• Skip to primary navigation
  • Skip to main content
  • Skip to primary sidebar
  • Skip to footer
Finance Train

Finance Train

High Quality tutorials for finance, risk, data science

  • Home
  • Data Science
  • CFA® Exam
  • PRM Exam
  • Tutorials
  • Careers
  • Products
  • Login

Continuous and Discrete Compounding

PRM Exam, PRM Exam I

This lesson is part 2 of 3 in the course Interest Rates and Time Value

When you invest a dollar today, you expect to receive more than a dollar after a period of time. The additional amount earned on your investment is the time value of money and is calculated based on the interest rate.

There are primarily two ways of calculating interest:

1. Discrete (Includes simple and compound interest)
2. Continuous compounding

Let us look at each of the above methods in detail:

Discrete compounding

Simple Interest: Simple interest is interest paid only on the “principal” or the amount originally borrowed, and not on the interest owed on the loan.

For example, the simple interest due at the end of three years on a loan of $100 at a 5% annual interest rate is $15 (5% of $100, or $5, for each of the three years). No interest is calculated in the second year on the $5 interest that was due after the first year, and no interest is calculated in the third year on the interest that was due after two years.

The future value (FV) using simple interest is calculated using the following formula:

FV = P (1+rt)

Where:
P is the principal
r is the interest rate
t is the time period

Compound interest: Compound interest is interest calculated, not only on the principal, or the amount originally borrowed, but also on the interest that has accrued, or built up, at the time of the calculation.

Here’s how the amount owed on a three-year loan at an interest rate of 5% would differ, depending on whether simple interest or compound interest was charged:

Simple Interest Compound Interest
Amount of Loan $100 $100
Amount Owed After One Year 105 105
Amount Owed After Two Years 110 110.25 ($105 plus 5% of $105)
Amount Owed After Three Years 115 115.7625 $110.25 plus 5% of $110.25)

The future value (FV) using compound interest is calculated using the following formula:

FV = P (1+r)^n

Where:
P is the principal
r is the interest rate
t is the number of periods

Instead of yearly interest calculations, the compounding can also be at more frequent intervals, for example, semi-annually, quarterly, or monthly. In such a situation, the future value is calculated as follows:

FV = P (1+r/m)^mt

Where:
P is the principal
r is the interest rate
t is the term of the loan or investment in years
m is the number of compounding periods in a year.

Let us take the same example above but this time let’s assume that the interest is compounded quarterly instead of annually. The future value of the principal will be:

FV = $100 (1+5%/4)^(4*3) = 116.0755

Continuous compounding

In case of continuous compounding, the interest is compounded continuously. This means that the time periods for compounding are so small that they literally equal zero.

The future value of the principal with continuous compounding is given as follows:

FV = P*e^(rt)

In our example, the future value using continuous compounding will be:

FV = $100*exp(5%*3) = 116.1834

In practice, no one compounds interest continuously but it is used extensively for pricing options, forwards and other derivatives.

Previous Lesson

‹ Interest Rates and Time Value

Next Lesson

›

Join Our Facebook Group - Finance, Risk and Data Science

Posts You May Like

How to Improve your Financial Health

CFA® Exam Overview and Guidelines (Updated for 2021)

Changing Themes (Look and Feel) in ggplot2 in R

Coordinates in ggplot2 in R

Facets for ggplot2 Charts in R (Faceting Layer)

Reader Interactions

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Primary Sidebar

In this Course

  • Interest Rates and Time Value
  • Continuous and Discrete Compounding

Latest Tutorials

    • Data Visualization with R
    • Derivatives with R
    • Machine Learning in Finance Using Python
    • Credit Risk Modelling in R
    • Quantitative Trading Strategies in R
    • Financial Time Series Analysis in R
    • VaR Mapping
    • Option Valuation
    • Financial Reporting Standards
    • Fraud
Facebook Group

Membership

Unlock full access to Finance Train and see the entire library of member-only content and resources.

Subscribe

Footer

Recent Posts

  • How to Improve your Financial Health
  • CFA® Exam Overview and Guidelines (Updated for 2021)
  • Changing Themes (Look and Feel) in ggplot2 in R
  • Coordinates in ggplot2 in R
  • Facets for ggplot2 Charts in R (Faceting Layer)

Products

  • Level I Authority for CFA® Exam
  • CFA Level I Practice Questions
  • CFA Level I Mock Exam
  • Level II Question Bank for CFA® Exam
  • PRM Exam 1 Practice Question Bank
  • All Products

Quick Links

  • Privacy Policy
  • Contact Us

CFA Institute does not endorse, promote or warrant the accuracy or quality of Finance Train. CFA® and Chartered Financial Analyst® are registered trademarks owned by CFA Institute.

Copyright © 2021 Finance Train. All rights reserved.

  • About Us
  • Privacy Policy
  • Contact Us