Before we have the technology we have right now in this modern time, computations and calculations were done manually. Then, banks would result in using the compound interest formula manually in compounding interest. This results in compound interest only four times a year. This process is so hassle that banks would have a day only for computing the interest and staffs had to work overtime. Today, we can do compound interest formula continuously with ease.

Four times a year, staffs from banks go home later to finish computing the interest that is compounded. If you had a savings account before there were computers, your savings would increase only four times a year. It would have the compound interest formula of (1 + r/4)4 with r as the interest rate and 4 as the number of times the interest is compounded. Today, banks are capable of using the compound interest formula continuously. It can compound the interest whenever or whatever the banks term is. Using the compound interest formula continuously is now more commonly used in banks and even in loans.

Using the Compound Interest Formula Continuously, Banks Today Can Compound Interest Every Month, Every Week, Every Day, or Even Every Hour or Minute.

This just means that the interest accrued can get increased every minute. Using calculators and computers today, we are now capable of computing complex formulas like the compound interest formula continuously whenever we want. This also means good for the people who invest in banks as they can get more money every minute of the day!

Now that we know the pros of the compound interest formula continuously but what exactly is it?

Let us use these variables in explaining the compound interest formula continuously.

• O is the outcome of the compound interest formula continuously.
  
• F is the first saved amount in the bank or also known as the principal amount.
  
• r is the interest rate of given by the bank.
  
• n is the number of times that interest is compounded.
  
• Y is the number of years of the investment or loan term is with their respective organizations.

Every year, this is what a compound interest formula continuously looks like:

On = F(1 + r/n)Yn

To make it more elaborate, we should get a derivation of a more appropriate formula:

O = limit F(1 + r/n)Yn

n -> infinite

Now, let us make the formula simple enough. Let us make a new variable of m as a substitute for n/r.

O = limit F(1 + 1/m)Ymr

m -> infinite

O = F(limit (1 + 1/m)m)Yr

m -> infinite

The part in the compound interest formula continuously where the limit is inside the parenthesis will now have a new constant variable called e. Leonhard Euler name this variable after himself as its discoverer. It has the constant value of 2.718

The end formula will now be:

O = FeYr