Question

The C.I. on Rs. 10000 at 20$\%$ per annum at the end of 1 year 6 months, if the interest is calculated half-yearly will be:

• A. $Rs.4340$
• B. $Rs.5320$
• C. $Rs.3310$
• D. $Rs.4590$

Answer 1

The correct option is C $Rs.3310$

Given that, $P=Rs.10000,R=20\%andT=1year6months$

To find out: The compound interest on the given some, if the interest is compounded half-yearly.

We know that, if the interest is compounded half-yearly, the rate of interest will be half and the time will be double.

Hence, $R=\frac{R}{2}=10\%$ and $T=2\times 1.5=3$

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

$\therefore CI=10000[{(1+\frac{10}{100})}^3-1]$

$\Rightarrow CI=10000[{\left(\frac{11}{10}\right)}^3-1]$

$\Rightarrow CI=10000[\frac{1331}{1000}-1]$

$\Rightarrow CI=10000\left[\frac{331}{1000}\right]$

$\therefore CI=Rs.3310$

Hence, the compound interest on $Rs.10000$ at $20\%$ per annum for $1$ year and $6$ months will be $Rs.3310$.