Question : Find the compound interest on INR 50,000 for one year at 8% per annum when compounded half-yearly.
Option 1: INR 3,900
Option 2: INR 3,880
Option 3: INR 4,080
Option 4: INR 3,950
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Correct Answer: INR 4,080
Solution : Given, Principal, P = INR 50,000 Rate of interest $r$ = 8% per annum compounded half-yearly = 4% per half-year Time = 1 years with half-yearly interest = 2 half years Amount = P × $(1+\frac{r}{100})^{\text{Time}}$ = 50000$(1+\frac{8}{2\times 100})^{2}$ = 50000$(1+\frac{4}{100})^{2}$ = 50000$(\frac{26}{25})^{2}$ = 50000 × $\frac{676}{625}$ = INR 54,080 Now, Compound interest = Total amount – Principal = 54080 – 50000 = INR 4080 Hence, the correct answer is INR 4080.
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