liabilities that must be met by the pension fund.
Keywords: Mathematics.
Actuarial Liability.
Projected Unit Credit.
Attained Age Normal Introduction A pension program is a form of old-age security provided to workers after they enter an unproductive age or stop working for certain reasons.
Pension programs are designed to provide income certainty in the future, so that workers can live their old age safely and prosperously without worrying about economic problems.
In Indonesia, especially for the State Civil Apparatus (ASN), the pension program is managed by PT Dana Tabungan dan Asuransi Pegawai Negeri Perusahaan Persero or commonly referred to as PT Taspen (Perser.
This company is a State-Owned EnteIDRrise that is responsible for managing pension funds and old-age savings.
In carrying out its duties, proper planning in managing pension obligations is very important.
One of the main components in such planning is the calculation of actuarial liabilities that reflect the amount of funds that must be prepared to meet future pension To calculate actuarial liabilities, there are two major methods that can be used, namely the Accrued Benefit Cost Method and the Projected Benefit Cost Method.
The Accrued Benefit Cost Method focuses on pension benefits that have been earned and will be paid until a certain date.
Meanwhile, the Projected Benefit Cost Method focuses on estimating pension benefits in the future, namely when participants reach retirement age.
Projected Unit Credit is one of the approaches included in the Accrued Benefit Cost Method, while Attained Age Normal is part of the Projected Benefit Cost Method.
Projected Unit Credit and Attained Age Normal have different approaches in calculating retirement benefits.
Therefore, a deeper understanding of the advantages and disadvantages of each method is required.
A comparison between these two methods can make a major contribution to improving the accuracy of estimating actuarial The selection of the right method will help PT Taspen (Perser.
to ensure the adequacy of pension funds that must be prepared, optimize pension fund management, and reduce the risk of underfunding in the future.
With this background, this study aims to analyze the comparison between the Projected Unit Credit and Attained Age Normal methods in the context of estimating actuarial liabilities at PT Taspen (Perser.
, and evaluate how the differences in these methods affect pension fund planning and management.
Through this analysis, it is expected to Muqtashida et al.
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find a method that is more suitable for the characteristics of pension participants and the long-term needs of PT Taspen (Perser.
in ensuring the sustainability of an efficient pension program.
Literature Review Pension According to Turner and Helms .
a pensioner is an individual who does not work full-time during the year and who receives some sort of pension from previous years of work.
In the context of modern financial and labor systems, pensions have two main functions.
First, as an old-age guarantee that aims to maintain the welfare of a person's life after being economically unproductive.
Second, as an appreciation or reward for the dedication and contribution of labor to the institution or state, especially in the context of Civil Servants (PNS) and State Civil Apparatus (ASN).
Therefore, the pension program must be managed with the principles of prudence and justice between generations so that its sustainability is maintained in the long term.
Mortality Table A mortality table is a statistical tool used to describe the mortality rate in a population group over a period of time, as well as showing survival rates from birth to death (Bowers et al.
, 1.
Generally, this table lists the probability of a person dying before reaching their next birthday, depending on their current age.
In their construction, mortality tables often represent the life history of a hypothetical cohort - a group of individuals who are assumed to be born at the same time and whose numbers gradually shrink due to death over time.
This table has an important role in the actuarial world, especially in designing and determining values in life insurance policies.
Annuity An annuity is a series of payments of the same amount made periodically in each period of time (Johnson, 1.
In this paper, the annuity used is a life annuity.
A life annuity is an annuity that is paid while a person is still alive (Bowers et al.
, 1.
The use of life annuities in pension programs provides two sides of the challenge.
From the participant's side, it provides certainty of income for life.
But from the side of the pension fund organizer, it requires careful actuarial calculations so that the funds collected during the working period are sufficient to pay the annuity for the rest of the participant's life, without causing a financial deficit.
Actuarial Liability In the Decree of the Minister of Finance of the Republic of Indonesia Number 510/KMK.
