Financial Mathematics for Actuarial Science, Lecture 1, Interest Measurement

Introduction to Time Value of Money00:00:00

Introduction to the course, the textbooks used (Broverman and Kellison), and the fundamental concept of the time value of money driven by factors like psychology, opportunity cost, and inflation.

Simple vs. Compound Interest00:03:38

Explaining the difference between simple interest (linear growth) and compound interest (exponential growth). The lecture defines key notation for compound interest, including the nominal rate and compounding frequency.

Timeline Perspective and Accumulation Functions00:12:34

Introducing the use of timelines to visualize and calculate future values by 'pushing' money forward, using the accumulation function a(t) to account for interest growth over time.

Continuous Compounding and Force of Interest00:18:37

Defining continuous compounding using the constant 'e' and introducing the 'force of interest' as the instantaneous relative rate of growth, allowing for more complex, non-constant interest rate models.

Present Value and Discount Factors00:30:14

Defining present value as the amount to be deposited now to reach a future goal. This involves the use of reciprocal functions and the discount factor (v) in compound interest scenarios.

Effective Discount Rates and Inflation00:41:43

Discussing the effective discount rate (d) and concluding with a discussion on real interest rates, explaining how inflation reduces purchasing power and why simple subtraction (I - R) is insufficient for calculating real returns.