If the difference between simple interest and compound interest for the same principal at 10

Table of Contents

• What is a Simple Interest?
• What is a Compound Interest?
• Differences Between Simple Interest (SI) and Compound Interest (CI)
• Similarities: How is SI similar to CI?
• How is Simple Interest related to Compound Interest: SI Vs. CI
• Calculating the Mathematical Difference Between SI and CI
• Frequently Asked Questions
• Wrapping Up

In financial terms, interest is an amount a lender receives against a particular sum lent. In general, there are two types of interest, or you can say two ways of calculating the value receivable, namely Simple Interest, and Compound Interest.

What are the differences between Simple Interest and Compound Interest?

Apart from the prime purpose, Simple Interest and Compound Interest are different from each other in nature, approach, consistency, returns, and more. While Simple interest is usually a percentage obtained from a principal sum that remains constant throughout, compound interest is calculated on a variable principal. 

What is a Simple Interest?

Simple interest, popularly known as SI, can be defined as an approach to calculate the payable/attainable interest against any specific sum of money. In SI, the interest implies a value that is directly dependent on the original principal amount. 

Calculating Simple Interest

Simple interest is calculated using the following formula : (P×r×n)/100

• P=Principal amount
• r=Annual interest rate
• n= duration (in years)

To understand the mathematical approach better, let us take an example : Someone took $1000 from one of your friends at a 10% rate of interest for one year. To calculate the interest that needs to be paid after a year, we've,

• SI = (Pxrxn)/100
• SI = (1000x10x1)/100
• SI = 100

Hence, the amount you'll need to pay after a year is (1000+100), i.e., 1100.

What is a Compound Interest?

Compound interest or CI is like the reinvestment of interest.

In other words, the scenario where the addition of interest to the existing sum of money takes place for obtaining the new principal, which is eventually used for calculating the latest interest, is termed as Compound Interest. 

CI, in simple words, is interest on interest which means it is a case of reinvesting interest rather than paying it out.

Calculating Compound Interest

Compound interest is calculated using the following formula.

Compound Interest = P {(1+r/100)'t -1}

• P=Principal amount
• r=Annual interest rate
• t=Number of years interest is applied

Let’s understand with a scene in hand : Suppose you lend 1000$ to your friend at a 10% rate of interest for two years. To calculate the interest that needs to be paid after two years, we've:

• CI = P {(1+r/100)'t -1}
• CI = 210

Hence, the amount you'll need to pay after a year is (1000+210), i.e., 1210.

Differences Between Simple Interest (SI) and Compound Interest (CI)

Overall Meaning

Simple Interest or SI is the value that is generally a percentage of the principal amount. Compound Interest or CI, on the other hand, is the interest acquired on both principal and the interest generated over any pre-existing period.

Formulae

Simple Interest = (P×r×n)/100

• P=Principal amount
• r=Annual interest rate
• n= duration (in years)

Compound Interest = P {(1+r/100)'t -1}

• P=Principal amount
• r=Annual interest rate
• t=Number of years interest is applied

Consistency

Simple interest remains constant over the years, while compound interest is different for different years.

Returns

The return amount a lender attains in the case of Simple Interest is less, while the same for compound interest is comparatively more.

Nature of the Principal Amount

In the case of simple interest, the principal amount remains constant throughout. On the contrary, when the interest is calculated in terms of CI, the principal keeps changing. The main reason is that the interest amount gets added to the initial sum of money to obtain the new principal.

Growth

The interest earned in SI sees constant growth throughout. At the same time, the principal amount and interest in the case of CI grows at a rapid rate.

Interest Charged

In SI, the interest is a percentage of the principal amount. On the other hand, Compounding deals with the interest value, which is charged on the amount obtained by adding the principal value with interest for the previous term.

Nature of Calculation

Calculating simple interest is pretty straightforward. Compound interest involves a comparatively complex set of calculations.

Usage

Implementing SI is a better practice when you decide to buy pieces of stuff on loan. On the other hand, CI is excellent with all the investment scenes as the funds tend to grow over time.

Comparison Chart: Simple Interest(SI) Vs Compound Interest(CI)

Similarities: How is SI similar to CI?

SI and CI are different in many ways, but at the same time, their overall purpose sits on a similar end. Both the values are actually a form of interest that is calculated over a sum of money called the principal.

Another interesting fact about Simple and Compound interest is that both end up giving similar values when calculated for one year. In other words, although bearing different approaches altogether, the interest obtained on a sum of money for a year is similar no matter whether you choose SI or CI.

As already discussed several times, a sum of money (principal) dispersed on the terms of CI sees considerable growth in the interest value over time, while the same for SI remains constant.

Hence, it is pretty evident that the value of compound interest is always greater than the simple interest (when calculated for more than one year). Mathematically, CI> SI.

Calculating the Mathematical Difference Between SI and CI

• For one year, CI-SI=0
• For two years, CI-SI is calculated using P(R/100) '2
• For three years, CI-SI is computed using 3 x P(R/100) '2 + P(R/100) '3

Frequently Asked Questions

👍 Which is better, SI or CI?

The answer to this question depends upon the situation in demand. SI brings in more profit while buying pieces of stuff on loan. All thanks to the consistent nature, you'll need to pay the same amount of interest each month. While Compound Interest sees benefits with all kinds of investment schemes. Going with the terms of CI will help you get better returns.

🤙 Which one is simple to calculate, SI or CI ?

Calculating compound interest is more challenging than simple interest, mainly when the term (in years) under concern is considerably large.

Wrapping Up

For anyone who has been living in a continuous state of confusion so far, differentiating Simple Interest (SI) and Compound Interest (CI), the solution lies right here. In this article, we've reached every section where these two sets of interest values sit a distance apart. Also, we've mentioned a few things that are common in both. In case you're familiar with any other element that can play a crucial role, make sure to let us know.

Sources

• https://www.investopedia.com/terms/s/simple_interest.asp
• https://www.investopedia.com/terms/c/compoundinterest.asp

Feel free to comment and discuss about the article in the comment space below if you have any information or remarks to add. If you think we made a mistake, you can also report it there.

About the Author: Nicolas Seignette

Nicolas Seignette, who holds a scientific baccalaureate, began his studies in mathematics and computer science applied to human and social sciences (MIASHS). He then continued his university studies with a DEUST WMI (Webmaster and Internet professions) at the University of Limoges before finishing his course with a professional license specialized in the IT professions. On 10Differences, he is in charge of the research and the writing of the articles concerning technology, sciences and mathematics.