In simple interest,

  the interest is on initial principal.

  Interest remains same every year

 

In compound Interest,

  the interest will be on total amount at the end of year

  Interest changes every year

 

Let’s take an example

 

Suppose I give Rs 10,000 to Sanjay at 10% per annum interest. Find the amount after 5 years

 

If interest is Simple Interest

Year

Principal

Interest

Amount

Year 1

10,000

10% × 10,000 = 1000

10,000 + 1000 = 11,000

Year 2

10,000

10% × 10,000 = 1000

11,000 + 1000 = 12,000

Year 3

10,000

10% × 10,000 = 1000

12,000 + 1000 = 13,000

Year 4

10,000

10% × 10,000 = 1000

13,000 + 1000 = 14,000

Year 5

10,000

10% × 10,000 = 1000

 14,000 + 1000 = 15,000

 

Interest = Rate × Principal

In this case, the principal remains same

So, this is simple interest.

 

If interest is Compound Interest

 

In compound interest,

The principal changes

Year

Principal

Interest

Amount

 1

10,000

10% × 10,000 = 1000

10,000 + 1000 = 11,000

 2

11,000

10% × 11,000 = 1100

11,000 + 1100 = 12,100

 3

12,100

10% × 12,100 = 1210

12,100 + 1210 = 13,310

 4

13,310

10% × 13,310 = 1331

13,310 + 1331 = 14,641

 5

14,641

10% × 14641 = 1464.1

 14,641 + 14641.1 = 16105.1

 

Here,

  Interest = Rate × Principal

 But Principal = Amount of previous year

 

Calculating compound interest like this could be difficult,

 

So we use formula

  Amount = P (1+R/100)^n

Here,

  P = Principal

  R = Rate

  n = Number of year

 

 

For Rs 10,000 at 10% p.a. What will be the compound interest after 4 years?

 

P = Rs 10,000

R = 10% p.a

T = 4 years

    Amount after 4 years = P (1+R/100)^n

= 10,000 (1+10/100)^4

= 10,000 (1+1/10)^4

= 10,000 ((10 + 1)/10)^4

Let’s take some examples

 

For Rs 10,000 at 10% p.a. What will be the compound interest after 4 years?

 

P = Rs 10,000

R = 10% p.a

T = 4 years

 

  Amount after 4 years = P (1+R/100)^n

      = 10,000 (1+10/100)^4

      = 10,000 (1+1/10)^4

                                     = 10,000 ((10 + 1)/10)^4

 

     = 10,000 (11/10)^4

     = 10,000 × 14,641/10,000

     = Rs 14,641

Now,

   Compound Interest = Amount – Principal

    = 14,641 − 10,000

    = Rs 4,641

 

Suppose I have Rs 1000 and I put it in a bank on compound interest. What would be the amount I have after 5 years, If Interest is 5%?

 

Given,

P = Rs 1000

R = 5% p.a

T = 5 years

 

  Amount = P (1+R/100)^n

= 1000 (1 + 5/100)^5

= 1000 (1 + 1/20)^5

= 1000 ((20 + 1)/20)^5

= 1000 × (21/20)^5

= 1000 × 4,084,101/3200000

= 4084101/3200

= Rs 1,276.282

 

  1. Chapter 8 Class 8 Comparing Quantities
  2. Concept wise
Ask Download

About the Author

Davneet Singh's photo - Teacher, Computer Engineer, Marketer
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.