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# When do we need Continuous Compounding?

When compounding is applied to an investment for an indefinite period and interests are added to the principal amount + interest on each period, it is called continuous compounding. In such an arrangement interest is added after each period and interest is compounded on the total amount in the next period (balance).

Continuous Compounding may be done on a regular basis, such as monthly quarterly, semi-annually and annually. The process goes on for indefinite number of periods and interest may be earned forever too. Thus banks and financial institutions prefer such kinds of investments.

One may seek Continuous Compounding for a variety of reasons, some of which are −

## Gains received perpetually

Returns on general and regular compounding stops after a certain period but in case of continuous compounding, interest, and payments go on increasing. This helps lenders build their portfolios stronger over time.

## Growing interest rates

In the case of continuous compounding, the interest rates go on increasing forever. This is in favor of the investor. This also helps multiply the returns on a given period. Reinvesting the interest allows the lenders to earn rates on exponential rates which are not seen in regular compounding.

**Note** − *Growing and perpetual incomes are two major advantages of continually compounding interest vehicles. Here the investor can gain immensely as the rate of income grows over every period instead of going down or staying intact over time*.

## Compounding Comparisons

Annual compounding in general terms means yearly interest rates being applied to the investments.

Total = [Principal × (1 + Interest)] ^Number of years

For example, for an investment of INR 10,000 for 2 years at 10% rate would yield,

= 10000 × (1+0.10) ^2

= 12100

The earnings = 12100 – 10000 = 2100

## Continuous Compounding

In the case of continuous compounding, the compounding is done for an infinite number of periods. So, the formula for calculating the interest is given by −

Total = Principal × e^(Interest × Years)

Here, e is the exponential function, which is equal to 2.71828.

Using this formula, if we calculate the continuously compounding investment,

10,000 × 2.71828^(0.10x 2)

= 10,000 × 1.2214

= 12214.0

The earnings = 12214 – 10000 = 2214

Which is more than general compounding earnings. The earnings show that earnings for lower interval levels are higher than higher interval levels as the power of e goes on decreasing with the increasing periods. Therefore, the smaller the interest periods and intervals are, the more is the value earned through continuous compounding.

**Note** − *The interest earned via a continuously compounding investment is more when the periods are low. With growing periods, the earnings go
down*.

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