Question

Find the amount and the compound interest on Rs. 120000 at 8$\%$ per annum for 1 year, compounded half-yearly.

Answer 1

Given that, $P=Rs.120000,R=8\%andT=1year$.

To find out: Amount and the compound interest after $1$ year, if compounded half-yearly.

As interest compounded half-yearly,

$R=\frac{8\%}{2}=4\%,andT=2\times 1=2$

We know that, $CI=P[{(1+\frac{R}{100})}^T-1]$

$\Rightarrow CI=120000[{(1+\frac{4}{100})}^2-1]$

$\Rightarrow CI=120000[\left(\frac{104\times 104}{100\times 100}\right)-1]$

$\Rightarrow CI=120000\left[(1.0816-1)\right]=120000\left(0.0816\right)=9792$

$\therefore CI=Rs.9792$

Now, Amount $=$ Principal + CI

$\therefore A=120000+9792=Rs.129792$

Hence, the amount and compound interest on $Rs.120000$ at $8\%$ per annum for $1$ year, compounded half-yearly is $Rs.129792$ and $Rs.9792$ respectively.