Question : If interest is compounded half-yearly, then find the compound interest on INR 8,000 at the rate of 20% per annum for 1 year.
Option 1: INR 1,675
Option 2: INR 1,690
Option 3: INR 1,685
Option 4: INR 1,680
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Correct Answer: INR 1,680
Solution : Given: Total sum = INR 8000, rate = 20% per annum and time = 1 year. Here, the interest is compounded half-yearly, So, interest rate (r) = $\frac{20}{2}$ = 10%, time (n) = 2, principle (p) = INR 8000 Compound interest (CI) = $p[(1+\frac{r}{100})^n-1]$ = $8000[(1+\frac{10}{100})^2-1]$ = $8000[(\frac{11}{10})^2-1]$ = $8000[\frac{121}{100}-1]$ = $8000×\frac{21}{100}$ = INR $1680$ Hence, the correct answer is INR 1680.
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