Question : Radha deposited INR 1,60,000 at a 10% rate of Compound Interest per annum for two years. If the interest is compounded semi-annually, then what is the Compound Interest (in INR)?
Option 1: 16,400
Option 2: 34,481
Option 3: 74,256
Option 4: 33,600
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Correct Answer: 34,481
Solution : Given: Radha deposited INR 1,60,000 at a 10% Compound Interest rate annually for two years. The rate compounded semi-annually, so the rate will be $\frac{10}{2}=5$% Time will be 2 × 2 = 4 $\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}$ ⇒ Compound interest = $160000(1+\frac{5}{100})^4-160000$ = $160000[(\frac{21}{20})^4-1]$ = $160000[(\frac{194481-160000}{160000})]$ = $160000[(\frac{34481}{160000})]$ = $34481$ So, the compound Interest is INR 34,481. Hence, the correct answer is 34,481.
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