Simple And Compound Interest Formula Explained With Examples

Interest is essentially the cost of borrowing money. When you borrow money from a bank, you are charged a certain percentage of the borrowed amount as interest. Interest is also the income earned on the money that you have invested. In this article, we’ll explain the difference between simple interest and compound interest and provide examples of how to use the formulas to calculate the interest.

Simple Interest Formula

Simple interest is calculated on the principal amount. The principal amount is the amount of money that you initially borrowed or invested. Simple interest is calculated as a percentage of the principal amount and the duration for which you have borrowed or invested the money. In simple interest, the interest earned or paid for each time period remains the same. The formula for simple interest is:

Simple Interest = (P × R × T) / 100

where P is the principal amount, R is the annual interest rate and T is the time in years.

Let’s say that you borrowed $10,000 from a bank for a period of five years at an annual interest rate of 5%. The calculation of simple interest would be:

Simple Interest = (10,000 × 5 × 5) / 100 = $2,500

Therefore, you would be required to pay back $12,500 in total to the bank after five years.

Compound Interest Formula

Compound interest is different from simple interest in that the interest is added to the principal amount at set intervals. In other words, you earn interest on interest. You can compound interest annually, semi-annually, quarterly, monthly, or even daily. The more frequently you compound interest, the quicker your money will grow. Understanding the Compound Interest Formula is essential for calculating the growth of your investment accurately.

Compound Interest = P (1 + R/100) ^t - P

where P is the principal amount, R is the annual interest rate, T is the time in years, and the symbol “^” represents the exponentiation of the value in parentheses to the power of T. 

For example, let’s say that you invested $10,000 for five years at an annual interest rate of 5% which is compounded annually. The calculation of compound interest would be:

Compound Interest = 10,000 (1 + 5/100) ^5 - 10,000 = $2,762.82

Therefore, the total amount you would have after five years with compound interest is $12,762.82.

Compound interest has a snowball effect. The more frequently you compound interest, the faster the interest will grow. Let’s say you invested the same $10,000 at 5% annual interest rate, but compounded it monthly for five years. The formula would be:

Compound Interest = 10,000 (1 + 5/100/12) ^(5*12) - 10,000 = $13,382.50

You can see from the above example that when you compound interest monthly, your interest grows faster, and you get a higher return on your investment. However, be mindful of the frequency of compound interest as most investments have a specific frequency of compounding. For example, a savings account may only compound interest annually or semi-annually.

Difference between Simple and Compound Interest

The fundamental difference between simple and compound interest is that in simple interest, the interest earned or paid for each time period remains the same, whereas, in compound interest, the interest is added to the principal amount at set interval. The more frequently you compound interest, the quicker your money grows. Compound interest has a snowball effect and helps your investment grow much faster than simple interest.

Simple interest is used in situations where the principal amount remains the same throughout the term, such as short-term loans or bonds. Whereas, compound interest is better suited for long-term investments, such as savings accounts, fixed deposits, and equity investments.

Conclusion

Interest is the cost of borrowing or the income earned on investment. Simple interest is calculated on the principal amount, and the interest earned for each time period remains the same. Compound interest is different from simple interest in that the interest is added to the principal amount at set intervals, making the interest grow much faster. The formula for compound interest is more complicated as it involves the exponentiation of values to the power of time. The more frequently you compound interest, the quicker your money will grow. Compound interest is preferable for long-term investments, while simple interest is best for short-term investments.