Continuous Compounding

Personalized homework help to elevate your understanding and boost your grades. Dive into a world where learning becomes easy, and complex topics transform into simple solutions.
  • ο‡š24/7 Assistance
  • ξ€³Expert Tutors
  • ο‚‘Guaranteed Results

The concept of continuously compounded interest rate can be explained by taking an example:

Say, an investment of $100 today is giving a return of $120 in the next year. So, the rate of return is 20%. If the interest is paid twice every year, and the rate of interest remains constant, and the amount earned at the end of the year is $120, the rate of interest can be given as:

Continuous Compounding 38

If the semi-annual interest rate is multiplied by 2, r becomes 19.08%. If you receive interest 12 times a year, then the rate of interest will be:

Continuous Compounding 39

If we multiply the monthly rate of interest by 12, r becomes 18.36%. Now, if you receive interest 365 times in a year, then the rate of interest will be:

Continuous Compounding 40

Multiply this daily rate of interest by 365 and r will be 18.25%.

The continuously compounded interest rate can be calculated by taking natural logarithm of 1 plus the simple rate of interest.

Continuous Compounding 41

Similarly, the simple rate of interest can also be calculated from the above formula:

Continuous Compounding 42

Continuously compounded interests can be added. These interest rates are symmetric. The range of continuously compounded interest rate lie between -∞ to +∞. Compounded interest rates are used in Black-Scholes option formula.


  1. Calculate the continuously compounded interest rate if a bond pays $150 for every investment of $100.
  2. If a bond pays an interest rate of 10% compounded continuously, the money received after maturity is reinvested 20% interest rate, which is also compounded continuously. What will the value of a present day investment of $100? Calculate the simple and continuously compounded rate of interest over the two periods.


Links of Previous Main Topic:-

Links of NextΒ Financial Accounting Topics:-

Download Our Solved Homework Solutions πŸ“š

Curious about the level of quality we deliver? Navigate through our carefully curated selection of solved assignments, neatly organized by subject and level. This is a great way to get a feel for our service before you submit your own assignments.

Go ahead, download, review, and let us help you excel! πŸš€

Accounting Homework

Corporate Accounting Sample

Biology Homework

Genetics Assignment Sample

Essay Writing Help

Business Plan Homework Sample

Statistics Homework

SPSS Assignment Sample

Score High with Our Experts

At MyHomeworkHelp, our experts are alumni from world-class universities and colleges. Each candidate undergoes a stringent check of their academic prowess and professional history before joining us as expert.

Hear It From Our Students

Real stories from students who’ve experienced our high-quality assistance. Discover how we’ve helped them excel!

Got Questions? We’ve Got Answers

How do I submit my homework?
Click on the "Get Help NowπŸš€" button at the top of our website. Fill in the required details about your assignment and our team will get back to you within 15 minutes with a free quote.
Is there a guarantee on the quality of work?
Absolutely! We ensure top-quality assistance. If you're unsatisfied with the results, we offer revisions and a money-back guarantee based on certain conditions.
How quickly can I expect my completed assignment?
Our experts work diligently to meet your deadlines. Depending on the complexity, we usually deliver assignments within the stipulated time mentioned in the quote.
Who are the experts assisting me?
Our team comprises professionals with academic expertise in various fields. Each expert is thoroughly vetted and has a track record of delivering excellence.
What if I need revisions?
Your satisfaction is our priority. If you need any revisions, contact us with the specific changes, and our experts will address them promptly.
How do you ensure the privacy of my information?
We take privacy seriously. All your data is encrypted and we follow strict confidentiality protocols. Your personal and assignment details will never be shared with third parties.