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