A sum of money is invested at a simple interest rate of 7.5% per annum for 4 years. If the same sum were invested for 5 years, the interest earned would increase by Rs 375. What was the initial principal amount invested?

Introduction / Context:
This question uses the simple interest concept where an extension in time leads to an increase in interest earned. Instead of directly knowing the total interest, we are told how much extra would be earned if the investment period were extended by one year. This allows us to first find the annual interest and then compute the principal.

Given Data / Assumptions:

• Rate of simple interest, R = 7.5% per annum.
• Initial time period, T1 = 4 years.
• Extended time period, T2 = 5 years.
• Additional interest for the extra 1 year, Delta SI = Rs 375.
• Principal, P, is unknown and must be calculated.

Concept / Approach:
In simple interest, interest grows linearly with time. Therefore, the extra interest earned by increasing the time by 1 year is equal to the interest for that single additional year on the same principal. The simple interest formula is:
SI = (P * R * T) / 100From the extra interest for 1 year, we can write:
Delta SI = (P * R * 1) / 100Then we solve this for P.

Step-by-Step Solution:
Step 1: Use the formula for extra one year interest.Delta SI = (P * R * 1) / 100375 = (P * 7.5 * 1) / 100Step 2: Rearrange to solve for P.P = (375 * 100) / 7.5Step 3: Compute the value.375 * 100 = 37,500P = 37,500 / 7.5 = 5,000Thus, the initial principal amount invested is Rs 5,000.

Verification / Alternative check:
We can verify by computing the interest for 4 years and 5 years. For 4 years, SI4 = (5000 * 7.5 * 4) / 100 = (5000 * 30) / 100 = Rs 1,500. For 5 years, SI5 = (5000 * 7.5 * 5) / 100 = (5000 * 37.5) / 100 = Rs 1,875. The difference SI5 - SI4 = 1,875 - 1,500 = Rs 375, which matches the given extra interest. So the principal is confirmed as correct.

Why Other Options Are Wrong:

• Rs 4,750, Rs 4,500, and Rs 3,750 would produce smaller annual interest and therefore a different extra amount than Rs 375.
• Only Rs 5,000 yields exactly Rs 375 as the extra simple interest for one additional year at 7.5%.

Common Pitfalls:
Candidates sometimes overcomplicate the problem by calculating total interest for both time periods instead of directly using the idea that the difference is the one year interest. Others may incorrectly treat 7.5% as 75% or misplace the decimal. It is important to remember that simple interest grows proportionally with time, making such problems ideal for using the concept of incremental interest over additional years.

Final Answer:
The initial principal amount invested was Rs 5,000.