Question : What is the compound interest on Rs.16400 for 1 year at 9% per annum when compounded half-yearly?
Option 1: Rs. 1640.40
Option 2: Rs. 1608.20
Option 3: Rs. 1509.21
Option 4: Rs. 1680.90
Correct Answer: Rs. 1509.21
Solution :
Principal = Rs. 16400
As it compounded half yearly, so Time = 2
Rate = $\frac{9}{2}$
Total Amount = Principal × $(1+\frac{\text{Rate}}{100})^{\text{Time}}$
$=16400(1+\frac{\frac{9}{2}}{100})^2$
$=16400(1+\frac{9}{200})^2$
$=16400×\frac{209}{200}×\frac{209}{200}$
$=17909.21$
Compound interest = 17909.21 – 16400 = 1509.21
Hence, the correct answer is Rs. 1509.21.
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