A lends an amount of 12500 to someone at simple interest and then in 4 years it is 15500. Find his interest rate.?

Appeared in: NORCET 6 mains-2024

Explanation

First, calculate the total simple interest earned over 4 years by subtracting the principal from the final amount (15500 - 12500 = 3000).
The formula for the rate of interest is R = (Simple Interest × 100) / (Principal × Time).
Plugging in the values: R = (3000 × 100) / (12500 × 4).
This simplifies to R = 300000 / 50000, which equals 6. Therefore, the interest rate is 6%.

Option A: A 3% rate would yield only 1500 in interest over 4 years (12500 × 0.03 × 4), not the required 3000.
Option B: A 4% rate would yield 2000 in interest over 4 years (12500 × 0.04 × 4), not 3000.
Option C: A 5% rate would yield 2500 in interest over 4 years (12500 × 0.05 × 4), not 3000.

Visual 1: Infographic: A visual breakdown of the simple interest formula (SI = PxRxT/100) showing how each component (Principal, Rate, Time) contributes to the final interest amount.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculating the rate of simple interest as background academic context rather than a clinical decision trigger.
While not a clinical skill, understanding basic financial calculations is a crucial life skill for personal finance management, such as planning savings, understanding loans, and managing income.
This skill is transferable to healthcare administration roles, where budgeting and financial planning are common tasks.
What if the interest was compounded annually? The calculation would be more complex, using the formula A = P(1 + R/n)^(nt), and the resulting rate would be different. For the same final amount, a compounded rate would be lower than the simple interest rate.

How to Approach the Question

First, identify all the given variables in the problem: Principal (P), Amount (A), and Time (T).
Calculate the Simple Interest (SI) by finding the difference between the final Amount and the initial Principal (SI = A - P).
Recall the formula for the Rate of interest: R = (SI × 100) / (P × T).
Substitute the known values into the formula and solve for R.
Compare the calculated rate with the given options to find the correct answer.

Concept Tested & Keywords

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Attempt every question from this paper in a timed mock, then review the full solution for each one.