What is Interest?

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Business or commercial maths is an integral part of our day-to-day life, and comprises mathematical concepts related to business. Commercial mathematics plays a major role in business in maximizing profits by analyzing costs, determining pricing and sales patterns. You can easily apply commercial maths to everyday life with Cuemath.

Interest is a form of commercial maths that is used in everyday life. Interest, in simple words, is defined as the cost of borrowing money, wherein the borrower pays a fee in the form of interest to the lender for the loan borrowed. The interest is calculated on the principal amount and is added to that principal amount over a given period of time. The borrower needs to pay that total loan amount (principal + interest) in the agreed period of time.

The interest, which is expressed in the form of a percentage, can either be simple or compounded. Simple and compound interest are used widely across financial services, especially banking. There are various categories of loans whose repayment is calculated based on simple interest such as mortgages, installments, auto, and educational loans among others while compound interest is used for paying interest in savings accounts as it pays more as compared to the simple interest.

What is simple interest?

Simple interest is the easiest method for calculating interest charged on a particular loan amount. It is based on the principal amount of the loan. In general, simple interest over a certain period is calculated based on a fixed percentage of the principal amount.

Simple interest is calculated with the help of a simple formula:

Simple interest = Principal (P) X annual interest rate (r) X term of the loan in years (n)

Let us understand simple interest with the help of an example.

Suppose a student borrows a loan of US$20,000, for his college tuition fees, for a period of 3 years at an interest rate of 5%. His simple interest will be calculated as follows:

Simple interest = 20,000 X 3 X 5 = 300,000

That means it will amount a total of US$300,000

As simple interest is calculated on a daily basis, consumers who repay their loan timely get benefitted from this. Considering the above scenario, if the student sends his amount by the first day of every month, then he would realize the principal balance amount shrinking faster and the same amount is paid he would be able to pay the loan off sooner.

On the contrary, if the same amount is paid at a later date, then most of it goes towards interest.

Categories of loans on which simple interest is calculated

Usually, simple interest is applied to short-term personal loans or automobile loans. Many times a home loan is disbursed on simple interest with the calculation of a loan on a daily basis as compared to the traditional mortgage where the calculation is done on a monthly basis.

The formula is simple. The daily interest rate is calculated by dividing the interest rate by 365 days and then multiplying the amount by the outstanding loan balance. As the total number of days calculated in a simple interest is more than a traditional mortgage calculation, the total interest consumers pay on a simple interest mortgage will be slightly bigger as compared to a traditional mortgage.

Consumers do not get any benefit for making extra payments on a simple interest mortgage. However, there is a risk for borrowers who do not plan to pay off their loan early. As the interest compounds on a daily basis, the principal, or the due amount, keeps increasing.

What is compound interest and how is it calculated

Whether you are managing your finances and somebody else is doing it for you, it is very important to understand the concept of compound interest. Compounding, in simple words, is a process of growing. It accounts for interest earned on the sum which was previously earned as interest.

Compound interest is added to the interest accumulated of previous periods. In simple words, it could be termed as interest on interest.

Compound interest is calculated with the help of the following formula:

Compound interest = Principal amount (P) X (1+annual interest rate (r))number of years (t) – P

In compound interest, borrowers pay interest accrued on the interest as well as on the principal amount.

How does compound interest work?

Compound interest is the most common form of interest, which is widely used as an interest-calculating instrument. It is also used to calculate the interest the consumer’s money accumulated if he sets up an interest-bearing account.

Compound interest is good for savings and making investments, but if you take a loan on compound interest, then it might work against you. The compound interest is quite powerful as it has high frequency, interest rate, deposits and period.

How to make best out of compound interest

There are many ways in which you can make compound interest work best for yourself:

 Everyone is aware of the fact that time matters a lot when someone is trying to grow money over a longer period. The longer you keep your money in an instrument that is capable of compounding, the higher are the chances of your increasing amount in your savings. The reason is that the compound interest is capable of growing exponentially over some time.

Suppose you are able to make a saving of $100 per month at a compound interest rate of 5% interest for 5 years. You will be able to save $6,100 in deposits and earned $836.63 as interest. Even if you decide to make no other deposit, after 20 years, you would have earned an additional $7,484.13 in interest, which is much more than your initial $6,100 in deposits, all because of the power of compounding.

Many bank products, like savings accounts and CDs, consider the compound interest and offer a true annual rate of interest.

With the help of compound interest, you can get rid of your debts earlier by paying extra whenever you can. Remember to keep the borrowing rates low because the interest rates on your loan determine how quickly you can pay your loan and also it affects your monthly loan cycle.

What gives the power to compound interest?

The term ‘compounding’ is itself very powerful. It simply means paying interest repeatedly. Over a period of time when money grows then the power of compounding can actually be realized in the real sense.

Some of the most important factors in compounding are frequency, time period, interest rate, principal amount and deposits:

Frequency: This matters the most. More is the frequency of compounding, more impressive and dramatic results you get. While opening a savings account, you must opt for the accounts that compound daily. You might not be able to see it, but interest is added on a daily basis while there are many accounts that calculate interest monthly or annually.

Interest rate: This is the second important factor for determining your account balance over time. Higher rates simply mean higher account balance. Over a long period of time, an account with compounding but a lower rate of interest can have a higher account balance as compared to an account with a simple calculation. You must do all these calculations before opening an account.

Starting amount: Your compounding is not dependent on the amount of deposit you start with. Whether it is just $100 or $1 million, the magic of compounding works in the same manner. So, it is best to keep all your focus on percentages and time frame when you are planning for your future.

Comparison between Simple and Compound interest

  • Simple interest is much easier to calculate as compared to compound interest
  • If we compare both simple and compound interest then we find that the return in simple interest is much lesser as compared to compound interest
  • In simple interest, the principal amount remains constant, while in compound interest, the principal amount keeps on changing during the entire loan period
  • The growth is uniform in simple interest, wherein growth, in compound interest increases rapidly
  • In simple interest, the borrower is charged for the principal amount, while in compound interest, the borrower is charged interest on both the principal amount and the accumulated interest

So now you understand the wide difference between the two. Next time whether you are applying for a loan or planning for a long term saving, just do your own calculations before jumping in interest rate related decisions.

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