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
3. Compound Interest

Compound Interest 