06/2002 concerning Funding and Solvency of Employer Pension Funds article 1 paragraph 5, it is stated that Actuarial Liability is the financial responsibility of the Pension Fund calculated with the assumption that the Pension Fund will continue to operate until all rights of Participants and Eligible Parties are fully fulfilled.
This liability is calculated using a specific actuarial method that considers projected retirement benefits, participant age, length of service, interest rates, and other demographic assumptions.
The objective is to ensure that sufficient funds are available to meet all obligations to participants until retirement is complete, thus ensuring the sustainability of the program.
Normal Contribution According to the Decree of the Minister of Finance of the Republic of Indonesia Number 510/KMK.
06/2002
concerning Funding and Solvency of Employers' Pension Funds article 1 paragraph 13.
Normal Contribution is the annual contribution required to finance part of the present value of the Pension Benefits allocated in that year.
The amount is calculated based on the higher value between the Participant's contribution as stipulated in the Pension Fund Regulations, and part of the present value of the current year's Pension Benefits, in accordance with the actuarial method used.
Normal contributions are an important aspect in maintaining the solvency of the pension fund.
If normal contributions are not calculated appropriately, there could be an underfunding in the future, or conversely, excess contributions that burden participants or employers.
Therefore, the determination of normal contributions is highly dependent on the actuarial method chosen.
Actuarial Calculation Methods Actuarial calculation methods can be grouped into two major methods, namely the Projected Benefit Cost Method and the Accrued Benefit Cost Method.
Each method has different assumptions and approaches in calculating pension Muqtashida et al.
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benefits that will be paid to participants.
Included in the Projected Benefit Cost Method are Entry Age Normal.
Attained Age Normal.
Individual Level Premium, and Aggregate Cost.
Meanwhile, those included in the Accrued Benefit Cost Method are Traditional Unit Credit and Projected Unit Credit (SPA-DP No.
Projected Unit Credit (PUC) Method The Projected Unit Credit method is part of the Accrued Benefit Cost Method category.
This method involves calculating by dividing the total pension benefit at normal retirement age by the entire service period, to obtain a unit pension benefit which is then allocated on an annual basis over the service period (Bowers et al.
, 1.
The PUC method is widely used in practice as it provides a realistic picture of the liabilities that will arise in the future.
This method is also the standard approach used in IFRS-based financial statements.
The advantage is that it produces an estimate of liabilities that better reflects the financial reality at retirement, but the disadvantage is that the contribution burden may increase as the retirement age of participants approaches.
Attained Age Normal (AAN) Method The Attained Age Normal method is part of the Projected Benefit Cost Method category.
This method calculates actuarial liabilities based on the total projected pension benefits until retirement, then spreads the financing of these benefits evenly from the current working age to the retirement age of the participant (Bowers et al.
, 1.
The main feature of this method is that the annual cost .
ormal cos.
is calculated as a fixed amount .
ercentage of earnings or cash value of benefit.
over the participant's remaining working life.
This means that even though future pension benefits increase as salary and years of service increase, the cost charged annually is fixed, based on the participant's attained age, not their initial age at joining the pension plan.
The advantage is that it provides more stable contributions from year to year and is suitable for long-term financing puIDRoses.
However, the disadvantage is that in the early years, this method tends to produce a larger estimated liability than other methods and does not directly reflect the benefits that have been obtained by participants, because the cost is calculated based on an average estimate of the future.
Materials and Methods Materials The object of this research is the active retirement participants of PT Taspen (Perser.
in 2023, with the type of secondary data obtained from the annual financial statements of PT Taspen.
The data analyzed includes actuarial liabilities, pension fund asset values, actuarial assumptions such as discount rates and retirement ages, and retirement The calculation method is supported by Microsoft Excel software to calculate the value of pension benefits, present value of future benefits (PVFB), and estimation of actuarial liabilities using the Projected Unit Credit (PUC) and Attained Age Normal (AAN) methods.
Methods According to Sugiyono .
2: .
AuIn general, research methods are defined as scientific ways to obtain data with specific puIDRoses and usesAy.
The type of research used in this research is comparative descriptive research.
