Compound Interest

Compound interest is a method used to calculate the interest earned by adding it back to the principal. In comparison with simple interest, compound interest is calculated on the initial principal as well as the previously accumulated interest. Simple interest, on the other hand, is calculated on principal only. In terms of investments, compound interest will multiply your amount at an accelerated rate, whereas, in terms of debt, the compound interest becomes a huge amount to pay off. Compared to simple interest the amount that is compounded will grow faster. 

The formula we use for compound interest is: 

A = P (1 + rn)nt - P

Where, 

A = Final amount after interest
P = Principal (starting/initial money)
r = Annual interest rate ( as a decimal)
n = number of times interest is compounded per year
t = time in years

If the frequency of the number of times the interest is compounded annually we use another formula similar to the first one to calculate the compounded amount.

                    A = P (1 + r / n)^nt - P

Interest can be calculated in compound interest on different frequencies of time like daily, monthly, quarterly, and annually. Higher the number of compounding periods, the larger the effect of the interest. In other words, it can be defined as interest on interest. 
 

There are records suggesting the application of compound interest as far back as the ancient Mesopotamia. The Babylonians used the records in their financial transactions, and they even calculated their interest growth over time on mathematical tablets. In the 4th century BC, Aristotle criticized the usage of compound interest, claiming that it was unnatural.

However, the Romans still widely used it in trade and banking. Today compound interest is the main concept in banking, investment, and economics assuring that money grows over time.
 

For compound interest, period of time is the most important one. For how long are you investing or taking the loan, you have to decide accordingly. Frequency of time is the only determining factor for the interest amount needs to pay in compound interest. 

In each of these formulas, A is the total amount (principal amount and compound interest). If there is a situation where you would like to calculate only the compound interest, we then need to subtract P (principal) from the formula. For example, for the formula compounded weekly, the formula would be A = P(1 + r / 52)^52t- P.
 

As a financial concept, compound interest helps in growing the money over a period of time. So here are a few reasons why compound interest is significant.

• Helps in the management of loans: If a loan with compound interest is not managed properly, the debt can grow rapidly. Understanding how interest accumulates can help prevent this and ensure proper management. 
  
   
• Boosts any savings and investments: If you understand how compound interest works it would help to maximize your savings and investments by choosing any option with higher compounding frequencies.
  
   
• It is a good way out for retirement. Savings can grow at an increased rate through compound interest
  
   
• Usually, credit card bills interest rates are compounded, so it sometimes helps in controlling purchase.

A student must keep in mind the key properties to understand the concept of compound interest. Below are some of the key properties that students must know.

• Growth of interest: Compound interest grows exponentially as the interest is calculated on both the principal and the accumulated interest. 
  
   
• Time period affects growth: The longer the time period, the greater the growth as interest continues to accumulate on previous interests.
  
   
• For a fast growth, a higher interest rate is needed: A higher interest rate results in quicker accumulation of interest and a faster growth. This could impact on any kind of savings or investment.
   

Compound interest can help you make smart financial decisions. So here are some tips and tricks to master the concept: 

 

• Understand the compounding frequency: Due to compound interest, the money can grow exponentially depending on the frequency of time period
  
   
• Double the money using the rule of 72: This is a quick method to know how long it will take for the money you have compounded annually to double. A formula is used to calculate this: Years = 72/interest rate. 
  
   
• Use online calculators for precise calculations: To make sure you are not making mistakes in calculations, use online compound interest calculators to quickly and accurately find how much money will grow.
  
   
• Keep in mind the various synonyms for per year: There are different synonyms used for per year. Remember that per year, annual, or per annum all mean the same.
  
   
• Make sure to memorize the formulas: It is very important to remember and memorize the standard formula for compound interest. This would make it easier to learn the other formulas as they are variations of the standard formula.
  
   
• Rule of 72 - It is a calculation for compound interest where one can find out how an investment can be doubled by multiplying 72 by annual interest rate. 

Compound interest is a powerful financial tool used in various aspects of our lives. Here are some real-world applications of compound interest:

Used in savings accounts: All banks use compound interest to calculate how much our savings will grow over time.

Repayment for loans: When you borrow money from the bank on compound interest and agree to repay by a certain date, it's significant to pay back the loan before the interest accumulates. Otherwise, debt would grow, and you would end up having to pay even more money than the initial amount.

Education funds and savings: When saving money for your college, like a college fund. The bank uses compound interest, so the money grows over time.