Ever vexed listening to the most often used terms in modern world today and that’s ultimately ” simple interest ” and ” compound interest “. These terms may sound slightly similar and simple but actually there is a giant difference that let people confuse with some regular basic stuff. These were some of those basic terms that rules banking, investing and financial industries today.

lets take a regular example for easy understanding which is mostly heard in banking while taking loans or making a deposit, You might heard something like ” we provide 10% simple/compound interest on your deposit “. If yes you might already associated with these terms but you never know what exactly it is? also you might have some questions related to this regular stuff which might include

- 1. what is the basic difference between simple interest and compound interest?
- 2. How does I calculate it?
- 3. what do I calculate it on my bank loans/deposits?
- 4. what is easiest way possible to calculate it accurately?

Lets together solve all these questions and conclude what exactly does these terms mean and how they differ each other.

Before directly going into the concept let us know the difference between some of the basic term which are inter related as far as this concept was concern.

**1. principle : **In this concept term principal refers to original the sum of the money borrowed to put into an investment or the initial sum of money in the act that had been deposited is called as a principle.

**2. Interest : **Interest is charge for privilege of borrowing money usually expressed in Annual percentage rate (APR).

**3. Rate : **It is amount charged, expressed as the percentage of principal, by a lender to a borrower for the use assets and usually expressed in Annual Percentage Rate (APR).

## Simple Interest

The simple interest is a result of simple annual interest rate which is interest amount per period multiplied by no of periods per years. It is also known as nominal interest rate. In the case of simple interest the principal Deposit/loan remains constant i.e, the interest rate will be only on the initial value. Let us practically see this with an example

Let ‘x’ takes a loan of $100 at a rate of 10% simple interest annually from ‘y’.

- For 0 years the amount remains same with is $100
- For 1 year the amount to be paid is $110 (10% on $100)
- For 2 years the amount to be paid is $120 ( 10% $100 for 2 years)
- For 3 years the amount to be paid is $130 ( 10% on $100 for 3 years)

So, The interest rate keep on increasing with number of years on simple initial loan. so, This is known as simple interest.

## Compound interest

The compound refers to in “addition to something” for example in addition to principal sum of loan or deposit. This statement emphasizing that particular loan or deposit is compounding to the principal. so it is called compound interest, in other words It is an official interest that to be paid be paid on interest.

Now let us practically see with an example

Let ‘x’ takes a loan of $100 at a rate of 10% compound interest annually from ‘y’.

- For 0 years the amount remain same which is $100
- For 1 year the amount to be paid is $110 ( because 10% on principle($100), which is $110)
- For 2 years the amount to be paid is $121 (now 10% should be paid on $110 which will be new principal, as we have studied earlier ‘ it is an interest on interest ‘ )
- For 3 years the amount to be paid is $133.1 (because 10% on $121)

The loan keep on compounding every year in addition to principal. so, This is known as compound interest.

## Difference between simple interest and compound interest

- Additional interest is not added to principal. So there’s no compounding
- It is also known as nominal interest rate.
- It is a result of simple annual interest rate which is interest amount per period multiplied by no of periods per year.

- Additional interest is always added to the principal. so there’s a compounding factor.
- It is also known as interest on interest.
- It is the result of reinvesting interest, rather than paying it out.

## Calculating simple interest and compound interest

The real difference comes into the act only when one compares the calculated interest value of simple interest and compound interest.

Earlier we have calculated simple interest with percentage method but when we need to calculate interest for bigger values or larger no of years, the problem gets complicated to solve. so, let us make use some of some simple formulas to solve calculations related simple and compound interests. so let’s start with calculating simple interest followed by compound interest

## Calculating simple interest

Let, P = Principal

r = rate and t or n = number of years

Now let’s derive the formula for simple interest with an example. so let principal (P) = $100, rate (r) = 10% and number of years (n) = 5

- For 0 years the interest is p
- For 1 year the interest is p + rp = p(1+r)
- For 2 years the interest is p + rp + rp = p(1+2r)
- For 3 years the interest is p + rp +rp +rp = P(1+3r)
- Therefor for n years the interest is P(1+nr)

Q) what is the simple interest for five years?

A) we have already considered some values as p, r and t. so, the simple interest for five years is

as per formula the simple interest for n years is P(1+nr), as n is number of years in the formula we will make it five as per our question. Therefore the simple interest for five years is

P(1+nr) = 100(1 + 5 * 10%) = 100(1 + 5 * 10/100) (since rate is a percentage valve)

= 100(1 + 0.5) = 100(1.5) = 150, Therefore $150

## Calculating compound interest

Let, P = Principal

r = rate and t or n = number of years

now let us derive the formula for compound interest with an example. so let Principal (P) = $100, rate(r) = 10% and number of years(n) = 5

- For 0 years the interest is p
- For 1 year the interest is P(1+r)
- For 2 years the interest is P(1+r)(1+r) = p(1+r)²
- For 3 years the interest is P(1+r)(1+r)(1+r) = P(1+r)³
- For n years the interest is P(1+r)(1+r)(1+r)….n times = P(1+r)
^{n}

Q) what is the compound interest for three years

A) we have already considered values as p, r and n. so, the simple interest for three years is

as per formula the compound interest for n years is P(1+r)^{n}

= 100(1 + 10%)³ = 100(1 + 10/100)³ = 100(1 + 0.1)³ = 100(1.1)³ = 100(1.331) = 133.1

Therefore the compound interest for 3 years is $133.1

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