Simple Interest (SI) is the interest calculated only on the original principal — never on the accumulated interest. Every year, the interest earned is the same fixed amount. Think of it like a daily wage job: you get the same pay every day regardless of how long you have been working. Contrast this with compound interest, where interest keeps adding to the base, like a snowball rolling downhill.
Here is the clearest way to see it: you deposit ₹1000 at 10% per year for 3 years. Under simple interest, you earn ₹100 every single year — year 1, year 2, year 3. Total interest = ₹300. The principal stays at ₹1000 throughout. That is the defining property.
The four variables you will always deal with:
The reason SI is a favourite in competitive exams is that it tests whether you can rearrange a single formula under time pressure. The formula itself is trivial. The challenge is reading the question carefully enough to plug in the right values — and manipulating it quickly when the unknown is R or T rather than SI.
In the Agniveer Army CEE, SI questions are direct. They rarely go beyond two-step problems. If you can do the basic SI = (P × R × T) / 100 confidently in both directions (finding SI, finding P, finding R, finding T), you will not drop a single mark here.
The master equation is:
And the amount formula:
From the SI formula, you get four working rearrangements — memorise all four, not just the first:
| Find | Formula | |------|---------| | SI | | | P | | | R | | | T | |
Look — when the question gives you Amount (A) and asks for SI, always subtract first: SI = A - P. Do not try to work backward from A directly.
A common Agniveer question type: "A sum doubles in N years. In how many years does it become M times?"
Here is the logic. If a sum doubles in N years, the SI in N years equals P (the principal itself). So:
Now, for the sum to become M times, the SI needed = (M - 1) × P. Use the same rate:
Shortcut result: If a sum doubles in N years at SI, it becomes M times in (M − 1) × N years.
Doubles in 8 years → becomes 5 times in (5 − 1) × 8 = 32 years. Done in 5 seconds.
When two amounts are invested at different rates for the same time period, calculate SI separately on each and add. There is no trick smarter than this — just do two clean multiplications and add.
Since T is common, you can factor it out: .
When someone borrows at rate and lends at rate (where ), their profit over time T is simply:
This is because both are applied to the same principal for the same time. You do not need to calculate two separate interests and subtract — one combined multiplication is enough.
This is a hybrid question that shows up in the PYQ set. The formula you need to know:
This is derived from the fact that CI for 2 years = and SI for 2 years = . Expand the CI expression and subtract SI — the extra term is exactly .
If you are given the difference and asked to find P:
Always check the time unit. If T is given in months, convert: T (years) = months / 12. If the rate is per month, either keep everything in months or convert to annual. Mixing units is the single biggest source of wrong answers in this topic.
Write the formula as a triangle: P × R × T at the top, 100 × SI at the bottom. Cover whatever you want to find — the remaining three form the expression. This is the same memory device used for speed-distance-time. Once you fix this visual in your head, you never need to re-derive. Cover SI → you see PRT/100. Cover P → you see (SI × 100)/(R × T). Standard working time without the triangle: 15-20 seconds of formula recall. With it: 3 seconds.
When a sum doubles in N years, it becomes M times in exactly (M − 1) × N years. This works because interest per year is constant (P/N), so every additional multiple of P takes exactly N more years. Example: doubles in 8 years → triples in 16, becomes 5× in 32, becomes 10× in 72. Standard method: derive rate first (100/N = 12.5%), then use T = SI×100/(P×R) — about 40 seconds. Pattern method: (5−1)×8 = 32 — under 5 seconds.
When a principal grows from P to A over T years, the total percentage growth = [(A−P)/P] × 100. Annual rate = total growth% / T years. Example: ₹6000 → ₹7200 in 2 years. Growth = 1200/6000 × 100 = 20%. Annual rate = 20/2 = 10%. This avoids writing the formula entirely. Standard method: set up SI = PRT/100 and solve algebraically — 30 seconds. This method: 10 seconds.
Instead of computing two interest amounts and subtracting, use: Profit = P × (R₂ − R₁) × T / 100. Example: borrow ₹8000 at 15%, lend at 18%, 3 years. Profit = 8000 × (18−15) × 3 / 100 = 8000 × 3 × 3 / 100 = 72000/100 = ₹720. Standard method (two separate calculations): 45 seconds. Rate-difference method: 15 seconds.