Sugiyono .
2: .
AuDescriptive research is research conducted to determine the value of independent variables, either one or more variables .
without making comparisons, or connecting one with another variableAy While comparative research is explained by Pawito .
7: .
, namely.
Aucomparative analysis seeks a comparison of similar symptoms or realities found in the case with those found in other cases very common in researchAy.
According to Sugiyono .
2: .
Aucomparative descriptive method, which is research that compares two or more variablesAy.
The implementation of this type of comparative descriptive research in this study is to describe the comparison of the results of estimating actuarial liabilities from two methods: Projected Unit Value (PUC) and Attained Age Normal (AAN) and assess their impact on funding conditions.
Mortality Table In the mortality table the number of people aged x is expressed in the symbol .
While the number of people who die between the ages of and is expressed in , where:
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Descriptions:
: Number of people who died between age and : Number of people who live exactly years : Number of people who live exactly years of age The probability that a person aged will live at least years, expressed in the symbol , where:
Descriptions:
: Probability that a participant aged years will work for : Number of active participants at age : Number of active participants at age years The probability that a person aged will die before the age of years, expressed in the symbol Descriptions:
: Probability that a participant aged years will die before the age of : Jumlah peserta meninggal pada usia : Jumlah peserta meninggal pada usia tahun Actuarial Basic Functions The actuarial basic functions used in the formulation of pension determination include the survival function, interest rate function, salary function, benefit function and annuity function (Winklevoss, 1.
The survival function is a function that shows the life chances of an employee will continue to work during the active working period until the time allowed for retirement.
The life expectancy is , with formula .
The interest function is used to discount a future payment to the present.
If is the assumed interest rate for year , with , the present value of a unit of money in years is indicated by:
Descriptions:
: Discount factor : Interest rate The current salary for a participant aged is denoted by age e to age , where , or can be indicated by:
, and is the accumulated amount of salary from entry Oc If the participant earns a salary increase of the salary at age is:
per year, the amount of the participant's salary at age Descriptions:
: Accumulated salary from entry age : Salary increase rate (%) to age , based on .
The benefit function is used to determine the amount of benefits paid at the time of retirement, personal termination, disability, and death.
According to (Mitchell, 1.
, there are three types of benefit formulas that are often used in defined benefit pension plans to determine the amount of retirement benefits at age ( ), namely based on the last salary, average salary during work and average salary for the last years.
Final salary:
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Descriptions:
: Participant's salary at age : Retirement age : Age of starting work : Proportion of salary set aside for retirement benefits The average salary during employment:
Descriptions:
: Total salary of the participant at age The average salary over Oc Descriptions:
: Time .
: Period of employment From pension benefits, the present value of pension benefits can be calculated.
The amount is:
Normal Contributions According to Anderson .
, the normal contribution of Attained Age Normal method is formulated by:
Descriptions:
( ) : Pension contributions for participants at age using the Attained Age Normal method : Present Value of Future Benefit when participant is years old : Age at which the participant starts the pension program : Retirement age : Pension annuity value at age : Pension annuity value at retirement age : Discount factor at age According to Winklevoss .
, normal contributions using the Projected Unit method are formulated as:
Descriptions:
( ) : Pension contributions for participants at age using the Projected Unit Credit method : Retirement age : Age at which the participant starts the pension program Actuarial Liability According to Anderson .
, the calculation of actuarial liabilities of a person aged Normal method can be found by:
Descriptions:
with the Attained Age Muqtashida et al.
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Value of actuarial liabilities at age using the AAN method Present value of pension benefits at age Normal annual fee Pension annuity value at age Pension annuity value at retirement age Discount factor at age According to Winklevoss .
, the calculation of actuarial liabilities using the Projected Unit Credit method can be written as:
Descriptions:
( ) :
Value of actuarial liabilities at age using the PUC method Age at which the participant starts the pension program Retirement age Present value of pension benefits at age Final Value of Normal Contributions In pension program financing to find out which method is recommended for participants, it is necessary to calculate the final value of normal contributions.
