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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