Simple and Compound Interest — Study Notes

Overview

Interest problems appear in every UP Police Constable exam and typically contribute 2–4 questions. This is a scoring topic because the formulas are straightforward and questions follow predictable patterns. Mastering Simple Interest (SI) and Compound Interest (CI) — especially compounding annually and half-yearly — is essential. Additionally, instalment-based questions test whether you can apply interest formulas in multi-step scenarios. Unlike topics requiring lengthy calculations, interest problems can be solved quickly if you know the core formulas and can identify which one applies. Focus on recognising the problem type, selecting the right formula, and executing calculations accurately within exam time constraints.

The key distinction: SI remains constant each year because interest is calculated only on the principal, while CI grows because interest itself earns interest in subsequent periods. Questions may ask you to find principal, rate, time, or the difference between CI and SI. Instalment problems require you to reverse-calculate the present value of future payments. This topic rewards methodical practice and formula recall.

Key Concepts

• **Simple Interest (SI)** — Interest calculated only on the original principal throughout the loan/investment period. The interest amount stays the same every year.
• **Compound Interest (CI)** — Interest calculated on principal plus accumulated interest from previous periods. The interest amount increases each period.
• **Principal (P)** — The initial amount borrowed or invested.
• **Rate (R)** — Annual interest rate expressed as a percentage per annum.
• **Time (T)** — Duration of the loan or investment, typically in years. For half-yearly compounding, adjust both rate and time.
• **Amount (A)** — Total money at the end, which equals Principal + Interest. For SI: A = P + SI. For CI: A is calculated directly using the CI formula.
• **Compounding frequency** — Annually means interest is added once per year. Half-yearly means twice per year (divide rate by 2, multiply time by 2). Quarterly means four times per year (divide rate by 4, multiply time by 4).
• **Difference between CI and SI** — For the same principal, rate and time, CI is always greater than SI (except for 1 year, when they're equal). The difference grows with time and is a common exam question.

Formulas / Key Facts

**Simple Interest:**

• SI = (P × R × T) / 100
• Amount = P + SI = P(1 + RT/100)
• P = (SI × 100) / (R × T)
• R = (SI × 100) / (P × T)
• T = (SI × 100) / (P × R)

**Compound Interest (Annual Compounding):**

• A = P(1 + R/100)^T