If a participant enters the pension program at the age of years and is still alive when entering the age of years, according to Amalia .
the final value of the total normal contribution paid by the participant at the age of years is denoted as ( ) :
Descriptions:
( )
Oc( ) ( The final value of the total normal contribution of participants who enter at age and retire at age Normal cost paid in the th year Interest rate Accumulated interest factor from year to retirement age Age at which the participant starts the pension program Retirement age Total Actuarial Liability The total actuarial liability is the amount of financial obligations that must be prepared by the company or pension fund to fulfill the payment of retirement benefits to participants in the future, based on actuarial calculations.
(Daulay et al.
, 2.
The formula for total actuarial liability is:
Descriptions:
: Actuarial liability of the -th person : Number of -th people Stages of Analysis The stages of analysis carried out to achieve the objectives of writing this final project are described as follows:
Compile a calculation table, based on the 1971 Group Annuity Table Male with an interest rate assumption of 7% .
Calculate the amount of pension benefits for each participant based on PhDP, with the participant's entry age, retirement age.
PhDP base salary and the proportion of salary prepared for retirement benefits k of 2.
Calculate the present value of pension benefits based on pension benefits at retirement age, discount factor, initial lifetime annuity at retirement age, and the probability that a person will live to n years .
Calculating normal contributions and actuarial liabilities using the Attained Age Normal Cost and Projected Unit Credit methods Muqtashida et al.
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Calculating the final value of normal contributions using the Attained Age Normal Cost and Projected Unit Credit .
Calculating the total actuarial liability by multiplying the actuarial liability per age by the number of participants at that age to obtain the aggregate total liability.
Results and Discussion Benefit Amount Calculation The following table shows the amount of participant benefits that depend on the PhDP with the participant's starting age, interest rate, pension age, and the PhDP of each participant.
Table 1: Benefit amount of PT TASPEN participants as of August 31, 2023
PhDP
IDR31,455,557
IDR24,378,056.
IDR31,455,557
IDR28,310,001.
IDR37,499,138
IDR24,374,439.
IDR37,499,138
IDR29,061,831.
IDR37,499,138
IDR33,749,224.
IDR53,424,110
IDR28,047,657.
IDR53,424,110
IDR41,403,685.
IDR53,424,110
IDR48,081,699.
IDR65,392,552
IDR34,331,089.
IDR65,392,552
IDR42,505,158.
IDR65,392,552
IDR50,679,227.
IDR82,696,800
IDR43,415,820.
IDR82,696,800
IDR53,752,920.
IDR69,579,963
IDR36,529,480.
IDR69,579,963
IDR45,226,976.
IDR69,579,963
IDR59,142,968.
IDR69,579,963
IDR64,361,466.
IDR69,896,400
IDR55,917,120.
IDR69,896,400
IDR64,654,170.
From the results of the benefit calculation above, it can be concluded that the employment benefit increases with the length of service and the amount of PhDP.
For participants with a longer service period and higher PhDp, the pension benefits received will be greater.
Present Value of Pension Benefits Calculation In the calculation of the present value of the benefit value is divided into two, namely, the value of pension benefits at the age of entry and the present value of pension benefits at the calculation age.
The following is a table of pension benefit values at entry age:
Table 2: Pension benefit outcome at entry age IDR24,378,056.
IDR30,481,968.
IDR28,310,001.
IDR25,169,854.
IDR24,374,439.
IDR42,893,459.
IDR29,061,831.
IDR36,338,492.
IDR33,749,224.
IDR30,005,758.
IDR28,047,657.
IDR69,546,377.
IDR41,403,685.
IDR51,770,567.
IDR48,081,699.
IDR42,748,475.
IDR34,331,089.
IDR85,126,642.
IDR42,505,158.
IDR74,799,393.
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IDR50,679,227.
IDR43,415,820.
IDR53,752,920.
IDR36,529,480.
IDR45,226,976.
IDR59,142,968.
IDR64,361,466.
IDR55,917,120.
IDR64,654,170.
