Compound Interest Research Articles

Modification of Adomian decomposition technique in multiplicative calculus and application for nonlinear equations

Multiplicative calculus is a mathematical system that offers an alternative to traditional calculus. Instead of using addition and subtraction to measure change, as in traditional calculus, it uses multiplication and division. The framework of nonlinear equations is an incredibly powerful tool that has proven invaluable in advancing our understanding of various phenomena across a wide range of applied sciences. This framework has enabled researchers to gain deeper insights into a vast array of scientific problems. The physical interpretation of iterative methods for nonlinear equations using multiplicative calculus offers a unique perspective on solving such equations and opens up potential applications across various scientific disciplines. Multiplicative calculus naturally aligns with processes characterized by exponential growth or decay. In many physical, biological, and economic systems, quantities change in a manner proportional to their current state. Multiplicative calculus models these processes more accurately than traditional additive approaches. For example, population growth, radioactive decay, and compound interest are all better described multiplicatively. The primary objective of this work is to modify and implement the Adomian decomposition method within the multiplicative calculus framework and to develop an effective class of multiplicative numerical algorithms for obtaining the best approximation of the solution of nonlinear equations. We build up the convergence criteria of the multiplicative iterative methods. To demonstrate the application and effectiveness of these new recurrence relations, we consider some numerical examples. Comparison of the multiplicative iterative methods with the similar ordinary existing methods is presented. Graphical comparison is also provided by plotting log of residuals. The purpose in constructing new algorithms is to show the implementation and effectiveness of multiplicative calculus.

Analysis of Student Errors in Solving Word Problems using Polya Steps

This research was motivated by the many difficulties experienced by students in the mathematics learning process which had an impact on the occurrence of errors in working on mathematics story problems. These errors need to be known so that it is easier to find solutions so that these errors can be minimized. This research aims to determine the types and causes of errors made by students in solving mathematics story problems on single interest and compound interest materials using Polya's steps. This research method is qualitative with descriptive research type. The research subjects consisted of 2 students from 13 class XI TKP SMKN 1 Pariaman students, with the criteria being 1 student each from the medium group and 1 student from the low group. Data collection techniques include tests and interviews. The results of the research show that the percentage of errors made by students in solving mathematics story problems on single interest and compound interest material using Polya steps is: in question number 1, the biggest error made in the step of understanding the problem was 23.08%. Question number 2, the biggest error made during the rechecking step was 15.38%. In question number 3, the biggest mistake made in the step of understanding the problem was 19.23%. The factors that cause students to make mistakes include, not being used to writing information on questions using their own words, not writing down what they know and what is asked in the question correctly, not focusing when working on questions, not being careful in carrying out the calculation process, not being used to checking again, and rushing through the settlement process.

Optimized Decentralized Reward Distribution(1)

In DeFi (Decentralized Finance) applications, and in dApps (Decentralized Application) generally, it is common to periodically pay interest to users as an incentive, or periodically collect a penalty from them as a deterrent. If we view the penalty as a negative reward, both the interest and penalty problems come down to the problem of distributing rewards. Reward distribution is quite accomplishable in financial management where general computers are used, but on a blockchain, where computational resources are inherently expensive and the amount of computation per transaction is absolutely limited with a predefined, uniform quota, not only do the system administrators have to pay heavy gas fees if they handle rewards of many users one by one, but the transaction may also be terminated on the way. The computational quota makes it impossible to guarantee processing an unknown number of users. We propose novel algorithms that solve Simple Interest, Simple Burn, Compound Interest, and Compound Burn tasks, which are typical components of DeFi applications. If we put numerical errors aside, these algorithms realize accurate distribution of rewards to an unknown number of users with no approximation, while adhering to the computational quota per transaction. For those who might already be using similar algorithms, we prove the algorithms rigorously so that they can be transparently presented to users. We also introduce reusable concepts and notations in decentralized reasoning, and demonstrate how they can be efficiently used. We demonstrate, through simulated tests spanning over 128 simulated years, that the numerical errors do not grow to a dangerous level.

Implementasi Model Pembelajaran Problem Based Learning (PBL) Berbantuan Lembar Aktivitas Siswa (LAS) Untuk Meningkatkan Kemampuan Siswa Dalam Memecahkan Masalah Matematika

This article discusses the implementation and results of implementing the Problem-Based Learning Model (PBL) using Student Activity Sheets (LAS) to evaluate the development of mathematical problem-solving abilities of class X MPLB 1 students at SMK N 2 Semarang on the topic of single interest and compound interest. Class X MPLB 1, consisting of 36 students, is the focus of this research. The research method was carried out in two cycles, where each cycle consisted of two meetings. The data collected comes from observations and tests, which are then analyzed using descriptive techniques. The research results showed that there was a significant increase in problem-solving abilities from cycle I to cycle II. Initially, the average problem-solving ability was 67.78, which then increased to 75 in cycle I and continued to increase to 88 in cycle II.

