Question

Find the amount and the compound interest on $Rs.6000$ for $1$ year at $10\%$ per annum compounded half-yearly.

Answer 1

Let,Prinicpal (P) = $Rs.6000$

Time (n) = $1$ year

$\Rightarrow n=1\times 2=2$ [As interest is compounded half yearly]Rate (r) = $10\%$

$\Rightarrow \frac{10\%}{2}=5\%$ [As interest is compounded half yearly]

Now, we know that,

$A=P\times (1+\frac{r}{100}{)}^n$

$=6000\times (1+\frac{5}{100}{)}^2$

$=6000\times (1+\frac{1}{20}{)}^2$

$=6000\times (\frac{21}{20}{)}^2$

$=6000\times \frac{21}{20}\times \frac{21}{20}$

$=15\times 441$

$=6615$

Hence, Amount ($A$) = $Rs.6615$

Now,$CI=A-P$

$=6615-6000$

$=615$

Hence, Compound Interest ($CI$) = $Rs.615$

Therefore, Amount = $Rs.6615$ and Compound Interest = $Rs.615$