Find the sum on which the difference between the simple interest and compounded interest at a rate of 8 per annum compounded annually would be Rs. 64 in 2years.

# Find the sum on which the difference between the simple interest and compounded interest at a rate of 8 per annum compounded annually would be Rs. 64 in 2years.

1. A
₹8,000
2. B
₹10,000
3. C
₹12,500
4. D
₹15,000

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### Solution:

Let the sum be ₹P.
SI=$\frac{\mathit{PRT}}{100}=\frac{P×8×2}{100}=\frac{4P}{25}$
CI=$P{\left(1+\frac{R}{100}\right)}^{n}-P=P{\left(1+\frac{8}{100}\right)}^{2}-P=\frac{104P}{625}$
CI-SI=64
$⇒\frac{104P}{625}-\frac{4P}{25}=64$
$⇒\frac{4P}{625}=64$
$⇒P=₹10000$

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