Question

If the difference between simple interest and compound interest on a sum invested for 2 years at 25% per annum is ₹200, then the sum invested is .

• A. ₹3200
• B. ₹2873
• C. ₹4200
• D. ₹1900

Answer 1

The correct option is A ₹3200

Given,
R = 25 %
The difference in S.I and C.I = ₹200
Period (n) = 2 years
Let the sum invested be P.

Now, by using compound interest formula,

$C.I=P\times {[1+\frac{R}{100}]}^n-P=P\times {[1+\frac{25}{100}]}^2-P=P\times {[1+\frac{1}{4}]}^2-P=P\times \left[\frac{25}{16}\right]-P=\frac{9P}{16}$

$S.I=\frac{P\times 25\times 2}{100}$
$=\frac{P}{2}$

Given, the difference between S.I and C.I is ₹ 200.

Hence, $\frac{9P}{16}-\frac{P}{2}=₹200\frac{P}{16}=₹200P=₹3200$