Judul: The Effects of Variance of Interest rate to Variance of Annuity Future Values
Abstrak: Time value of money is a concept that refers to the difference of the value of money due to time difference. The value of money for present time would not be the same as the value of money in the future. The value of money for present time is called as Present Value (PV) of the money and the value of money for future time is called Future Value (FV) of the money. Determination the value of money, for present and future time, depends on the time and rate of return. The value of money is determined by several factors such as inflation, fluctuation of interest rates, and government policy in securities and taxation. Due to fluctuation of the value of money we need a FV formulation, it is useful for knowing whether an investment can be profitable or not, and this information is useful also in budget analysis. Annuity is defined as a series of payments made for a specific period. The payment, fixed or varied, can be made at the beginning or at the end of the period. Annuity paid at the beginning of the period is called annuity-due and annuity paid at the end of the period is called immediate annuity-certain. The accumulated value of the annuity after few years later is called as a final value or a future value. Burnecki et al. (2003) have discussed about the FV of a fixed-rate annuity in which payments are made according to the arithmetic or geometric series. They have also examined FV for annuities in which payments are made according to arithmetic or geometric series with random rates of interest. This paper examines FV for annuity-due in which payments are made according to arithmetic or geometric series with interest rates as a random variable, which is normal distribution ,  . Future value formula is expressed in recursive form. FV for annuity-due which payments are made according to the arithmetic or geometric series with random rates of interest is calculated by theoretical way and simulation way. The random rates of interest is denoted as k k i  i  , where k i an independent random variable; i is a constant and k  is a random variable which has normal distribution ,  . By using the determined parameters, a sequence of random rates of interest are generated for theoretical calculation. Meanwhile for the simulation, the random rates of interest is generated 1000 times for the simulation. The generated data give mean value, variance, and standard deviation. Moreover, error of mean value, variance, and standard deviation from the theoretical and simulation results are calculated. Error calculation uses Symmetric Mean Absolute Percentage Error (SMAPE). The smaller the value of SMAPE is the more accurate the simulation. The interest rate variances are varied from 0.000036 to 0.0001 to study the relationship between variance of rates of interest and variance of future value. The theoretical and simulation results show that when the variance of random rates of interest increases, then the variance of FV increases linearly. FV of the annuity-due in
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Judul: Calculation of Premium for Life Insurance and Life Annuity Policies when Interest Rates are Modeled Using Moving Average
Abstrak: Mengikuti program asuransi jiwa adalah suatu usaha yang dapat dilakukan untuk meminimumkan risiko keuangan yang diakibatkan oleh kematian. Ketika seseorang mengikuti program asuransi, orang tersebut memiliki kewajiban untuk membayar sejumlah uang yang disebut premi. Salah satu faktor penting yang menentukan besar premi yang harus dibayar adalah tingkat bunga yang digunakan. Penelitian ini bertujuan untuk membandingkan besar premi tunggal bersih beberapa polis asuransi jiwa dan anuitas hidup saat tingkat bunga dimodelkan dengan proses moving average dan saat tingkat bunga dimodelkan dengan model independent and identically distributed. Data yang digunakan adalah data tingkat bunga BI 7-day (Reverse) Repo Rate periode April 2016 sampai April 2021 dan Tabel Mortalitas Indonesia IV. Berdasarkan hasil penghitungan, premi tunggal bersih yang dihasilkan saat tingkat bunga dimodelkan dengan proses moving average lebih besar daripada saat dimodelkan dengan model independent and identically distributed., Joining a life insurance program is an effort that can be done to minimize the financial risk due to death. When someone joins an insurance program, that person must pay a certain amount of money so-called premium. One of the important factors that determine the amount of premium to be paid is the interest rate used. This study aims to compare the net single premium of several life insurance and life annuity policies when the interest rate is modeled using a moving average process and when the interest rate is modeled using an independent and identically distributed model. The data used are BI 7-day (Reverse) Repo Rate for the period April 2016 to April 2021 and the Indonesia Mortality Table IV. Based on the calculation, the net single premiums produced when the interest rate is modeled using a moving average process is higher than those when the interest rate is modeled using an independent and identically distributed model.
Keyword: interest rate, life annuity, life insurance, moving average, net single premium

Judul: Transfer DNA Bacillus licheniformis ke dalam sel Escherichia coli dengan menggunakan MgCl2 dan PEG - 6000
Abstrak: Penelitian ini mencoba mentransformasikan sifat genetik yang ada pada Bacillus licheniformis ke dalam sel Escherichia coli dengan perlakuan MgCl2 dan PEG-6000. Sifat genetik utama yang diharapkan tertransformasi adalah enzim protease pada B. licheniformis ke dalam sel E. coli yang semula tidak memiliki sifat proteolitik. Proses transformasi dimulai dengan mengisolasi DNA B. licheniformis dengan menggunakan sodium dodesil sulfat 25 persen untuk memecah dinding dan membran sel. Agar dinding sel lebih mudah pecah, sebelum penambahan sodium dodesil sulfat 25 persen dilakukan sonikasi pada frekuensi 100 kHz selama 8 10 menit. DNA diekstrak dari campuran komponen- komponen sel lainnya dengan menggunakan pelarut-pelarut organik, yaitu sodium perklorat 5M dan kloroform-isoanil alkohol (24: 1) serta sentrifusi, selanjutnya DNA digumpal- kan dengan campuran etanol 70 persen NaCl 5M (10:1). Pembentukan protoplas E. coli dilakukan dengan menggunakan enzim lisosim 10 mg/ml bufer TEN untuk memecah dinding sel dan protoplas yang diperoleh disuspensikan dalam larutan sukrosa 1M MgCl2 0.04M (1:1) untuk mencegah lisis karena tekanan osmosis. Transformasi dilakukan pada suhu kamar ...
Keyword: Transfer DNA, Bacillus licheniformis, Escherichia coli, MgCl2, PEG 6000, Struktur dan sifat umum DNA, Replikasi DNA, Isolasi DNA dari bakteri