IDR63,368,570.
IDR107,652,946.
IDR94,592,890.
IDR90,577,725.
IDR79,589,171.
IDR60,263,835.
IDR53,452,971.
IDR65,305,264.
IDR53,696,065.
Next is the table of the present value of pension benefits at the calculation age:
IDR24,378,057
IDR28,310.
IDR24,374,440
IDR29,061,832
IDR33,749,224
IDR28,047,658
IDR41,403,685
IDR48,081,699
IDR34,331,090
IDR42,505,159
IDR50.
679,228
IDR43,415,820
IDR53,752,920
IDR36,529,481
IDR45,226,976
IDR59,142,969
IDR64,361,466
IDR55,917,120
IDR64,654,170
Table 3: Pension benefit outcome at calculation age
IDR34,943,134
IDR40.
579,123
IDR49,190.
IDR58,650.
IDR68,110.
IDR79,809,176
IDR117,813,546
IDR136,815,731
IDR138,062,549
IDR170.
934,585
IDR203,806,620
IDR215,355,940
IDR307,179,845
IDR299,879,540
IDR371,279,430
IDR563,512,685
IDR613,234,392
IDR620.
057,455
IDR716,941,432
Based on the two tables above, it can be concluded that the present value of pension benefits (PVFB) will increase as the participant's age increases and the participant gets closer to retirement age.
The first table shows the calculation of the value of retirement benefits calculated from the entry age, while the second table is calculated from the current age .
aluation ag.
It can be seen that the PVFB value calculated from the current age (Table .
tends to be larger because the time to retirement is shorter, so the discount factor is smaller and the chance of living to retirement is In contrast, the PVFB value from the entry age (Table .
is lower because the benefits are still far in the future and need to be discounted for longer.
This comparison shows the importance of timing in the valuation of retirement benefits: the closer to retirement, the greater the liability burden reflected.
Normal Contributions Calculation Before determining the amount of pension fund liabilities that must be prepared, it is important to first calculate the normal contributions paid annually by participants.
In this section, we will compare the results of calculating normal contributions using two methods, namely the Attained Age Normal (AAN) and Projected Unit Credit (PUC) methods, to see the differences more clearly.
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Table 4: Normal contributions using the Attained Age Normal method IDR30,481,968.
IDR25,169,854.
IDR42,893,459.
IDR36,338,492.
IDR30,005,758.
IDR69,546,377.
IDR51,770,567.
IDR42,748,475.
IDR85,126,642.
IDR74,799,393.
IDR63,368,570.
IDR107,652,946.
IDR94,592,890.
IDR90,577,725.
IDR79,589,171.
IDR60,263,835.
IDR53,452,971.
IDR65,305,264.
IDR53,696,065.
( )
IDR2,349,920.
IDR1,940,398.
IDR3,546,518.
IDR3,004,540.
IDR2,480,936.
IDR6,393,132.
IDR4,759,069.
IDR3,929,703.
IDR9,263,016.
IDR8,139,261.
IDR6,895,421.
IDR13,663,857.
IDR13,806,777.
IDR25,237,175.
IDR22,175,494.
IDR31,268,789.
IDR27,734,871.
IDR0.
IDR0.
Next is the normal contribution calculation table using the Projected Unit Credit method.
Table 5: Normal contributions using the Projected Unit Credit method
( )
IDR34,943,134
IDR1,127,198
IDR40,579,123
IDR1,127,198
IDR49,190,786
IDR1,891,953
IDR58,650,553
IDR1,891,953
IDR68,110,319
IDR1,891,953
IDR79,809,176
IDR3,800,437
IDR117,813,546
IDR3,800,437
IDR136,815,731
IDR3,800,437
IDR138,062,549
IDR6,574,407
IDR170,934,585
IDR6,574,407
IDR203,806,620
IDR6,574,407
IDR215,355,940
IDR10,255,045
IDR307,179,845
IDR11,814,609
IDR299,879,540
IDR14,279,978
IDR371,279,430
IDR14,279,978
IDR563,512,685
IDR16,573,902
IDR613,234,392
IDR16,573,902
IDR620,057,455
IDR19,376,795
IDR716,941,432
IDR19,376,795
From the two tables above, it can be seen that the calculation of normal contributions using the Attained Age Normal (AAN) method tends to produce larger and more variable annual contribution values than the Projected Unit Credit (PUC) method.
