Question : The compound interest on a sum of INR 20,000 at 15% p.a. for $2 \frac{2}{3}$ years, interest compounded yearly, is:
Option 1: INR 9,098
Option 2: INR 8,896
Option 3: INR 9,000
Option 4: INR 9,095
Correct Answer: INR 9,095
Solution :
We know, $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
Total amount $= 20000 × (1+ \frac{15}{100})^{2} (1 + \frac{\frac{2}{3}×15}{100})$
$= 20000 × (\frac{23}{20})^{2}× \frac{11}{10}$
$= 5 × 23 × 23 × 11$
$= 29095$
$\therefore$ Interest = Amount – Principal = INR (29095 – 20000) = INR 9095
Hence, the correct answer is INR 9,095.
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