Wize University Introduction to Finance Textbook > Time Value of Money
Effective Rates with Continuous Compounding
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Continuous Compounding
Continuous compounding is the mathematical limit that compound interest can reach if it's calculated and reinvested into an account's balance over a theoretically infinite number of periods. While this is not possible in practice, the concept of continuously compounded interest is important in finance.
Where:
Periodicity desired expressed in years (monthly = 1/12, weekly = 1/52, etc)
The base of the natural log (2.71828...)
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Example: Continuous Compounding
A savings account advertised on Facebook caught your eye because it claims to offer a savings rate of APR 5.2% compounded continuously. Your current account is paying you an effective annual rate of 5.3%, should you switch your savings to the new account?
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Practice: Continuous Compounding
You borrowed money from your friend's uncle Rocco. The money was lent under the terms 6% APR compounded continuously, and you intend on making monthly payments over the next few years to pay it off.
What is the interest rate required to compute the payment on your loan?