The simple interest on a principal of Rs 400 for 10 years amounts to Rs 280. What is the annual rate of simple interest (per annum) charged by the lender?

Introduction / Context:

This question checks your understanding of simple interest, one of the most basic and frequently tested topics in aptitude exams. You are given the principal amount, the time in years, and the total simple interest earned. From this, you must determine the annual rate of interest. It is a direct formula-based question and is ideal for practicing percentage and interest calculations.

Given Data / Assumptions:

• Principal P = Rs 400.
• Time T = 10 years.
• Simple interest SI = Rs 280.
• Rate of interest per annum is R% and needs to be found.
• The interest is simple interest, not compound interest.

Concept / Approach:

The standard simple interest formula is SI = (P * R * T) / 100. When simple interest, principal, and time are known, we can rearrange this formula to find the rate R. This involves basic algebra and careful substitution of the values given in the question. Once R is computed, we interpret it as a percentage per annum.

Step-by-Step Solution:

Verification / Alternative check:

We can verify by recalculating the simple interest using R = 7%. Using SI = (400 * 7 * 10) / 100, we get SI = (400 * 70) / 100 = 28000 / 100 = 280. This exactly matches the given simple interest amount, confirming that the rate is correct.

Why Other Options Are Wrong:

• 8%: At 8%, SI would be (400 * 8 * 10) / 100 = 320, which is higher than 280.
• 5%: At 5%, SI would be (400 * 5 * 10) / 100 = 200, which is less than 280.
• 6%: At 6%, SI would be (400 * 6 * 10) / 100 = 240, still less than 280.
• 7.5%: At 7.5%, SI would be (400 * 7.5 * 10) / 100 = 300, which does not match the given interest.

Common Pitfalls:

Learners sometimes forget to divide by 100 in the formula or mix up the relationship between rate and time. Another error is to miscalculate the multiplication 400 * 10 or to mistakenly treat 10 years as 10 months. To avoid mistakes, always write the formula clearly, substitute values systematically, and simplify gradually instead of doing all steps mentally.

Final Answer:

The annual rate of simple interest is 7%.