Continuous Rate | Quantitative Methods – 21 | CFA Level 1 | FRM Part 1

In this lecture, you’ll learn:

What continuous compounding actually means
Why continuous rates are used in valuation, derivatives & risk models
How increasing compounding frequency affects returns
The role of the natural number e
How to convert continuous rate (RCC) → effective annual yield (EAY)
How to convert EAY → continuous rate using ln
Practical numerical examples comparing annual, semi-annual & continuous compounding

Class notes written on the board are available in the App under the ‘Quantitative Methods’ - ‘Time Value of Money’ chapter. Please note that the lectures are to be done as per the order of the playlist and not the textbook.
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(00:00) – Why Continuous Rates Exist
(02:10) – Annual to Daily Compounding
(04:30) – Real-Life Continuous Return Examples
(06:40) – When Compounding Frequency → Infinity
(08:30) – Mathematical Transition to Continuous Compounding
(10:30) – Introducing ‘e’ and FV = eʳ
(13:00) – RCC to EAY Conversion
(15:20) – Using ln to Convert EAY → RCC
(18:00) – Back-Calculating Continuous Rate
(20:30) – Price Relative & ln(Pn/P0)
(23:00) – Why Mugging Formulas Fails
(25:30) – Linking Continuous Rate with Geometric Mean
(28:00) – Why AM Fails & GM Works
(31:00) – Power Properties of ‘e’
(34:00) – Why Continuous Rates Are Powerful in Models
Graphs, pricing, smooth curves.
(37:00) – Discrete Rates vs Continuous Rates
(39:00) – Treating RCC Like Simple Interest
(41:30) – Mixed Returns Over Multiple Years
(44:30) – Equivalent Rates Concept
(47:00) – Example: 8% Quarterly → RCC
(49:30) – Practical Rule: What does 1 become in 1 year?
(52:00) – Common Mistakes with ln & RCC
(54:30) – Final Intuition Recap

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Faculty- Aswini Bajaj, a qualified CA, CS, CFA, FRM, CAIA, CFP, CIPM, CCRA, CIRA, CIIB, AIM, and RV. He is also a guest lecturer (across 180+ colleges and 35+ IITs and IIMs), corporate trainer, and CEO of Leveraged Growth (Research and Consulting).

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