Simple Interest & Compund Interest

 Simple Interest

Simple Interest is an easy method of calculating the interest for a loan/principal amount. Simple interest is a concept that is used in many sectors such as banking, finance, automobile, and so on. When you make a payment for a loan, first it goes to the monthly interest and the remaining goes towards the principal amount. In this article, let us discuss the definition, simple interest formula, and how to calculate the simple interest with examples.

What is Simple Interest?

Simple Interest (S.I) is the method of calculating the interest amount for some principal amount of money. Have you ever borrowed money from your siblings when your pocket money is exhausted? Or lent him maybe? What happens when you borrow money? You use that money for the purpose you had borrowed it in the first place. After that, you return the money whenever you get the next month’s pocket money from your parents. This is how borrowing and lending work at home.

But in the real world, money is not free to borrow. You often have to borrow money from banks in the form of a loan. During payback, apart from the loan amount, you pay some more money that depends on the loan amount as well as the time for which you borrow. This is called simple interest. This term finds extensive usage in banking.

Simple Interest Formula

The formula for simple interest helps you find the interest amount if the principal amount, rate of interest and time periods are given.

Simple interest formula is given as:

$\begin{array}{l}\mathbf{SI}\mathbf{=}\frac{\mathbf{PTR}}{\mathbf{100}}\end{array}$

Where SI = simple interest

P = principal

R = interest rate (in percentage)

T = time duration (in years)

In order to calculate the total amount, the following formula is used:

Amount (A) = Principal (P) + Interest (I)

Where,

Amount (A) is the total money paid back at the end of the time period for which it was borrowed.

The total amount formula in case of simple interest can also be written as:

A = P(1 + RT)

Here,

A = Total amount after the given time period

P = Principal amount or the initial loan amount

R = Rate of interest (per annum)

T = Time (in years)

Compound Interest Definition

Compound interest is the interest calculated on the principal and the interest accumulated over the previous period. It is different from simple interest, where interest is not added to the principal while calculating the interest during the next period. In Mathematics, compound interest is usually denoted by C.I.

Compound interest finds its usage in most of the transactions in the banking and finance sectors and other areas. Some of its applications are:

1. Increase or decrease in population.
2. The growth of bacteria.
3. Rise or Depreciation in the value of an item.

Compound Interest in Maths

In Maths, Compound interest can be calculated in different ways for different situations. We can use the interest formula of compound interest to ease the calculations. To calculate compound interest, we need to know the amount and principal. It is the difference between amount and principal.

Compound Interest Formula

As we have already discussed, the compound interest is the interest-based on the initial principal amount and the interest collected over the period of time.  The compound interest formula is given below:

Compound Interest = Amount – Principal

Here, the amount is given by:

Where,

• A = amount
• P = principal
• r = rate of interest
• n = number of times interest is compounded per year
• t = time (in years)

Alternatively, we can write the formula as given below:

CI = A – P

And

$\begin{array}{l}𝐶𝐼=𝑃{(1+\frac{𝑟}{𝑛})}^{𝑛𝑡}-𝑃\end{array}$

This formula is also called periodic compounding formula.

Here,

• A represents the new principal sum or the total amount of money after compounding period
• P represents the original amount or initial amount
• r is the annual interest rate
• n represents the compounding frequency or the number of times interest is compounded in a  year
• t represents the number of years

It is to be noted that the above formula is the general formula for the number of times the principal is compounded in a year. If the interest is compounded annually, the amount is given as:

$\begin{array}{l}𝐴=𝑃{(1+\frac{𝑅}{100})}^{𝑡}\end{array}$

Thus, the compound interest rate formula can be expressed for different scenarios such as the interest rate is compounded yearly, half-yearly, quarterly, monthly, daily, etc.

Simple Interest