MathematicsFind 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.

A
₹8,000
B
₹10,000
C
₹12,500
D
₹15,000

Solution:

Let the sum be ₹P.
SI=

\frac{PRT}{100} = \frac{P \times 8 \times 2}{100} = \frac{4 P}{25}

CI=

P {(1 + \frac{R}{100})}^{n} - P = P {(1 + \frac{8}{100})}^{2} - P = \frac{104 P}{625}

CI-SI=64

\Rightarrow \frac{104 P}{625} - \frac{4 P}{25} = 64

\Rightarrow \frac{4 P}{625} = 64

\Rightarrow P = ₹ 10000

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