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Introduction
Many simple interest problems give the interest earned (SI), the rate (R), and the time (T), and ask for the original sum - the principal (P). Knowing how to reverse the SI formula is essential for loan, investment, and backward-calculation problems.
Pattern: Finding Principal (P)
Key concept: Rearrange SI = (P × R × T) / 100 to solve for P.
Formula:
P = (SI × 100) / (R × T)
Step-by-Step Example
Question
The simple interest earned on a sum for 3 years at 6% per annum is ₹540. Find the principal.
Options:
A. ₹2,500
B. ₹3,000
C. ₹3,500
D. ₹4,000
Solution
-
Step 1: Identify the given values
SI = 540, R = 6%, T = 3 years. -
Step 2: Write the rearranged formula
P = (SI × 100) / (R × T) -
Step 3: Substitute values
P = (540 × 100) / (6 × 3) -
Step 4: Simplify numerator and denominator
Denominator = 6 × 3 = 18
Numerator = 540 × 100 = 54,000 -
Step 5: Divide to get the principal
P = 54,000 ÷ 18 = 3,000 -
Final Answer:
₹3,000 → Option B -
Quick Check:
Yearly SI = (3,000 × 6)/100 = 180; for 3 years → 180 × 3 = 540 ✅
Quick Variations
1. SI given for fractional time (e.g., 2.5 years) - use T as decimal in formula.
2. SI given for months - convert months to years before substituting (e.g., 9 months = 0.75 year).
3. SI for multiple rates/time segments - compute total SI, then use overall R×T equivalent if applicable or split into parts and sum.
Trick to Always Use
- Step 1 → Always convert time to years (months → divide by 12).
- Step 2 → Rearrange formula clearly: P = (SI × 100) / (R × T).
- Step 3 → Simplify numerator and denominator stepwise before final division to avoid arithmetic errors.
Summary
- Use P = (SI × 100) / (R × T) to find the principal when SI, rate, and time are known.
- Ensure rate is in percent and time is converted to years.
- Always verify by recalculating SI using the found principal.
- Simplify numerator and denominator before division to avoid mistakes.
Example to remember:
SI = ₹540 at 6% for 3 years → Principal = ₹3,000.