An amount earns a total simple interest of Rs. 3200 at the rate of 6.25 percent per annum in 4 years. For this simple interest investment, what is the principal amount in rupees that was originally invested?

Introduction / Context:
This question is a standard simple interest problem in which the total interest, rate, and time are given, and the principal must be found. It is a direct application of the simple interest formula and is commonly asked in introductory quantitative aptitude and banking exams. The rate is given as 6.25 percent per annum, which can also be expressed as a fraction to make calculations easier.

Given Data / Assumptions:

• Total simple interest SI = Rs. 3200.
• Rate of interest r = 6.25 percent per annum.
• Time t = 4 years.
• Principal P is unknown.
• Interest is purely simple interest, not compounded.

Concept / Approach:
The simple interest formula is:
SI = (P * r * t) / 100.
We are given SI, r, and t, so we rearrange the formula to solve for P:
P = (SI * 100) / (r * t).
Because r = 6.25 percent, we may express it as 6.25 = 25/4 percent for easier multiplication and division. Substituting the numbers and simplifying gives us the principal amount.

Step-by-Step Solution:
Step 1: Write the simple interest formula: SI = (P * r * t) / 100. Step 2: Substitute the given data: 3200 = (P * 6.25 * 4) / 100. Step 3: Compute the denominator: 6.25 * 4 = 25. Step 4: So 3200 = (P * 25) / 100. Step 5: Rearranging for P: P = (3200 * 100) / 25. Step 6: Compute the numerator: 3200 * 100 = 320000. Step 7: Divide: 320000 / 25 = 12800. Step 8: Therefore, the principal amount invested is Rs. 12800.

Verification / Alternative check:
We can verify quickly by checking the interest generated by P = 12800 at 6.25 percent for 4 years. SI = (12800 * 6.25 * 4) / 100. First compute 6.25 * 4 = 25, so SI = (12800 * 25) / 100 = 12800 * 0.25 = 3200, which matches the given interest. This confirms that the principal must be Rs. 12800.

Why Other Options Are Wrong:
At P = 11800 or 13800, the resulting simple interest would not be exactly 3200. For example, with 11800, SI would be (11800 * 25) / 100 = 2950, which is too small. With 14800, SI would be 3700, and with 16000 it would be 4000. Only P = 12800 gives SI equal to Rs. 3200 at 6.25 percent over 4 years, making all other options incorrect.

Common Pitfalls:
One frequent mistake is mishandling the decimal rate 6.25 percent, such as treating it as 6.5 or 6.2. Another issue is forgetting to multiply by 100 when rearranging the formula. Some students also confuse simple interest with compound interest and attempt unnecessary compounding steps. Writing the formula clearly and simplifying step by step helps avoid these errors.

Final Answer:
The principal amount that earns Rs. 3200 as simple interest at 6.25 percent per annum in 4 years is Rs. 12800.