Classical Study of Real Life Applications of Exponential Function

One of the most prevalent applications of exponential function involves growth and decay modes. Exponential growth and decay show up in a host of applications. From population growth and continuously compounded interest to radioactive decay and Newton’s law of cooling exponential function are ubiquities in nature. In this section, we examine exponential growth and decay in the context of some of the application. In the preceding section, we examined a population growth problem in which the population grew at a fixed percentage each year. In that case, we found that the populations can be described by an exponential function. A similar analysis will show that any process in which a quality grows by a fixed percentage each year (or each day, hours, etc) can be modeled by an exponential function. Compound interest is a good example of such a process. Other applications of exponential function are bacterial growth, bacterial decay, population decline are obtained in this project (see [1-27])

Piqued: Compounded Interest and the Intersubjective Scene

In conversation with Silvan Tomkins, William James, Sianne Ngai, and others, “Piqued: Compounded Interest and the Intersubjective Scene” further theorizes one of the most taken-for-granted of the classic affects: interest. This essay argues that the piquing of interest is essential for projection, attachment, or resentment, even, to follow. Interest not only compounds, or accumulates with itself, sometimes sharpening or transforming into those more intense affects that we tend to associate with driving forces. It also acts combinatorially, as an elemental ingredient of all affects. Because of interest’s fundamental role in initiating momentum, combining with other affects, switching registers—in transmissible, communal, or mediated forms—it is worth confronting interest’s ubiquity to better understand how it, once provoked, functions culturally. To better demonstrate interest as a foundational, compounding affect in coexperienced dynamics and their representations, the author unpacks scenes of intersubjectivity in the television series Killing Eve (bbc America, 2018–22).

Study and Analysis of Some Real Life Applications of Exponential Function Based on Population Growth Rate of Nepal

This research investigates various real-world applications of exponential functions that are present in a country or region. Our goal was to gain an understanding of the exponential function. The exponential function is most commonly used in the growth and decay model. An introduction to the exponential function opens the project. We have got some real-world applications of the exponential function in this project, including: a. population growth: b. compound interest; c. bacterial proliferation; d. an increase in internet users; and so on. This work is motivated by the works of [1-13].

Investing in Rural Agriculture in the Face of Innovative Financial Services: Does Financial Literacy Matter in Nigeria?

The complex nature of formal financial products and services and the frequently associated innovations occasioned by disruptive technologies inform researchers’ calls for studies on financial literacy, particularly in African rural communities. As a response to the calls, this study explores how financial literacy relates to performance, access to credit facilities, and payment preferences among smallholder rural farmers in Nigeria. Further, the rural farmers’ financial literacy level on each of the four dimensions of the Standard and Poor Global Financial Literacy criteria was assessed. A random sample was drawn from the registered rural farmers in the Central Bank of Nigeria’s Anchored Borrower’s Program for the 2022 farming year. Quantitative data were collected from rural farmers using the Standard and Poor Global Financial Literacy questionnaire. The proposed hypotheses were tested with partial least squares structural equation modeling (PLS-SEM), while descriptive statistics were used to analyze the data. The outcomes show that financial literacy significantly predicts performance, access to credit facilities, and mode of payment preferences among smallholder rural farmers. Also, the analyses of the four dimensions of financial literacy show that the farmers are more literate in risk diversification and inflation than numeracy and compound interest. It is concluded that financial literacy is cardinal to profitable investments in rural farming, and as such, there is a need for the Nigerian government and financial authorities to embark on financial literacy drive with more emphasis on numeracy and compound interest where the rural farmers are more deficient.