The AAN method considers age and years of service until retirement, so contributions are divided equally over the remaining working life, while the PUC method calculates contributions based on projected pension benefits for each year of service, which makes them more stable and tends to be smaller at the beginning of the working life.
This comparison shows that the choice of method greatly affects the number of contributions that participants have to pay.
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Actuarial Liability Calculation After knowing the amount of normal contributions per year, the next step is to calculate the actuarial liability (AL).
This calculation shows the total obligation of the company to participants who have worked until a certain age, calculated based on the same AAN and PUC methods as in the previous normal contribution calculation.
IDR34,943,134
IDR40,579,123
IDR49,190,786
IDR58,650,553
IDR68,110,319
IDR79,809,176
IDR117,813,546
IDR136,815,731
IDR138,062,549
IDR170,934,585
IDR203,806,620
IDR215,355,940
IDR307,179,845
IDR299,879,540
IDR371,279,430
IDR563,512,685
IDR613,234,392
IDR620,057,455
IDR716,941,432
Table 6: Value of actuarial liabilities using Attained Age Normal method
( )
687 IDR2,349,920.
687 IDR1,940,398.
212 IDR3,546,518.
212 IDR3,004,540.
212 IDR2,480,936.
3002 IDR6,393,132.
3002 IDR4,759,069.
3002 IDR3,929,703.
6816 IDR9,263,016.
6816 IDR8,139,261.
6816 IDR6,895,421.
2399 IDR13,663,857.
4869 IDR13,806,777.
0929 IDR25,237,175.
0929 IDR22,175,494.
6032 IDR31,268,789.
6032 IDR27,734,871.
IDR0.
IDR0.
( )
IDR4,461,165.
IDR15,409,268.
IDR6,297,327.
IDR22,312,060.
IDR38,104,560.
IDR10,262,798.
IDR66,042,978.
IDR94,067,255.
IDR52,935,907.
IDR96,135,191.
IDR140,438,049.
IDR107,702,993.
IDR212,586,954.
IDR209,301,814.
IDR291,690,258.
IDR503,248,849.
IDR559,781,420.
IDR620,057,454.
IDR716,941,432.
Next is the table of calculation of actuarial liabilities using the Projected Unit Credit method.
Table 7: Value of actuarial liabilities using the Projected Unit Credit method
( )
( )
IDR34,943,134
IDR1,127,198
IDR2,254,396
IDR40,579,123
IDR1,127,198
IDR7,890,385
IDR49,190,786
IDR1,891,953
IDR3,783,907
IDR58,650,553
IDR1,891,953 IDR13,243,673
IDR68,110,319
IDR1,891,953 IDR22,703,440
IDR79,809,176
IDR3,800,437
IDR7,600,874
IDR117,813,546
IDR3,800,437 IDR45,605,244
IDR136,815,731
IDR3,800,437 IDR64,607,428
IDR138,062,549
IDR6,574,407 IDR46,020,850
IDR170,934,585
IDR6,574,407 IDR78,892,885
IDR203,806,620
IDR6,574,407 IDR111,764,921
IDR215,355,940
IDR10,255,045 IDR102,550,448
IDR307,179,845
IDR11,814,609 IDR200,848,360
IDR299,879,540
IDR14,279,978 IDR242,759,628
IDR371,279,430
IDR14,279,978 IDR314,159,518
IDR563,512,685
IDR16,573,902 IDR530,364,880
IDR613,234,392
IDR16,573,902 IDR580,086,587
IDR620,057,455
IDR19,376,795 IDR620,057,455
IDR716,941,432
IDR19,376,795 IDR716,941,432
Muqtashida et al.
/ International Journal of Quantitative Research and Modeling.
