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Simple & Compound Interest for CAT: Formulas, Weightage & Question Types

Compounding, simple against compound, instalments, and a sum split across rates.

Simple & Compound Interest formula sheet

Everything CAT needs from Simple & Compound Interest, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place. PP is the principal, rr the annual rate in per cent, tt the time in years.

Simple interest — the same amount every year

InterestSI=Prt100\text{SI} = \dfrac{Prt}{100}
AmountA=P(1+rt100)A = P\left(1+\dfrac{rt}{100}\right)
Shapean arithmetic progression — equal steps

Compound interest — the same factor every year

AmountA=P(1+r100)tA = P\left(1+\dfrac{r}{100}\right)^{t}
InterestCI=A−P\text{CI} = A - P
Shapea geometric progression — equal multipliers

Compounding more often

kk times a yearA=P(1+r100k)ktA = P\left(1+\dfrac{r}{100k}\right)^{kt}
Half-yearlyrate halves, periods double: (1+r200)2t\left(1+\dfrac{r}{200}\right)^{2t}
Effective annual rate, half-yearly(1+r200)2−1\left(1+\dfrac{r}{200}\right)^2 - 1
6% half-yearly is really6.09%6.09\% a year

The gap between them

Over 2 yearsCI−SI=P(r100)2\text{CI} - \text{SI} = P\left(\dfrac{r}{100}\right)^2
Over 3 yearsCI−SI=P(r100)2(3+r100)\text{CI} - \text{SI} = P\left(\dfrac{r}{100}\right)^2\left(3+\dfrac{r}{100}\right)
Over 1 yearthey are equal

Year-on-year interest under CI

Each year's interestis (1+r100)\left(1+\dfrac{r}{100}\right) times the previous year's
So two consecutive yearsgive the rate directly, by division
And two amounts nn years apartgive (1+r100)n\left(1+\dfrac{r}{100}\right)^n by division

Repaying by instalments

Each instalment II paid after nn years is worthI(1+r100)n\dfrac{I}{\left(1+\frac{r}{100}\right)^{n}} today
So a loan PP repaid in two equal instalmentsP=I1+r100+I(1+r100)2P = \dfrac{I}{1+\frac{r}{100}} + \dfrac{I}{\left(1+\frac{r}{100}\right)^2}
A part-payment mid-loangrow the balance to that date, subtract the payment, then grow what is left

The 6 Simple & Compound Interest question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

  1. 01

    One sum split across several rates

  2. 02

    Compounding, often half-yearly

  3. 03

    Simple against compound

  4. 04

    A loan repaid in instalments

  5. 05

    Consecutive years divide to give the rate

  6. 06

    Two investors, balances compared

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Simple & Compound Interest in CAT: quick answers

How many Simple & Compound Interest questions come in CAT Quant?
About 0.9 questions in a 22-question Quant section, worth roughly 3 marks. Simple & Compound Interest appeared in 19 of the 24 CAT papers from 2017 to 2025, 20 questions in all, which ranks it 12 of 25 Quant chapters.
Are Simple & Compound Interest questions in CAT MCQ or TITA?
55% of the Simple & Compound Interest questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Simple & Compound Interest questions does CAT ask?
CAT keeps returning to 6 question shapes in Simple & Compound Interest: One sum split across several rates; Compounding, often half-yearly; Simple against compound; A loan repaid in instalments; Consecutive years divide to give the rate; Two investors, balances compared.

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