Force of Interest and Pth Payable Interest Rates Explained Clearly. Continuous Compounding скачать в хорошем качестве

Force of Interest and Pth Payable Interest Rates Explained Clearly. Continuous Compounding

Force of Interest ,Pth Payable Interest Rates Explained Clearly. Continuous Compounding. Accumulation Factor. 0:00 Why compounding frequency matters 2:40 Annual, half-yearly, daily compounding intuition 6:10 Moving from discrete to continuous compounding 9:30 Limiting idea and emergence of e 12:40 Meaning of force of interest δ 16:00 Constant vs variable force of interest 20:30 Using e^{∫ δ(t) dt} 25:00 Practical examples with variable δ(t) 30:10 Accumulation factor concept 33:30 Continuous growth intuition using real life examples 38:40 Annuities with frequent payments 42:50 n-bar annuity and limiting behavior 47:30 Key takeaways and exam relevance In this class, you build a clear intuition for how money grows over time when interest is applied yearly, half-yearly, daily, every second, and continuously. You start with simple compounding. You then move step by step toward continuous compounding and force of interest. You learn why different compounding frequencies all converge to a single limiting expression. You see how e^δ naturally appears, not as a formula to memorize, but as a consequence of compounding more and more frequently. Key ideas covered in this session: • Growth of money using annual, half-yearly, daily, and continuous compounding • Why compounding frequency increases growth • Meaning of force of interest δ • Relationship between i, i^(p), and δ • Why 1 + i = e^δ • Intuition behind continuous growth using real life examples • Constant force of interest vs variable force of interest • Derivation and meaning of e^{∫ δ(t) dt} • Accumulation factor notation and interpretation • Connection between accumulation factor and compounding • Annuities with frequent and continuous payments • Why daily, hourly, and continuous payments give almost the same value • Meaning of n-bar annuity and limiting behavior • How actuarial formulas simplify real world cash flow problems This lecture builds the foundation required for: • Actuarial Science CM1 • Financial Mathematics • Annuities and Accumulation • Force of Interest Problems • Continuous Time Finance Models #ForceOfInterest #ContinuousCompounding #ActuarialScience #CS1 #CM1 #FinancialMathematics #Annuities #AccumulationFactor #InterestTheory #DataScienceFinance