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

 

Let's do 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)

      = 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 × (4,084,101/32.00,000)

= 4084101/3200

= Rs 1,276.282

 

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

About the Author

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.