CAT Quant · Study & Practice

Compound Interest

AreaArithmetic DifficultyModerate CAT weightage1–3 questions (directly + inside growth/depreciation, instalments and DI)

Compound interest is the engine behind almost every "growth over time" question CAT can throw at you — from money in a fixed deposit to a city’s population, a startup’s revenue, or a machine losing value. The single idea is that interest itself earns interest: at the end of each period the interest is added to the principal, and the next period’s interest is computed on this larger amount. That one change from simple interest makes the amount grow as a geometric progression, A = P(1+r/100)ⁿ, rather than a straight line. CAT does not reward students who plug into the formula blindly; it rewards those who think in multipliers (a 10% rate is just ×1.1 per year), who can switch the compounding to half-yearly or quarterly without panic, and who know the tidy two-year and three-year shortcuts for the gap between CI and SI. This chapter builds that fluency: annual compounding and the multiplier mindset, faster non-annual compounding, the symmetry between growth and depreciation (and population growth), and finally the precise CI−SI relationships that turn a 90-second problem into a 20-second one. Every section pairs the concept with the fastest CAT method and the traps that quietly cost marks.

Topics

1 Annual Compounding 4 worked · 5 practice · 8-Q test Start → 2 Half-Yearly & Quarterly 4 worked · 5 practice · 8-Q test Start → 3 Growth & Depreciation 4 worked · 5 practice · 8-Q test Start → 4 SI vs CI 4 worked · 5 practice · 8-Q test Start →

⚡ CAT shortcuts & speed methods

The fastest ways to crack this chapter under time pressure — the techniques that separate a 95+ percentiler from the rest.

  • Think in multipliers, not powers: 10% = ×1.1, 25% = ×5/4, 12.5% = ×9/8, 20% = ×6/5. Chain them year by year.
  • Non-annual compounding: halve the rate AND double the periods (half-yearly), quarter the rate AND quadruple the periods (quarterly).
  • CI − SI for 2 years = P(r/100)² — it is just the interest earned on the first year’s interest.
  • CI − SI for 3 years = P(r/100)²·(3 + r/100). Use it to back out P or r from one difference.
  • Depreciation = compound interest with a minus sign: value = P(1 − r/100)ⁿ (reducing-balance).
  • For "value n years ago", DIVIDE by (1 ± r/100)ⁿ; for mixed years, just chain the up/down multipliers.

⚠️ Common mistakes & traps

CAT is designed so that careless errors here cost you marks. Internalise each trap before the exam.

  • For half-yearly, changing only the rate (to r/2) but forgetting to double the time (to 2n), or vice versa.
  • Treating CI and SI as equal beyond year 1 — they match only for the first year.
  • Adding successive growth percentages instead of multiplying the multipliers (10% then 10% ≠ 20%, it is 21%).
  • Applying depreciation on the original cost each year instead of on the reduced (written-down) value.
  • Using the 2-year shortcut P(r/100)² for a 3-year difference — the 3-year formula has the extra (3 + r/100) factor.

📈 CAT exam insight & PYQ analysis

In CAT and XAT, compound interest appears as 1–2 focused questions and often hides inside growth, depreciation or instalment problems rather than as a textbook "find the CI" prompt. The recurring patterns are: the CI−SI difference (2- and 3-year), finding the rate or time when a sum grows by a clean ratio (so the answer is a perfect power like 1.21 or 1.331), half-yearly/quarterly switches, and reducing-balance depreciation of assets. Difficulty is Moderate; speed comes from multiplier thinking and from spotting that the given amounts are nice powers. SNAP and NMAT lean slightly more computational, so the shortcut formulas pay off most there.

🎴 Flashcards — instant recall

Tap a card to reveal the answer. Drill these until they are automatic.

Amount with annual compounding?Tap to reveal
A = P(1 + r/100)ⁿ
Compound interest formula?Tap to reveal
CI = P[(1 + r/100)ⁿ − 1]
Half-yearly compounding amount?Tap to reveal
A = P(1 + r/200)^(2n)
Quarterly compounding amount?Tap to reveal
A = P(1 + r/400)^(4n)
CI − SI for 2 years?Tap to reveal
P(r/100)²
CI − SI for 3 years?Tap to reveal
P(r/100)²·(3 + r/100)
Depreciation (value falls r%/yr)?Tap to reveal
A = P(1 − r/100)ⁿ
Effective rate of 10% compounded half-yearly?Tap to reveal
10.25% (1.05² − 1)
Multiplier for a 25% rate?Tap to reveal
×5/4
Do CI and SI ever match?Tap to reveal
Yes — only for the first year
A sum doubles in 5 yrs at CI; when is it 4×?Tap to reveal
10 years (4 = 2²)
"Value n years ago" — multiply or divide?Tap to reveal
Divide by (1 ± r/100)ⁿ

📌 Quick revision

Compound interest adds each period’s interest to the principal, so A = P(1+r/100)ⁿ and CI = A − P. For half-yearly use r/2 over 2n periods; for quarterly use r/4 over 4n — change both rate and time. The same formula models population growth, and with a minus sign it models reducing-balance depreciation, value = P(1−r/100)ⁿ. The high-value CAT shortcuts are CI − SI = P(r/100)² for 2 years and P(r/100)²·(3 + r/100) for 3 years. Think in multipliers, chain them for mixed up/down years, divide to go back in time, and never add successive growth percentages.

Chapter test

📝 Compound Interest — Chapter Test
25 fresh questions · timed · full solutions
Start chapter test →
📊 My CAT analytics
Track scores, accuracy by topic and progress over time.
View analytics →

🏆 Vidaara CAT success checklist

You have truly mastered Compound 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 checkpointTarget
Concept theory & formulas understood100%
Topic practice sets attempted (4 topics)4/4
Best topic-test score— → 80%+
Chapter test score— → 80%+
Flashcards drilled to instant recall12 cards