Vol.
No.
3, pp.
377-390, 2025
From the two actuarial liability tables above, it can be concluded that the Attained Age Normal (AAN) and Projected Unit Credit (PUC) methods provide different results in calculating the company's responsibility to pension In general, the PUC method tends to produce a larger liability figure for participants with a longer working age, because the contribution burden is calculated based on the length of service each year.
The AAN method, on the other hand, is more equitable and consistent as it divides the liability proportionally until retirement This shows that the method chosen will greatly affect how much coverage the company must prepare.
Next, we will discuss the final value of normal contributions to see the total pension fund burden as a whole.
Final Value of Normal Contributions In addition to actuarial liabilities, the final value of normal contributions is also calculated to see the total contributions accumulated until retirement age.
This calculation is important to determine whether the contributions paid during the working period are sufficient to finance the retirement benefits that participants will receive.
Table 8: Final value of normal contributions using the Attained Age Normal method
( )
IDR30,481,968.
IDR377,577,478.
IDR25,169,854.
IDR404,469,711.
IDR42,893,459.
IDR413,216,318.
IDR36,338,492.
IDR450,121,736.
IDR30,005,758.
IDR482,180,795.
IDR69,546,377.
IDR523,562,549.
IDR51,770,567.
IDR641,277,498.
IDR42,748,475.
IDR686,951,260.
IDR85,126,642.
IDR640,854,682.
IDR74,799,393.
IDR720,583,754.
IDR63,368,570.
IDR784,940,954.
IDR107,652,946.
IDR810,438,346.
IDR94,592,890.
IDR911,265,412.
IDR90,577,725.
IDR681,891,807.
IDR79,589,171.
IDR766,726,330.
IDR60,263,835.
IDR871,602,292.
IDR53,452,971.
IDR905,993,151.
IDR65,305,264.
IDR851,483,077.
IDR53,696,065.
IDR910,113,439.
Next is the table of the final value of normal contributions using the Projected Unit Credit method.
Table 9: Final value of normal contributions using the Projected Unit Credit method
( )
IDR34,943,134
IDR283,549,901
IDR40,579,123
IDR388,967,089
IDR49,190,786
IDR338,688,478
IDR58,650,553
IDR334,031,945
IDR68,110,319
IDR652,864,591
IDR79,809,176
IDR464,960,601
IDR117,813,546
IDR956,010,972
IDR136,815,731
IDR1,311,433,376
IDR138,062,549
IDR804,339,161
IDR170,934,585
IDR1,176,919,071
IDR203,806,620
IDR1,653,811,229
IDR215,355,940
IDR1,254,643,035
IDR307,179,845
IDR1,184,000,050
IDR299,879,540
IDR1,747,069,418
Muqtashida et al.
/ International Journal of Quantitative Research and Modeling.
Vol.
No.
3, pp.
377-390, 2025
IDR371,279,430
IDR563,512,685
IDR613,234,392
IDR620,057,455
IDR716,941,432
( )
IDR2,556,333,717
IDR5,050,776,669
IDR6,080,689,417
IDR5,200,398,410
IDR7,109,024,273
Based on the results of the calculation of the final value of normal contributions using the Attained Age Normal (AAN) and Projected Unit Credit (PUC) methods, it can be seen that although both calculate pension contributions, the final results can differ quite significantly.
Generally, the final value of normal contributions from the AAN method tends to be smaller than the PUC method, especially for participants with a younger entry age and longer service period.
This is because the AAN spreads the contribution burden evenly from the beginning of the working period until retirement, while the PUC focuses more on liabilities that increase with age and working period.
In other words, the PUC method tends to produce a larger final contribution value because it assumes a gradual increase in pension liability.
Total Actuarial Liability The total actuarial liability is calculated as the present value of pension benefits that have been recognized up to the participant's current age.
This value is multiplied by the number of participants .
in each age category or data group to get the total liability.
In the Attained Age Normal method, the obligation is calculated based on the full pension benefit multiplied by the proportion of the service period that has been served.
