Compound Interest

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

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

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) 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 × (4,084,101/32.00,000)

= 4084101/3200

= Rs 1,276.282