Pedagogical potential of competence tasks as a means of developing critical thinking of future economists

Purpose. The purpose of the article is to present the means of training future economists for analytical professional activity, which contributes to the development of critical thinking of specialists in economic specialties. Results. The article is devoted to one of the urgent problems of training future bachelors in economics: developing critical thinking in the professional training of economists. We prove that competency-based tasks of economic content are an essential means of developing the critical thinking of future economics specialists. The main competence tasks with economic content include problems with labor productivity, cost, elasticity, rent, interest, compound interest, profitability, market equilibrium, profit, income taxes, credit, optimal decision-making, etc. The competence tasks bind economic concepts with their quantitative and qualitative characteristics and connections. These tasks reflect real economic situations, and solving them contributes to the familiarisation of students with economic concepts and cause-and-effect relationships between them (at the level of representation, assimilation, or consolidation), mathematical models in the economy, development of skills to build and research mathematical models of economic situations, apply mathematical methods and regularities in specific production processes. Scientific novelty. The theory and practice of training economists, which uses competence tasks of economic content as a leading means of developing their critical thinking, has gained further development. The results of the survey of teachers and students confirmed the feasibility of the proposed approach to the use of competence tasks with economic content for the development of critical thinking of future economists. Practical value. Solving competence tasks contributes to developing students’ critical thinking, as it illustrates the process of applying knowledge, skills, and abilities to solving any problems that arise in practice (formalisation, solving a problem within a built model, interpretation). It is advisable to offer such tasks in studying specialised economic disciplines and the first courses in studying “Higher Mathematics”.

Study and Analysis of Some Real Life Applications of Exponential Function

The exponential function as a mathematical concept plays an important role in the Corpus of mathematical knowledge, but unfortunately Students have problems grasping it. Paper exposes examples of exponential function application in a real-world (life).One of the most prevalent applications of exponential functions Involves growth and decay models. Exponential growth and decay show up in a host of natural applications. From population growth and continuously compounded Interest to radioactive decay and Newton's law of cooling, exponential functions are ubiquitous in nature. In this section, we examine exponential grown and decay in the context of some of the applications. In the preceding section, we examined a population growth problem in which the population grew at a fixed percentage each year. In that case, we found that the population can be described by an exponential function. A similar analysis will show that any process in which a quantity grows by a fixed percentage each year (or each day, hour etc.) can be modeled by an exponential function. Compound Interest is a good example of such a process. Other applications of exponential function are bacterial growth, bacterial decay, population decline, are obtained in this project.

Mathematical structures of simple and compound interest: An analysis of secondary teachers’ relational thinking

Mathematical structures of simple and compound interest: An analysis of secondary teachers’ relational thinking

Multiple Contracts with Simple Interest: The Case of SACRE-F

In a previous paper de Faro and Lachtermacher (2023), considering a particular version of the so-called System of Increasing Amortization in Real Terms, SACRE-F, in the case of compound interest, was shown that if a single contract is substituted by multiple contracts, one for each payment of the single contract, the financing institution may derive substantial fiscal gains. In terms of the present value of the corresponding income taxes.
 Notwithstanding, the Brazilian Jurisprudence, cf. Jusbrasil (2023), has repeatedly determined that the use of compound interest implies the occurrence of anatocism. The payment of interest on interest. Mari & Aretusi (2019) reported the same kind of determination by the Italian justice.
 Therefore, the analysis should also consider the hypothesis of the use of simple interest. SACRE-F, in the case of simple interest has shown that if a single contract is substituted by multiple contracts, one for each payment of the single contract, the financing institution may derive substantial fiscal gains, as in the compound interest case.

On Computing General Root Algorithms Based on Binomial Expansion, Bernoulli’s Method of Continuous Compound Interest, Series Expansion and Other Modification Methods

Most of the Pth root algorithms exhibit high latency or small convergence rates when iteratively computing the roots. Here we present a slew of algorithms based on series expansions of binomial form, and exponential terms that show low latency or small computational cost for finding the Pth root. The latency decreases if the family of series taken are truncated at higher terms. We show that Babylonian method converges quadratically while the binomial series show an increase in convergence rate from quadratic, cubic and higher order O(t^N) convergence rate as the series is sequentially truncated at higher order terms.

Application of the Compound Interest Model in Analyzing Long-Term Investments on Nvdia Company Stock

Long-term investment is a strategic decision that requires careful planning and in-depth analysis. One approach to analyze the potential returns from long-term investments is through the application of the compound interest model. This model considers the accumulation of interest on both the principal amount and the previously earned interest, providing a more realistic picture of investment growth over time.This research aims to explore how the application of the compound interest model can enhance the analysis of long-term investments. The analysis of these variables provides a comprehensive picture of the dynamics of investment growth and opens up opportunities for more informed investment decision-making. This research emphasizes the importance of a thorough understanding of the key variables in the compound interest model to enhance the accuracy of investment decisions.The findings of this research are expected to offer practical guidance for investors and financial practitioners in managing their portfolios more intelligently and measurably. These findings make a significant contribution to the development of more effective long-term investment strategies, thereby enhancing portfolio performance and overall investment outcomes.

