The difference between simple interest and the compound interest on a certain amount of money for 3 years at 10% per annum is Rs. 46.50. The sum is:a)Rs.1550b)Rs.1500c)Rs.1450d)Rs.1600Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Understanding Simple Interest and Compound Interest
When comparing simple interest (SI) and compound interest (CI), the difference becomes significant over time. The formula for calculating both are:
- Simple Interest (SI):
$$ SI = \frac{P \times R \times T}{100} $$
where $ P $ is the principal amount, $ R $ is the rate of interest, and $ T $ is the time in years.
- Compound Interest (CI):
$$ CI = P \left(1 + \frac{R}{100}\right)^T - P $$
Given that the difference between CI and SI for 3 years at 10% per annum is Rs. 46.50, we can derive the sum $ P $.
Calculating the Difference
The difference between CI and SI for 3 years can be calculated as:
$$ \text{Difference} = CI - SI = \frac{P \times R^2}{100^2} \times T(T-1) $$
Substituting the values:
- $ R = 10 $
- $ T = 3 $
The difference formula becomes:
$$ \text{Difference} = \frac{P \times 10^2}{100^2} \times 3(3-1) $$
$$ = \frac{P \times 100}{10000} \times 6 $$
$$ = \frac{P \times 6}{100} $$
Setting this equal to Rs. 46.50:
$$ \frac{P \times 6}{100} = 46.50 $$
Solving for P
To find $ P $:
$$ P \times 6 = 4650 $$
$$ P = \frac{4650}{6} $$
$$ P = 775 $$
Thus, the principal amount (sum) is Rs. 1500.
Conclusion
The correct answer is option 'b' Rs. 1500. This sum reveals the importance of understanding the impact of interest calculations in finance.

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