Question : What is the compound interest on Rs. 20000 at 10% per annum for 1 year 6 months, compounded half-yearly?
Option 1: Rs. 3215.5
Option 2: Rs. 3200
Option 3: Rs. 3152.5
Option 4: Rs. 3300
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Correct Answer: Rs. 3152.5
Solution : Principal = Rs. 20000 Rate = 10% yearly, $\frac{R}{2}$ = 5% compounded half yearly Time = 1 year 6 months compounded half yearly = 3 times We know that, $ A= P(1+\frac{\frac{R}{2}}{100})^{T}$ ⇒ $ A= 20000(1+\frac{5}{100})^{3}$ ⇒ $ A= 20000(\frac{105}{100})^{3}$ ⇒ $ A= 20000\times\frac{21}{20}\times\frac{21}{20}\times\frac{21}{20}$ ⇒ $ A= \frac{20}{8}\times9261$ ⇒ $ A=23152.5$ Thus, compound interest = Amount – Principal = 23152.5 – 20000 = Rs. 3152.5 Hence, the correct answer is Rs. 3152.5.
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