The following table shows the calculation of total actuarial liabilities using the Attained Age Normal method.
Table 10: Total actuarial liabilities with the Attained Age Normal method IDR4,461,165.
IDR15,409,268.
IDR6,297,327.
IDR22,312,060.
IDR38,104,560.
IDR10,262,798.
IDR66,042,978.
IDR94,067,255.
IDR52,935,907.
IDR96,135,191.
IDR140,438,049.
IDR107,702,993.
IDR212,586,954.
IDR209,301,814.
IDR291,690,258.
IDR503,248,849.
IDR559,781,420.
IDR620,057,454.
IDR716,941,432.
Total IDR1,610,480,865.
IDR5,562,745,913.
IDR2,103,307,215.
IDR7,452,228,126.
IDR12,726,923,260.
IDR1,118,645,053.
IDR7,198,684,688.
IDR10,253,330,857.
IDR3,070,282,619.
IDR5,575,841,105.
IDR8,145,406,888.
IDR538,514,965.
IDR1,062,934,772.
IDR45,627,795,462.
IDR63,588,476,357.
IDR109,708,249,214.
IDR122,032,349,644.
IDR6,200,574,547.
IDR7,169,414,320.
IDR420,746,185,877.
In the Projected Unit Credit method, the liability is calculated based on the proportion of pension benefits that have been recognized up to the time of evaluation.
The following is a table calculating the total actuarial liability using the Projected Unit Credit method.
Muqtashida et al.
/ International Journal of Quantitative Research and Modeling.
Vol.
No.
3, pp.
377-390, 2025
Table 11: Total actuarial liabilities with the Projected Unit Credit method
IDR2,254,396
IDR7,890,385
IDR3,783,907
IDR13,243,673
IDR22,703,440
IDR7,600,874
IDR45,605,244
IDR64,607,428
IDR46,020,850
IDR78,892,885
IDR111,764,921
IDR102,550,448
IDR200,848,360
IDR242,759,628
IDR314,159,518
IDR530,364,880
IDR580,086,587
IDR620,057,455
IDR716,941,432
Total
IDR813,836,859
IDR2,848,429,005
IDR1,263,824,815
IDR4,423,386,853
IDR7,582,948,892
IDR828,495,258
IDR4,970,971,550
IDR7,042,209,696
IDR2,669,209,285
IDR4,575,787,346
IDR6,482,365,407
IDR512,752,238
IDR1,004,241,800
IDR52,921,598,816
IDR68,486,774,938
IDR115,619,543,769
IDR126,458,875,997
IDR6,200,574,547
IDR7,169,414,320
IDR421,875,241,393.
Based on the results of the calculation of the total actuarial liabilities of the two methods, it is found that the total value of actuarial liabilities with the PUC method is slightly greater than the AAN method.
The AAN method produces a total liability of IDR420,746,185,877.
40, while the PUC method produces a total liability of IDR421,875,241,393.
This difference shows that the PUC method tends to provide a higher estimate of liabilities because it takes into account the proportion of years of service linearly to the total pension benefits to be received.
Conclussion This study compares two actuarial methods, namely Attained Age Normal (AAN) and Projected Unit Credit (PUC), in estimating actuarial liabilities and pension fund financing at PT Taspen.
Based on the calculation of the value of benefits, the present value of pension benefits, normal contributions, the final value of normal contributions, and total actuarial liabilities, it is found that each method produces different estimates.
The AAN method tends to produce larger but more stable and equitable annual contributions, while the PUC method produces liabilities that increase as the length of service increases, so it tends to better reflect the actual conditions of participants with long service periods.
In total, the actuarial liability value generated by the PUC method is slightly higher at IDR421,875,241,393.
compared to the AAN method of IDR420,746,185,877.
This difference shows that the method used in the calculation greatly affects the number of obligations that must be fulfilled by the pension fund.
The results of this analysis are expected to be taken into consideration for PT Taspen in choosing the method of calculating actuarial liabilities that best suits the characteristics of participants and the company's long-term goals.
References