Compound interest is the interest calculated on the initial principal amount and the accumulated interest from previous periods. Unlike simple interest, which is calculated only on the principal amount, compound interest considers both the principal and the interest earned over time.

Compared to simple interest, this compounding effect causes the overall value to increase more significantly over time, especially when the interest is compounded more frequently or over longer periods. It contributes to long-term wealth building and is essential to many financial instruments, including investments, loans, mortgages, and savings accounts.

How Does Compound Interest Work?

Here's how compound interest works:

• Initial Principal: The amount of money that you begin with is known as the principal.

• Interest Rate: This principal amount is subject to an interest rate, which is added to it over time and included in the new, bigger principal amount.

• Compounding Periods: There are several frequency options for compounding interest such as annual, semi-annual, quarterly, monthly, and even daily. The more frequently it's compounded, the faster the interest will grow.

Formula

The formula to calculate the future value of an investment with compound interest is:

A= p(1+r/n)nt

where:

A = the future value of the investment/loan, including interest

P = the principal investment amount 

r = annual interest rate

n = number of times that interest is compounded per year

t = time the money is invested for in years

Example

Let's say we have Rs. 1,00,000 (P) invested for 5 years at an annual interest rate of 8% (0.08 in decimal) compounded annually (n = 1).

Using the formula:

A =1,00,000×(1+0.08/1)5

A =1,00,000×(1+0.08)5

A = 1,00,000×1.469328

A ≈ 1,46,932.80.

So, after 5 years at an 8% annual interest rate compounded annually, the total amount accumulated would be approximately Rs. 1,46,932.80. In comparison, simple interest would give a total corpus of Rs. 1,40,000. In the long run, compound interest can lead to substantial wealth accumulation. 

Compound Earnings Vs. Compound Interest

Compound earnings and compound interest both involve the idea of growth through reinvesting earnings, but they are used in slightly different contexts.

Compound Interest: Compound interest specifically refers to the interest earned on an initial amount of money (the principal) that accumulates over time. It's commonly used in the context of savings accounts, investments, loans, or any situation where interest accrues on both the initial principal and the accumulated interest. Compound interest helps to have exponential growth as the interest is added to the principal, leading to increased earnings.

Compound Earnings: Compound earnings, on the other hand, refer to the overall growth of an investment or asset. It also includes any additional income, dividends, capital gains, or reinvested earnings. Compound earnings take into account all sources of growth or income, contributing to the overall appreciation of an investment's value over time.

In short, compound interest focuses specifically on the interest component. However compound earnings provide a broader perspective, considering all forms of earnings and growth generated by an investment or asset. Both concepts highlight the power of reinvesting earnings to achieve greater growth and accumulation over time. Compound interest is necessary because it makes money work harder, allowing individuals to harness the power of time and growth to build wealth when compared to just simple interest.