Simple and Compound Interest — Study Notes

Overview

Simple and Compound Interest is a high-scoring topic in SOF IMO that connects everyday banking and finance with mathematical computation. Students must master the formulas for SI and CI, understand the difference between them, and solve multi-step word problems involving principal, rate, time, and amount. This topic frequently appears in the Everyday Mathematics section and occasionally in the Achievers Section when combined with other concepts like profit-loss or time-work.

The key challenge is not just applying formulas but interpreting real-world scenarios: loans, deposits, recurring payments, and instalment schemes. Problems may involve finding any unknown variable (principal, rate, time, or amount), comparing SI and CI on the same sum, or breaking down payments into instalments. Strong arithmetic and algebraic manipulation skills are essential.

Expect 2–4 questions directly on this topic in the exam, with marks ranging from straightforward one-step calculations to multi-layered HOTS problems worth 3–4 marks each.

Key Concepts

• **Simple Interest (SI)** is calculated only on the original principal for the entire period. The interest earned each year remains constant.

• **Compound Interest (CI)** is calculated on the principal plus accumulated interest from previous periods. Money "grows on itself," leading to exponential growth.

• **Amount (A)** is the total sum returned at the end of the period: Amount = Principal + Interest.

• **Rate (R)** is always expressed as a percentage per annum unless stated otherwise (half-yearly, quarterly compounding changes the effective rate).

• **Time (T)** is measured in years unless specified otherwise. For half-yearly compounding, double the time and halve the rate; for quarterly, quadruple the time and quarter the rate.

• **Instalment problems** require working backward: the present value of each instalment (discounted back to the start) must sum to the principal borrowed.

• **Difference between CI and SI** over the same period on the same principal at the same rate increases with time and can be used to find unknowns.

• When interest is compounded annually but time is fractional (e.g., 2.5 years), compound for whole years and apply simple interest for the remaining fraction.

Formulas / Key Facts

• **Simple Interest**: SI = (P × R × T) / 100

• **Amount under SI**: A = P + SI = P(1 + RT/100)