Question : If interest is being compounded annually, then what sum will amount to Rs. 4036.8 in 2 years at the rate of 16% per annum at compound interest?
Option 1: Rs. 3000
Option 2: Rs. 1500
Option 3: Rs. 4000
Option 4: Rs. 2500
Correct Answer: Rs. 3000
Solution :
Amount = Rs. 4036.8
Time = 2 years
Rate = 16%
Let the principal be $P$.
We know that,
$ A= P(1+\frac{R}{100})^{T}$
⇒ $ 4036.8= P(1+\frac{16}{100})^{2}$
⇒ $ 4036.8= P(\frac{29}{25})^{2}$
⇒ $ 4036.8= P\times\frac{29}{25}\times\frac{29}{25}$
⇒ $ P=\frac{4036.8\times25\times25}{29\times 29}$
$\therefore P=3000$
Hence, the correct answer is Rs. 3000.
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