Question : Rs. 2400 is lent at the rate of 10% per annum. Which of the following statement(s) is/are correct?
I. The compound interest (compounding annually) for 3 years is Rs. 794.4.
II. The difference between simple interest and compound interest (compounding annually) after 3 years is Rs. 75.8.
Option 1: None of the statements are correct.
Option 2: Only statement I is correct.
Option 3: Only statement II is correct.
Option 4: Both statements I and II are correct.
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Correct Answer: Only statement I is correct.
Solution :
I.
The formula for compound interest,
$\text{Total Amount}=\text{Principal}×(1+\frac{\text{Rate}}{100})^{\text{Time}}-\text{Principal}$
$=\text{2400}×(1+\frac{\text{10}}{100})^{\text{3}}-\text{2400}$
$=\text{2400}×(\frac{\text{11}}{10})^{\text{3}}-\text{2400}$
$=\text{2400}×(\frac{\text{1331}}{1000}) -\text{2400}$
$=(\frac{\text{15972}}{5}) -\text{2400}$
$=\frac{\text{3972}}{5} $
$= 794.4$
So, the Statement I is correct.
II.
The formula for simple interest,
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}=\frac{\text{2400 × 10 × 3}}{100}$ = Rs. 720
The difference between the compound interest and the simple interest = 794.4 – 720 = 74.4
$\therefore$ Statement II is incorrect.
Hence, the correct answer is "Only statement I is correct".
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