Question : Find the Compound Interest on INR 10,000 for $1 \frac{1}{2}$ years at 20% per annum, interest is payable half-yearly.
Option 1: INR 3,315
Option 2: INR 3,310
Option 3: INR 3,305
Option 4: INR 3,320
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Correct Answer: INR 3,310
Solution :
Given:
Principal = INR 10,000
The rate compounded half yearly, so the rate will be $\frac{20}{2}=10$%
Time will be 1.5 × 2 = 3
$\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$
⇒ Compound interest = $10000(1+\frac{10}{100})^3-10000$
⇒ Compound interest = $10000[(\frac{11}{10})^3-1]$
⇒ Compound interest = $10000[(\frac{1331-1000}{1000})]$
⇒ Compound interest = $10000[(\frac{331}{1000})]$
⇒ Compound interest = $3310$
Hence, the correct answer is INR 3,310.
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