Interaction of a Triruthenium ortho-Metallated Phenazine with Cytochrome P450 Enzymes

The triruthenium ortho-metallated phenazine [Ru3O(CH3COO)5(py)2(dppzCl)]PF6 (1, py = pyridine; dppz-Cl = 7-chlorodipyrido[3,2-a:2’,3’-c]phenazine) is a potential metallo-drug candidate with in vitro anticancer and trypanosomicidal activities. It also showed strong interactions with deoxyribonucleic acid (DNA) and human serum albumin due to the presence of the planar and π-conjugated phenazine in its structure. Pursuing our interest in compound 1 behavior in a biological environment, we described its interaction with the cytochrome P450 (CYP450) enzymes present in human liver microsomes through a preliminary in vitro metabolism assay. This study showed that the human liver microsomes metabolized compound 1 in a concentration dependent manner. A phenotyping study suggests that CYP3A is the primary enzyme involved in the interaction, even though other isoforms metabolized 1 in a minor extent. It is worth mentioning that the results of phenotyping using supersomes should be interpreted cautiously, taking into account the inhibitory effect of the surfactant employed. Blind molecular docking results agreed with the experimental trend, showing the highest interactive profile with the isoforms CYP3A4 and 3A5, and suggested hydrophobic, π-stacking, and hydrogen bonds as the primary intermolecular forces responsible for the protein-compound interaction.

Multiple Contracts: The Case of the German System of Amortization in Compound Interest

Multiple Contracts: The Case of the German System of Amortization in Compound Interest

Exploring Exponential Functions Using Geogebra

Exponential functions, symbolized by the expression f(x)=ax, are a fundamental mathematical concept widely applicable to real-world scenarios such as population growth, compound interest, and radioactive decay. This abstract underscores the significance of exponential functions and highlights GeoGebra's crucial role in interactive visualization and analysis as an intuitive mathematical software. This study utilizes GeoGebra's dynamic interface to explore and comprehend exponential functions, bridging the gap between theoretical concepts and practical applications. It includes a comparative analysis between classical methods and GeoGebra solutions for exponential functions. The software's ability to validate mathematical outcomes through visual confirmation is explored, emphasizing its role in not only enhancing understanding but also providing a reliable means of verification. GeoGebra and mathematical analysis illustrations consistently yield results through practical examples, demonstrating the software's effectiveness in fostering a deeper understanding of exponential growth. In addition, surveys was conducted and engaged in direct comparison of solutions with students in the classroom setting to observe firsthand how learners interact with the material and identify common mistakes made during problem-solving. The survey results informed the development and refinement of the approach, ensuring a comprehensive understanding of both the benefits and challenges associated with learning exponential functions through GeoGebra.

МЕТОДИЧНІ ТА ПРАКТИЧНІ АСПЕКТИ КРЕДИТНОЇ ПІДТРИМКИ ОНОВЛЕННЯ ОСНОВНИХ ЗАСОБІВ ПРОМИСЛОВИХ ПІДПРИЄМСТВ

Purpose. In market conditions of business, the competitiveness of enterprises is largely determined by the condition of their fixed assets. The need to replace outdated technologies and equipment with modern ones requires the availability of appropriate financial resources. Inadequacy of own internal sources of investment for the renewal of fixed assets encourages enterprises to widely use external, in particular, credit. At present, in the economic theory and practice of management, there is no clearly developed mechanism for investing in the renewal of fixed assets with the involvement of credit resources. Inadequate development of such issues as the choice of a profitable loan option, the optimal loan rate, the terms and conditions of loan repayment, calls for the development of methodical and practical approaches to effective investment in the renewal of the fixed assets of enterprises. Design/methodology/approach. The article uses the discounting method and the balance sheet method for calculating and analyzing the parameters of the process of attracting credit resources. The method of economic-mathematical modeling was used to study the influence of the use of borrowed funds in investing in the renewal of fixed assets on the pace of development of production potential. Findings. The article considers a number of problems of a methodological and practical nature regarding investment support for the renewal of fixed assets of enterprises, in particular with the involvement of credit resources. The parameters of the loan attraction process, which determine its effectiveness for the enterprise, are analyzed. The most important of these parameters include: the term of the loan; interest rate for the loan; loan payment amounts. To determine the size of the payment for the loan, the appropriate ratio based on the use of compound interest was considered. Derived dependencies for calculating the annual payment for the loan, the annual payment from one monetary unit of the loan, as well as the total amount of funds that must be paid for the entire period of the loan. The values of these parameters are calculated depending on the value of the credit rate and the credit term, which makes it possible to quantitatively assess their trends. The results of the calculations are presented in tabular form. The impact of attracting credit funds in investments for the renewal of fixed assets was studied by modeling this process. An approach to determining the marginal interest rate at which it is still profitable for the enterprise to attract loan funds is proposed. For this purpose, appropriate computer calculations were carried out. Calculations were carried out for the option of fixed assets renewal with own funds, as well as with the involvement of a loan at various interest rates. An important conclusion was made that the dynamics of production development depends on the relationship between the interest rate and the growth rate of capital investments in the basic version, when production development is carried out only at the expense of own investment funds. Practical implications. The methodical and practical results obtained in the research process can be used in the selection of credit support options for the renewal of fixed assets and the development of specific measures aimed at improving the investment activity of industrial enterprises. Originality/value. The article quantitatively evaluates the parameters of credit support for the fixed assets renewal of enterprises. By means of economic-mathematical modeling, the impact of attracting loan funds on the dynamics of changes in the production potential of the enterprise was analyzed.

