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. ₹2,873
• B. ₹3,200
• C. ₹4,200
• D. ₹1,900

Answer 1

The correct option is B ₹3,200

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

Now, the compound interest for first year will be,

$C.I=\left[\frac{P\times R}{100}\right]=\left[\frac{P\times 25}{100}\right]=\frac{P}{4}$
New principal after on year
$=P+\frac{P}{4}$
$=\frac{5P}{4}$
Now, the compound interest for second year will be,

$C.I=\left[\frac{5P\times R}{4\times 100}\right]=\left[\frac{5P\times 25}{400}\right]=\frac{5P}{16}$
Total $C.I.=\frac{5P}{16}+\frac{P}{4}=\frac{9P}{16}$

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

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

Hence, $\frac{9P}{16}-\frac{P}{2}=₹200\frac{P}{16}=₹200P=₹3,200$