Simple & compound interest: Quantitative Aptitude Notes for NIA Recruitment

📚 Study Notes – Simple & Compound Interest

(NIA Recruitment – Quantitative Aptitude)

1️⃣ Simple Explanation

Term	What it Means
Principal (P)	Initial amount of money invested or borrowed.
Rate of Interest (R)	Annual percentage at which interest is charged or earned.
Time (T)	Number of years (or fraction of a year) the money is invested/lent.
Simple Interest (SI)	Interest earned only on the principal, not on previously earned interest.
Compound Interest (CI)	Interest earned on the principal and on any accumulated interest from prior periods.

Why it matters
Simple interest is often used for short‑term loans or savings.
Compound interest is the real driver of long‑term wealth growth (e.g., in bank deposits, mutual funds, or loans).

2️⃣ Key Points & Formulas

Concept	Formula	Notes
Simple Interest	`SI = P × R × T / 100`	R in % per year; T in years.
Simple Total Amount	`A = P + SI`	Equivalent to `A = P (1 + R × T / 100)`
Compound Interest (annual compounding)	`A = P (1 + R/100)^T`	T can be fractional (e.g., 6 months → 0.5).
Compound Total Amount	`CI = A – P`	If you need just the interest earned.
Number of Compounding Periods (n)	`n = T × m`	m = times interest applied per year (e.g., 4 for quarterly).
Compound Interest Formula (general)	`A = P (1 + R/(100m))^n`	For semi‑annual, quarterly, monthly, etc.
Effective Annual Rate (EAR)	`EAR = (1 + R/(100m))^m – 1`	Useful when comparing different compounding frequencies.
Rule of 72 (approximate doubling time)	`Doubling Time ≈ 72 / R`	R in percent.

Tip: Always convert percentages to decimals before plugging into formulas.

3️⃣ Worked Example

Problem

A ₹10,000 investment is made at an annual interest rate of 8%.

a) Calculate the simple interest for 3 years.
b) Calculate the compound interest for the same period, compounded quarterly.

Solution

a) Simple Interest

P = ₹10,000
R = 8%
T = 3 years
SI = P × R × T / 100
   = 10,000 × 8 × 3 / 100
   = 10,000 × 24 / 100
   = 2,400

Total amount
A = P + SI = 10,000 + 2,400 = ₹12,400.

b) Compound Interest (quarterly)

Convert rate to decimal per period
r = R / (100 × m) = 8 / (100 × 4) = 0.02
(2% per quarter)
Total number of periods
n = T × m = 3 × 4 = 12 quarters
Compound amount
A = P (1 + r)^n
A = 10,000 × (1 + 0.02)^12
A = 10,000 × (1.02)^12
A ≈ 10,000 × 1.26824 = 12,682.40
Compound interest earned
CI = A – P = 12,682.40 – 10,000 = ₹2,682.40

Result

Simple interest: ₹2,400

Compound interest (quarterly): ₹2,682.40
The compound interest is higher because interest is earned on previously accumulated interest.

4️⃣ Quick Revision Summary

Simple Interest
- SI = P × R × T / 100
- No compounding; linear growth.
Compound Interest
- Annual compounding: A = P (1 + R/100)^T
- General compounding: A = P (1 + R/(100m))^(T×m)
- Use n = T×m periods, r = R/(100m) per period.
Key Differences
- SI: Interest only on principal.
- CI: Interest on principal and on previously earned interest.
Quick Checks
1. Convert R to decimal before use.
2. For quarterly/montly compounding, divide R by 4 or 12 respectively.
3. Remember to subtract principal from total amount if you need only the interest earned.
NIA Tip
- Practice by converting between SI and CI for the same P, R, T – it solidifies understanding of compounding effects.

✅ Practice Question

A sum of ₹5,000 is invested at 6% per annum.
Find the amount after 4 years if the interest is compounded monthly.

(Try solving it first, then check against your notes.)

Good luck with your NIA preparation! 🚀