At what annual rate of simple interest will a principal of Rs 415 grow to an amount of Rs 514 in 4 years?

Introduction / Context:
This question tests your ability to determine the rate of simple interest when the principal, total amount, and time period are known. It is a typical bank deposit or loan style problem in aptitude tests where small numerical inaccuracies can lead to selecting the wrong close option, so careful calculation is important.

Given Data / Assumptions:

• Principal, P = Rs 415.
• Final amount after 4 years, A = Rs 514.
• Time period, T = 4 years.
• Annual simple interest rate, R%, is unknown.
• Simple interest is assumed, not compound interest.

Concept / Approach:
The relationship between amount, principal, and simple interest is:
A = P + SIand simple interest is given by:
SI = (P * R * T) / 100First we find the interest by subtracting principal from amount, then use the simple interest formula to solve for the rate R. This involves straightforward algebra, but division must be done accurately to match the closest option given.

Step-by-Step Solution:
Step 1: Find the simple interest earned.SI = A - P = 514 - 415 = Rs 99Step 2: Use the simple interest formula for rate.SI = (P * R * T) / 10099 = (415 * R * 4) / 100Step 3: Simplify the expression.99 = (1660 * R) / 10099 = 16.6 * RStep 4: Solve for R.R = 99 / 16.6R is approximately 5.963855..., which is about 5.96%

Verification / Alternative check:
To verify, use R = 5.96% in the formula and check if the amount is close to Rs 514. Simple interest with R = 5.96% is:
SI = (415 * 5.96 * 4) / 100= (415 * 23.84) / 100= 9,898.6 / 100 ≈ 98.986This is approximately Rs 99, which brings the amount back to roughly Rs 514. This confirms that 5.96% is the correct rate when rounded to two decimal places.

Why Other Options Are Wrong:

• 4.58% and 4.98% give smaller interest and would not reach a total of Rs 514 in 4 years.
• 6.52% gives a slightly higher interest than Rs 99 and would overshoot the required amount.

Common Pitfalls:
Errors often occur when performing the division 99 / 16.6, especially if candidates round too early or misplace the decimal point. Some learners also forget that time is 4 years and may mistakenly use 1 year in the formula. Writing the steps clearly and using approximate decimal calculations only at the final stage helps maintain accuracy.

Final Answer:
The required annual rate of simple interest is approximately 5.96% per annum.