Simple & Compound Interest

Principal, rate, time, interest and amount; simple interest formulas and problems (finding P, R, T; doubling and multiple times; changes in rate); compound interest — annual, half-yearly, quarterly and monthly compounding, amount formula, effective rate; difference between CI and SI for 2 and 3 years; compound interest with different rates in successive years; fractional years; instalments (equal annual instalments under SI and CI); depreciation and growth as compound interest; population problems; rule of 72 approximation — with fully worked examples.

Simple & Compound Interest

CIVILGYAN TEST SERIES · civilgyantests.com — free study notes for civil engineering exams

📑 Contents (7 sections)

Last reviewed 16 Sept 2026 · 5 min read

Basic terms

Term	Meaning
Principal (P)	Money borrowed or invested
Rate (R)	Interest per ₹ 100 per year (% per annum)
Time (T or n)	Period (years)
Interest (I)	Extra money paid/earned
Amount (A)	Principal + interest

Simple interest (SI)

Interest is calculated only on the original principal.

FormulaSimple interest

S I = \frac{P \times R \times T}{100}, A = P + S I = P (1 + \frac{R T}{100})

P = \frac{100 \times S I}{R T}, R = \frac{100 \times S I}{P T}, T = \frac{100 \times S I}{P R}

A sum becomes n times in T years at SI: $R \times T = 100 (n - 1)$
SI is the same every year (linear growth)

Compound interest (CI)

Interest is added to the principal at the end of each period, and interest earns interest.

FormulaCompound interest

Annual compounding:

A = P (1 + \frac{R}{100})^{n}, C I = A - P

Half-yearly: rate $R /2$ , periods $2 n$ ; quarterly: rate $R /4$ , periods $4 n$ ; monthly: rate $R /12$ , periods $12 n$ Different rates in successive years: $A = P (1 + \frac{R _{1}}{100}) (1 + \frac{R _{2}}{100}) (1 + \frac{R _{3}}{100})$ Fractional years (e.g. $2 \frac{1}{4}$ years): $A = P (1 + \frac{R}{100})^{2} (1 + \frac{R /4}{100})$ Effective annual rate for compounding k times a year: $[(1 + \frac{R}{100 k})^{k} - 1] \times 100$

CI vs SI differences

FormulaDifference between CI and SI

2 years: $C I - S I = P (\frac{R}{100})^{2}$
3 years: $C I - S I = P (\frac{R}{100})^{2} (3 + \frac{R}{100})$

For the first year (annual compounding), CI = SI.
CI of successive years grows by a factor of $(1 + R /100)$ — second-year CI = first-year CI × $(1 + R /100)$ .

Doubling and multiples

At CI, if a sum doubles in t years, it becomes 4 times in 2t, 8 times in 3t years.
Rule of 72 (approximation): years to double ≈ $72/ R$ .

Downloaded from civilgyantests.com · Not for resale. Verify every code clause and date against the official source.

This chapter is in the syllabus of

Open an exam to see where this chapter sits in its syllabus, and to practise it.

AAI Junior Executive (Civil)AAI Manager (Civil)RRB JE CBT-1 NTPC NGEL Engineer Civil IOCL Graduate Engineer Civil MbPA AEE & EE Civil DSSSB AE Civil DSSSB JE Civil NCRTC Supervisor Civil PSSSB JE Civil MP Vyapam Sub Engineer Civil

✅ Free — no sign-up needed

How ready are you for Quantitative Aptitude?

Ten questions from the real syllabus, about five minutes. You will see your score and which subject is holding you back — before you create any account.

10 questions · no timer · no payment