Question : What is the compound interest (in Rs.) for 1 year on a sum of Rs. 20,000 at the rate of 40% per annum compounded half-yearly?
Option 1: 8000
Option 2: 8650
Option 3: 8750
Option 4: 8800
Correct Answer: 8800
Solution :
Principal amount, $P$ = Rs. 20000
Rate, $R$ = 40%
Term, $n = 1$ year
Compound interest after 1 year = $P[(1+\frac{\frac{R}{2}}{100})^{2n} –1)]$]
= $20000[(1+\frac{40}{200})^{2} –1)]$
= $20000[(1.2)^{2} –1)]$
= $20000[1.44–1)]$
= $20000 × 0.44$
= Rs. 8800
Hence, the correct answer is 8800.
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