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6.Interest
medium
If the simple interest on a sum of money for $2$ years at $5 \%$ per annum is ₹ $50,$ what is the compound interest (In ₹) on the same sume at the same rate and for the same time?
A
$51.25$
B
$52$
C
$54.25$
D
$60$
Solution
$\text { S.I. } =P \times 2 \times \frac{5}{100}=50$
$P =₹ 500$
$\text { C.I. } =P\left[\left(1+\frac{5}{100}\right)^{2}-1\right]=500 \times\left[\left(\frac{21}{20}\right)^{2}-1\right]$
$=500 \times \frac{\left(21^{2}-20^{2}\right)}{20^{2}}$
$=\frac{500 \times 41 \times 1}{400}=\frac{205}{4}=₹ 51.25$
Standard 13
Quantitative Aptitude
