The difference between the compound interest (compounded annually) and simple interest on a sum of money deposited for 2 years at 5% per annum is Rs. 15. What is the sum of money deposited?a)Rs. 6,000b)Rs. 4,800c)Rs. 3,600d)Rs. 2,400Correct answer is option 'A'. Can you explain this answer?

Question

Answer

Understanding Interest Types
When you deposit money in a bank, you can earn interest in two ways: simple interest (SI) and compound interest (CI). The difference between these two types of interest can help us find the sum of money deposited.
Formulas for Interest Calculation
- Simple Interest (SI):
$$ SI = \frac{P \times R \times T}{100} $$
where P = principal amount, R = rate of interest per annum, T = time in years.
- Compound Interest (CI):
$$ CI = P \left(1 + \frac{R}{100}\right)^T - P $$
This can also be expressed as:
$$ CI = P \times \left(1 + \frac{R}{100}\right)^T - P $$
Given Information
- Rate of interest (R) = 5%
- Time (T) = 2 years
- Difference between CI and SI = Rs. 15
Calculating Simple Interest (SI)
For 2 years:
$$ SI = \frac{P \times 5 \times 2}{100} = \frac{10P}{100} = \frac{P}{10} $$
Calculating Compound Interest (CI)
For 2 years:
$$ CI = P \left(1 + \frac{5}{100}\right)^2 - P $$
$$ CI = P \left(1.05^2\right) - P = P \left(1.1025 - 1\right) = 0.1025P $$
Finding the Difference
Now, we can find the difference:
$$ CI - SI = 0.1025P - \frac{P}{10} = 15 $$
Convert $\frac{P}{10}$ to a decimal:
$$ 0.1025P - 0.1P = 15 $$
$$ 0.0025P = 15 $$
$$ P = \frac{15}{0.0025} = 6000 $$
Conclusion
The sum of money deposited is Rs. 6,000, which corresponds to option 'A'.

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