The assessment of integrative potential of simple and compound interest models in increasing students’ financial literacy

Introduction. The article studies the contradiction between the unprecedented surge in financial technologies, which determines the relevance of financial decision-making, and the lack of the educational process organization in an economic university that takes into account the cumulative effect of using formalized models of simple and compound interests in terms of integrating academic disciplines. The objectives of the study are (1) to identify opportunities to increase students’ financial literacy using the integrative potential of academic disciplines and (2) to assess the relationship between skills in applying formalized methods of financial decision-making based on the models of simple and compound interests, and the dynamics of financial literacy that contributes to positive financial behaviors. Materials and Methods. The methodological basis of the study is the Pareto principle, or the 20/80 rule, which says that 20 % of efforts give 80 % of the result and vice versa. Financial literacy of 224 students of Omsk economic universities was evaluated by means of an online survey. The questions reflected the objective level of respondents’ financial literacy, the subjective level and the need for further knowledge and skills in financial literacy. Results. The study has identified the possibilities of increasing students’ financial literacy by using formalized models of simple and compound interests in terms of integrating academic disciplines. The results of the analysis confirm that a higher level of financial literacy correlates to skills in applying simple and compound interest models and reveal a positive dynamics of the cumulative effect of integrating academic disciplines. The use of the Pareto principle in this study confirms that skills in applying formalized models of simple and compound interests, which account for about 20 % of financial literacy (in terms of attitudes, knowledge and skills), determine 80 % of the positive dynamics in the overall financial literacy level. Based on the findings, recommendations for managing educational process in order to ensure the positive dynamics of digital financial literacy have been provided. Conclusions. The study suggests that it is a promising idea to use the integrative potential of simple and compound interest models in increasing financial literacy that contributes to positive financial behaviors of economic university graduates.

Мониторинг динамики финансовой грамотности студентов в условиях интеграции учебных дисциплин

The article is devoted to the problem of the formation of financial literacy of students of economic universities in the context of the integration of academic disciplines. The aim of the work is to identify the possibilities of integrative links between academic disciplines in improving the level of financial literacy within the framework of the continuity of educational programs for undergraduate and graduate programs. As a means of integration, it is proposed to use the models of simple and compound percent. The importance of formalized models in the performance of financial operations of accumulation, discounting and, accordingly, in assessing the effectiveness of financial decision-making is noted. The paper presents the results of monitoring the dynamics of the level of financial literacy of students of the University of Economics. An online survey of undergraduate students was conducted in the context of courses of study and undergraduates. Respondents were asked questions related to identifying the objective level of financial literacy (knowledge of financial terms, activity in the financial services market, knowledge of simple and compound interest formulas, etc.). A separate block includes questions about the subjective level of financial literacy of respondents and the need for additional knowledge and skills in financial literacy. he results of the analysis of empirical material indicate a positive correlation between the objective and subjective levels of financial literacy of students, as well as the need for additional knowledge on financial literacy. At the same time, higher levels of financial literacy are associated with skills in mastering simple and compound interest models and demonstrate a positive trend in the cumulative effect of integrating academic disciplines. In its turn, the study of student activity in the financial services market determines the widespread use of digital financial instruments. The findings determine the need for students of economic universities to master formalized methods for assessing financial decision-making, which in the future will allow avoiding costly mistakes in practice and maintaining the required level of digital financial literacy.