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
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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