What Is Compound Interest? Definition And Meaning

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What is compound interest definition and formula

Compound interest is a very different type of interest than simple interest and when it comes to investing, compounding is one big effect.

This type of interest accumulate much more rapidly than simple interest, so it is very good for money you have in your possession, but very costly for loans you are paying.

Understanding the Concept of Compounding

Compound interest is interest which accumulates depending on the interest rate and amount of periods.

This is a much more complex calculation than simple interest rate, due to how the interest from previous periods is added into the interest calculation for the current period.

The frequency of the periods has a large effect on the total amount of interest. For example, $500 will accumulate more interest when it is compounded semi-annually at 2% than if it were compounded annually at 4%.

Although they should both come out to be 4% annually, since the 2% is also paying interest on the outstanding interest from the first six month period.

In the second six month period, there will be a larger amount of interest compounded. This is the importance of the frequency of payments in the compound interest computation.

Its no surprise that top finance icons like Robert Kiyosaki in his book – Rich Dad Poor Dad, helped a lot of readers to understand how powerful compounding is in business.

Also Read: Compound VS Simple interest difference

Compound Interest Definition?

Compound interest is the interest on a loan which is paid on the principal and accumulated interest from the previous periods of the loan.

There are multiple types of compounding interest based on the frequency it is compounded. These vary from anywhere from continuous to annual compounding.

This makes a significant difference, as the more often interest is compounded the higher the amount grows.

Compound interest is more frequently utilized than simple interest, and is applicable to both investments and loans. For investments, it helps money grow quickly, while with loans it creates a larger loan amount to pay off.

Must Read: 10 great investment books you must read today

How to Calculate Compound Interest (Formula)

There are two different formulas for calculating compound interest, which give the same value. The variables for these formulas are P, i, and n.

Compound Interest Formula

Compound Interest = Total amount of Principal and Interest in future (or Future Value) less Principal amount at present (or Present Value)

= [P (1 + i)n] – P

 = P [(1 + i)– 1]

(Where P = Principal, i = nominal annual interest rate in percentage terms, and n = number of compounding periods.)

In the formula,

P = the principal amount of the loan.

I = the interest rate of the loan as a decimal, so a 5% interest rate would be 0.05.

N = the term of the loan, for example 3 years.

The first way to calculate compound interest is P*(1+i)^n – P. Using this formula, you calculate the interest rate plus 1 and multiply it to the nth power.

Next, you multiple this times the principal amount, and then finally subtract the original principal amount to find the amount of interest.

An alternate version of this formula is P*( (1+i)^n – 1). In this formula, you add the interest rate and one, take this to the nth power, and then subtract one.

After this, you multiple the answer by the original principal amount, and you have the interest of the loan.

Here’s an example below:

Thus, if simple interest is charged at 5% on a $10,000 loan that is taken out for three years, the total amount of interest payable by the borrower is calculated as:

$10,000 [(1 + 0.05)3 – 1] = $10,000 [1.157625 – 1] = $1,576.25.

Also Read: Major kinds of loan and their features

Compound Interest Key Takeaways

– The frequency of the periods of compounding is very important and has a great effect on the compound interest calculation

– Compound interest is paid on the principal, as well as any interest which has accumulated in previous periods of the principal

– The formulas are P*((1+i)^n)-P and P*((1+i)^n-1)

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