The difference between CI and SI for exactly 2 years is always P×R²/10000. If you know the difference and rate, isolate P instantly: P = Difference × 10000 / R². Example: difference = ₹225, R = 15%. P = 225 × 10000 / 225 = ₹10000. Standard method: write full CI expansion, expand, subtract SI term by term — 60 seconds minimum. Formula method: 10 seconds.
Read the question and immediately identify: what is the unknown (SI, P, R, or T)?
Step 1. Is Amount (A) given instead of SI? If yes, compute SI = A − P before anything else.
Step 2. Is the unknown SI? → Direct plug-in: (P × R × T) / 100. Done.
Step 3. Is the unknown T or R? → Use T = (SI × 100) / (P × R) or R = (SI × 100) / (P × T).
Step 4. Is the unknown P? → Use P = (SI × 100) / (R × T).
Step 5. Does the question say "doubles in N years, find time to become M times"? → Answer is (M − 1) × N. No formula needed.
Step 6. Two investments at different rates, same time? → Calculate SI separately, add.
Step 7. Borrow at one rate, lend at another? → Profit = P × (R₂ − R₁) × T / 100.
Step 8. CI vs SI difference for 2 years? → P × R² / 10000 = Difference.
Time units: if months are given, divide by 12 before applying the formula.
Why this question: This is the most direct application of the SI formula — the kind you should solve in under 20 seconds.
Solving path: P = 2500, R = 5, T = 3. SI = (2500 × 5 × 3) / 100 = 37500 / 100 = 375. No traps here — standard plug-in.
Why this question: Tests your ability to extract T when Amount is given — a very common question structure in Agniveer CEE.
Solving path: SI = 25800 − 15000 = 10800. Now use T = (SI × 100) / (P × R) = (10800 × 100) / (15000 × 12) = 1080000 / 180000 = 6 years. The trap is forgetting to subtract P from A first.
Why this question: Two-step problem — find rate from first scenario, apply to second. Tests whether you stay organised under pressure.
Solving path: SI on ₹6000 for 2 years = 7200 − 6000 = 1200. Rate = (1200 × 100) / (6000 × 2) = 10%. Now SI on ₹9000 for 3 years = (9000 × 10 × 3) / 100 = 2700. Answer: ₹2700.
Why this question: Tests rate-finding. Many candidates stumble because the SI is not a round number — use exact arithmetic, not approximation.
Solving path: SI = 2662 − 2000 = 662. R = (662 × 100) / (2000 × 3) = 66200 / 6000 ≈ 11.03%. The options say 11% — match to the nearest. The question is testing recognition that R is "approximately 11%".
Why this question: The "doubles in N years" pattern — if you know the (M−1)×N rule, this is a 5-second question.
Solving path: Doubles in 8 years → (M−1)×N = (5−1)×8 = 32 years. The longer route: R = 100/8 = 12.5%. For 5P, SI needed = 4P. T = (4P × 100) / (P × 12.5) = 400/12.5 = 32. Both paths reach 32 years.
Using A instead of SI in the formula. The formula is SI = PRT/100, not A = PRT/100. When the question gives Amount, always subtract P first to get SI. This is the most frequent error.
Mixing time units. If T is given in months, you must divide by 12 before using the annual rate. A question saying "3 months at 12% per annum" means T = 3/12 = 0.25, not T = 3.
Treating "becomes M times" as SI = M×P. If a sum "becomes 5 times", the Amount = 5P, so SI = 4P (not 5P). The extra multiple is Amount, not interest.
Forgetting that rate difference drives re-lending profit. Students often calculate both interest amounts separately and subtract — correct, but slow. The rate-difference shortcut P×(R₂−R₁)×T/100 is faster and less error-prone.
Applying the CI−SI formula blindly to 3-year differences. The formula P×R²/10000 is valid only for exactly 2 years. For 3 years the expression is different. If a question asks for 3-year CI vs SI difference, expand fully — do not use this shortcut.
Not checking which variable is unknown before calculating. A common exam-hall panic move: plugging numbers in and computing the same unknown the question asked for (e.g., computing SI when the question asked for Rate). Read the question, identify the unknown, then pick the right rearrangement.