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: Penentuan Premi Tahunan Berjangka pada Reversionary Annuity dengan Tingkat Bunga Mengikuti Model Vasicek
Abstrak: Salah satu produk anuitas multiple life adalah reversionary annuity, yaitu pembayaran santunan akan diberikan kepada ahli waris saat salah satu peserta asuransi meninggal. Perusahaan asuransi sebagai penyedia asuransi memiliki kewajiban untuk menetapkan harga premi yang optimal. Salah satu faktor yang mempengaruhi premi adalah suku bunga. Perubahan tingkat bunga dapat dimodelkan dengan suku bunga stokastik, yaitu model Vasicek. Pada penelitian ini, ditentukan premi tahunan berjangka untuk kasus reversionary annuity menggunakan tingkat bunga konstan dan model Vasicek. Pendugaan parameter model Vasicek menggunakan metode ordinary least square. Data yang digunakan untuk peramalan suku bunga adalah rata-rata per tahun BI 7-day (Reverse) Repo Rate periode April 2016 sampai Maret 2023. Model Vasicek digunakan untuk membangkitkan suku bunga yang baru untuk sepuluh tahun mendatang yang selanjutnya digunakan untuk menghitung premi bersih tahunan berjangka. Hasil perhitungan premi dengan suku bunga konstan secara umum lebih tinggi dibandingkan hasil perhitungan premi dengan suku bunga model Vasicek untuk semua kasus penerima manfaat., One of the multiple life annuity products is reversionary annuity, which is a compensation payment that will be given to the heirs when one of the insurance participants dies. Insurance companies as insurance providers have an obligation to set optimal premium prices. One of the factors that affect the premium is the interest rate. Changes in interest rates can be modeled using stochastic interest rates, namely the Vasicek model. In this study, the term annual premium was determined for the case of reversionary annuity using a constant interest rate and the Vasicek model. The parameter estimation of the Vasicek model uses the ordinary least squares method. The data used for forecasting interest rates is the BI 7-day (Reverse) Repo Rate average per year from April 2016 to March 2023. The Vasicek model is used to generate a new interest rate for the next ten years which is then used to calculate the annual futures net premium. The result of premium calculation with a constant interest rate is generally higher than that of premium calculation with the Vasicek model interest rate for all beneficiary cases.
Keyword: insurance, premium, interest rate, Vasicek model, reversionary annuity

Judul: Telaah pengklonan gen protease dari Bacillus stearo thermophilus ke dalam Escherichia coli
Abstrak: Fragmen-fragmen genom dari Bacillus stearothermophilus, yang dipotong secara parsial dengan Eco RI atau HindIII, telah diklon dalam Escherichia coli dengan teknik shot gun cloning menggunakan plasmid pRK415 sebagai vektornya untuk gen protease. Media agar MacConkey (Jennings dan Beacham, 1989) dengan sedikit modifikasi dipakai untuk deteksi koloni pembawa plasmid rekombinan atau plasmid nonrekombinan. Media tersebut terdiri dari 10 g tripton, 5 g ekstrak kha­ mir, 10 g laktose, 0.075 g neutral red, 15 g agar dalam 1 L dH20, pH diatur pada 7 .4. Untuk deteksi ekspresi gen protease, media tersebut ditambahkan 2 % susu skim. Media ini dinamakan SMMCA (skim milk modified MacConkey agar). Penghilangan kristal violet, garam empedu dan garam memberikan hasil yang baik untuk deteksi koloni-koloni tersebut. Sel koinpeten untuk keperluan pengklonan disiapkan dengan metode miniprep, sesuai prosedur Lederberg dan Cohen (1974) dengan sedikit modifikasi, dilakukan dengan cara mensentrifusi 1.5 mL kultur fase log dalam tabung mikro setelah sebe­lumnya diinkubasikan selama 30 menit pada 0°C. Pelet sel dicuci dengan 1 mL 0.1 M CaC12 dingin, kemudian sel disuspensikan dalam 0.5 mL 0.1 M CaC12 dingin dan diinkubasikan pada 0°C selama 20 menit, sentrifusi terakhir dilakukan dan pelet sel disuspensikan dalam 0.2 mL 0.1 M CaC12 dingin, pada kondisi ini sel siap digu­ nakan untuk transformasi. Isolasi DNA kromosom dengan metode Marmur (1961) mendapatkan DNA dengan kualitas yang cukup baik, dan dapat dipakai untuk keperluan kloning, walauiv pun dilakukan tidak sampai pada tahap pemurnian lanjutan seperti penghilangan RNA dan pemekatan. Dari 500 mL kultur fase log diperoleh lebih kurang 2 mg DNA kromosom. ...
Keyword: Escherichiacoli, Proteinase