Compound Interest when interest is compounded half-yearly

Let's do this by taking examples

For Rs 10,000 at 10% p.a. What would be the compound interest (compounded half -yearly) after 2 years?

Given,

  Principal = Rs 10,000

Here rate is compounded half-yearly,

  So, rate of interest = R = 10/2 %

= 5%

Time = 2 years

n = number of half years

n = 2 × 2

n = 4

Amount = P (1 + R/100) ⁿ

      = 10,000 (1 + 5/100) ⁴

      = 10,000 (1 + 1/20) ⁴

      = 10,000 ((20 + 1)/20) ⁴

      = 10,000 (21/20) ⁴

      = 10,000 × (194481/160000)

      = 194481/16

      = Rs 12155.06

Now,

Amount = Principal + Interest

12155.06 = 10,000 + Interest

Interest = 12155.06 − 10,000

Interest = Rs 2155.06

Suppose I have Rs 1000 and I put it in a bank on compound interest, where interest is compounded half-yearly. What would be the amount I have after 1 1/2 years, if interest rate is 20% pa.?

Given,

  P = Rs 1000

Here rate is compounded half-yearly,

  So, rate of interest = R = 20/2 %

 = 10%

Time = 1 1/2 years

n = number of half years

n = 2 × 1 1/2

n = 2 × 3/2

n = 3

  Amount = P (1 + R/100) ⁿ

        = 1000 (1 + 10/100) ³

= 1000 (1 + 1/10) ³

= 1000 ((10 + 1)/10) ³

= 1000 (11/10) ³ 

= 1000 × (1331/1000)

= 1331