Question

The difference between simple interest and compound interest on a sum for 2 years at $8\%$ per annum is ₹160. If the interests were compounded half yearly, find the difference between interests in the two years. $\left[4\text{Marks}\right]$

Answer 1

Given, principle amount is same for both simple and compound interest at 8% for 2 years.
According to question,
$C.I.-S.I.=160$
$\Rightarrow P{(1+\frac{8}{100})}^2-P-\frac{P\times 8\times 2}{100}=160$
$\Rightarrow P[{\left(\frac{108}{100}\right)}^2-1-\frac{16}{100}]=160$
$\Rightarrow P\times 0.0064=160$
$\Rightarrow P=25000$ $\left[2\text{Marks}\right]$

If the compound interest was compounded half-yearly, then the new difference between the two interests will be
$25000{(1+\frac{8}{100})}^4-25000-\frac{25000\times 8\times 2}{100}$

$\Rightarrow 34012.22-25000-4000=₹5012.22$ $\left[2\text{Marks}\right]$