Question

Find the compound interest on $Rs.1000$ at the rate of $8\%$ per annum for $1\frac{1}{2}$ years when interest is compounded half-yearly.

Answer 1

Given: Principal (P) = $Rs.1000$

Time (t) = $1\frac{1}{2}$ years

$\Rightarrow 1\frac{1}{2}\times 2=3$ [As interest is compounded half-yearly.]

Rate (R) = $8\%$ per annum

$\Rightarrow \frac{8\%}{2}=4\%$ [As interest is compounded half-yearly.]

Now, we know that,

$A=P(1+\frac{R}{100}{)}^t$

$\Rightarrow A=1000(1+\frac{4}{100}{)}^3$

$\Rightarrow A=1000(\frac{104}{100}{)}^3$

$\Rightarrow A=1000\times \frac{104}{100}\times \frac{104}{100}\times \frac{104}{100}$

$\Rightarrow A=Rs.1124.8$

$\therefore$ CI = A$-$P =$1124.8-1000=Rs.124.8$

Hence, compound interest earned = $Rs.124.8$