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Simple Interest and Compound Interest

Concept of Simple and Compound Interest

The concept of simple interest and compound interest are widely used in Banking. In most competitive exams 1 to 2 questions come from this topic directly. We can use this concept in other chapters also. Let us discuss the concept of Simple and compound interest in this chapter.

Principal:

It is the sum of money that is deposited or borrowed. This principal is also known as capital.

Interest:

Interest is a fixed percentage of the principal, which is paid by the borrower to the lender.

Amount:

The amount is the sum of principal and interest

Time:

This is the duration for which money is deposited or borrowed.

Rate of Interest:

The rate at which interest is charged on principal.

Simple Interest:

When the interest is uniformly calculated on the principal for a certain period of time then that is simple interest.

We usually use the following notations.

Let us take few examples

Example 1: 

Find the simple interest on RS 10000 at 14% per annum for 5 years.

Solution:

From the above formula

Here,

P = 10000 RS.

r = 14% per annum.

t = 5 years

Example 2:

A sum of money doubles in 6 years. Find the simple interest rate.

Solution:

Let principal = P

Rate of interest = r% per annum

Time = 6 year

So, amount after 6 years = 2P

Interest = 2P – P = P

Now,

Example 3:

A certain sum of money in 4 years becomes 1488 and in 7 years becomes 1704 RS. If the simple interest rate is charged then find interest rate and principal.

Solution:

Now,

Case – 1 When simple interest, Rate of interest (r), and time (t) known, 

Then,

Example

On a certain sum of money at 5% p.a. simple interest is RS. 192 for 3 years RS. Find the sum of the money.

Solution:

Case – 2 When simple interest, time (t), and principal (p) are known, 

Then,

Example 

Interest of RS. 1300 in 3 years is 234 RS. Find the Rate of interest?

Solution:

Case – 3  When Simple interest. Principal (p) and the rate of interest are known

Then,

Example 

In how many years simple interest of 1440 RS at a rate of 10% per annum becomes 576 RS?

Solution: 

Compound Interest:

In this case, interest is charged on the basis of the previous total amount for every next period of time.

Let us discuss it.

Suppose, the rate of interest is 10% and it compounds annually.

So, for 100 RS. In first-year interest is RS 10

But for the 2nd year, the principal will be (100 + 10) RS. = 110 RS.

And we need to calculate interest on 110 RS.

For 2nd year interest at 10% is 11 RS.

Now, when we calculate interest for 3rd year we need to take (110 + 11) RS. = 121 RS. as principal to calculate the interest.

Remembered one thing,

For, the first period of time on a certain sum of money,

But after the first period of time,