Question
A sum of ₹5000 is invested at an annual interest rate of 8% for 3 years. Find the Simple Interest earned.
Solution — Step by Step
Principal (P) = ₹5000, Rate (R) = 8% per annum, Time (T) = 3 years.
We need: Simple Interest (SI).
The Simple Interest formula is:
This formula works because R% means R per 100 per year. So for T years, the interest on ₹P is P × R × T / 100.
Numerator: 5000 × 8 = 40000, then 40000 × 3 = 1,20,000.
Simple Interest = ₹1200
Amount = Principal + SI = 5000 + 1200 = ₹6200
Board exams frequently ask for Amount alongside SI, so always compute both.
Why This Works
The key insight is what “8% per annum” actually means: for every ₹100, the bank pays ₹8 every year. So on ₹5000, the yearly interest is 5000 × 8/100 = ₹400.
Over 3 years, that’s simply 400 × 3 = ₹1200. The formula PRT/100 is just this logic packed into one expression.
Notice that in Simple Interest, the interest amount is the same every year — ₹400 each year in this case. That’s what makes it “simple”. Compound interest changes this, but that’s a Class 9 story.
Alternative Method
Unitary method — useful if you’re uncomfortable with the formula.
Step 1: Interest on ₹100 for 1 year = ₹8 (that’s what 8% means).
Step 2: Interest on ₹1 for 1 year = 8/100 = ₹0.08.
Step 3: Interest on ₹5000 for 1 year = 5000 × 0.08 = ₹400.
Step 4: Interest for 3 years = 400 × 3 = **₹1200**.
Same answer, different route. The formula is faster, but this method shows you why the formula exists.
Common Mistake
The most common error is forgetting to divide by 100 — writing SI = P × R × T instead of SI = PRT/100. This gives ₹1,20,000 instead of ₹1200, which is clearly absurd (you’d earn more than 20 times your principal!). Always sanity-check: SI should be a fraction of P, not a multiple of it.
Quick mental check: at 8% per year for 3 years, you earn 8 × 3 = 24% of the principal. So SI = 24% of ₹5000 = 5000 × 24/100 = ₹1200. This percentage shortcut saves time in MCQ rounds.