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Financial Mathematics for Actuarial Science, Lecture 1, Interest Measurement

Begin your journey toward a career in finance or as an actuary! This lecture introduces the foundational concepts of the theory of interest: the time value of money, simple interest, compound interest, and various ways of mathematically representing compound interest. This content is essential if you want to understand annuities and bond markets. Financial Math (for Actuarial Exam FM, a.k.a. Actuary Exam 2) Course Lecture 1. TI BAII Plus Calculator: https://amzn.to/2Mmk4f6. Mathematics of Investment and Credit, 6th Edition, by Samuel Broverman: https://amzn.to/2s9SZEQ. Amazon Prime Student 6-Month Trial: https://amzn.to/3iUKwdP. (0:00) Introduction and textbook. (1:48) The time value of money (most people would prefer $1 right now than one year from now). (3:35) Simple interest and compound interest formulas, both for the interest earned and the accumulated amount (future value). (4:52) Linear growth versus exponential growth. Linear growth has a constant rate of change: the slope is constant and the graph is straight. Exponential growth has a constant relative rate of change (percent rate of change). Mathematica animation. (8:27) Actuarial notation for compound interest, based on the nominal interest rate compounded a certain number of times per year. (11:38) The graph of the accumulation function a(t) is technically constant, because banks typically make discrete payments of interest. (12:34) It's very important to make timelines to help you solve problems (time diagrams). (15:46) Relating equivalent rates (when compounding occurs at different frequencies) and the effective annual interest rate. (18:37) Continuously compounded interest and the force of interest, which measures the constant instantaneous relative rate of change. Given the force of interest, you can also recover the amount function a(t) by integration. (26:04) An odd-ball example where the force of interest is sinusoidal with a period of 1. (30:08) Present value basic idea: how much should you deposit now to grow to A after t years? (32:48) Present value discount factor. For a constant value of i, it is v = 1/(1+i) = (1+i)^(-1). Example when i = 0.10. Also think about timelines and pulling amounts back in time. (37:43) Present value for a varying force of interest and the odd-ball example. (41:40) The present value discount rate d = i/(1+i) = 1 - v (percent rate of growth relative to the ending amount). Bond rates are often sold at a discount. Other relationships worth knowing. The ID equation i - d = id. (45:30) Equivalent ways of representing the accumulation function a(t) and its reciprocal. (46:45) Inflation and the real interest rate. The real rate is (i - r)/(i + r). Overall Video Topic: Financial Quantities Representing Growth and Decay (especially exponential). Check out my blog: https://infinityisreallybig.com/ Playlist of Chapter 1 Problem Solving Videos (6th edition of Broverman):    • Actuarial Exam FM/2 Prep: Use an Equa...   Playlist of All Problem Solving Videos for Financial Math:    • Actuarial Exam FM/2 Prep: Use an Equa...   Bill Kinney, Professor of Mathematics at Bethel University in St. Paul, MN. Bill Kinney Math. AMAZON ASSOCIATE As an Amazon Associate I earn from qualifying purchases.