Simple Interest
Simple Interest is the cleanest entry point into the entire financial-mathematics block of CAT Quant. The idea is small but powerful: when you lend or borrow a principal, the interest is charged only on that original principal, every single period — it never gets added back to grow on itself. That one rule, SI = PRT/100, is all the machinery you need, yet it underpins a surprising number of exam questions: finding a missing rate or time, comparing two loans, splitting a sum into parts that earn different rates, working out equal annual instalments, and answering the favourite CAT staple "in how many years does a sum double, treble or grow n-fold?". Because the interest each year is constant, simple-interest situations are linear — the amount grows in a straight line — and that linearity gives you fast shortcuts that compound interest does not allow. This chapter builds the topic from the four core variables (Principal, Rate, Time, Interest) up to full CAT applications: instalments, mixed-rate splits, and doubling problems. Master it well and Compound Interest, the harder sibling, becomes far easier because you already own the vocabulary and the reverse-calculation habits.
Topics
⚡ CAT shortcuts & speed methods
The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.
- For "becomes n times" use R × T = (n − 1) × 100 — no principal needed (doubles ⇒ RT = 100, trebles ⇒ RT = 200).
- Yearly SI is constant: compute P×R/100 once, then multiply by the number of years instead of redoing PRT/100.
- Two amounts, two times: one year’s interest = (A₂ − A₁)/(T₂ − T₁); scale back to recover principal and rate.
- Convert time to years before plugging in — months ÷ 12, days ÷ 365 — rate is always per annum.
- For split-sum problems assign the whole as a clean value (or LCM of denominators) so each rate gives integer interest.
- In equal-instalment SI loans, earlier instalments carry extra interest: the first of n instalments accrues (n−1) more years.
⚠️ Common mistakes & traps
CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.
- Confusing the amount (P + SI) with the interest alone — "amounts to" includes the principal.
- Forgetting to convert months or days to a fraction of a year before applying SI = PRT/100.
- Using "doubles in T years" as if the rate were 100/(2T) — it is 100/T, because SI then equals the principal.
- Treating an instalment problem like a single lump sum and ignoring the extra interest earlier instalments accrue.
- Mixing up which part of a split sum carries which rate, or forgetting the two parts must add to the whole.
📈 CAT exam insight & PYQ analysis
🎴 Flashcards — instant recall
Tap a card to reveal the answer. Drill these until they are automatic.
📌 Quick revision
Chapter test
🏆 Vidaara CAT success checklist
You have truly mastered Simple Interest when you can tick every box below.
- Recall every formula in this chapter without looking them up
- Solve each topic’s practice set with at least 80% accuracy
- Use the chapter shortcuts to cut your solving time in half
- Spot and avoid every common trap listed above
- Score 80%+ on the timed chapter test
📋 Chapter mastery scorecard
Track where you stand. Aim for the target before moving to the next chapter.
| Skill checkpoint | Target |
|---|---|
| Concept theory & formulas understood | 100% |
| Topic practice sets attempted (3 topics) | 3/3 |
| Best topic-test score | — → 80%+ |
| Chapter test score | — → 80%+ |
| Flashcards drilled to instant recall | 12 cards |
Formula Reference Sheet
Core simple-interest relations
| Simple interest | SI = P × R × T / 100 |
|---|---|
| Amount (maturity value) | A = P + SI = P(1 + RT/100) |
| Principal from SI | P = 100 × SI / (R × T) |
| Rate from SI | R = 100 × SI / (P × T) |
| Time from SI | T = 100 × SI / (P × R) |
CAT power-tools
| Sum becomes n times in T years | R × T = (n − 1) × 100 |
|---|---|
| Yearly interest (a constant) | I per year = P × R / 100 |
| Equal annual instalment (loan, SI) | See instalment formula in SI Applications |
| Two amounts ⇒ principal & rate | Yearly interest = (A₂ − A₁)/(T₂ − T₁) |
| Average rate over split sums | Total SI / (Total P × Total T) × 100 |