Question : What would be the compound interest on Rs.15,750 at 20% per annum, in two years, if the interest is compounded half-yearly?
Option 1: Rs. 5,213.25
Option 2: Rs. 3,307.5
Option 3: Rs. 7,305.975
Option 4: Rs. 7,309.575
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Correct Answer: Rs. 7,309.575
Solution : Principal amount, $P$ = Rs. 15,750 Time calculated half-yearly, $t$ = 2 × 2 = 4 half-years Rate of interest for a half year $r$ = $\frac{20}{2}$% = 10% Amount after $t$ half years with interest is compounded at $r$% per half-year = $P(1+\frac{r}{100})^t$ = $15750(1+\frac{10}{100})^4$ = $23059.575$ Compound interest = Rs. (23059.575 – 15750) = Rs. 7309.575 Hence, the correct answer is Rs. 7309.575.
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