Simple & compound interest: Quantitative Aptitude Notes for Lakshadweep Patwari / Lekhpal

Simple & Compound Interest – Study Notes

(For Lakshadweep Patwari / Lekhpal – Quantitative Aptitude)

1. Simple Explanation

Concept	What it means	When it is used
Simple Interest (SI)	Interest earned only on the original principal.	Short‑term loans, savings at fixed rate, when the rate is quoted per annum.
Compound Interest (CI)	Interest earned on the principal and on the interest that has already accumulated.	Savings, loans with periodic compounding (annually, semi‑annually, quarterly, monthly, daily).
Rate (r)	Annual rate of interest expressed as a percentage.
Time (T)	Number of years (or fraction of a year) the money is invested/borrowed.
n	Number of times interest is compounded in one year (n = 1, 2, 4, 12, 365, …).
Principal (P)	The initial amount of money.
Maturity Value / Amount (A)	Total amount after interest is added.
Interest (I)	The extra money earned or paid.

Key idea – In simple interest the “interest on interest” never happens; in compound interest it does (once per compounding period).

2. Key Points & Formulas

Type	Formula	Explanation
Simple Interest	`SI = P × R × T / 100`	`P` = principal, `R` = annual rate, `T` = time in years.
Amount (A)	`A = P + SI = P (1 + R T / 100)`	Final amount after simple interest.
Compound Interest	`CI = P × [(1 + r/n)^(nT) – 1]`	`r` = annual rate in decimal (e.g., 8 % → 0.08).
Amount (A)	`A = P × (1 + r/n)^(nT)`	Final amount after compound interest.
Effective Annual Rate (EAR)	`EAR = (1 + r/n)^n – 1`	Gives the annual yield if compounded `n` times.
Continuous Compounding	`A = P × e^(rT)`	`e` ≈ 2.71828.
Rule of 72	`Years to double ≈ 72 ÷ R`	Quick estimate of doubling time for simple interest.
Present Value (Discount)	`PV = A / (1 + r/n)^(nT)`	Value today of a future amount `A`.

Common Variations

Scenario	Formula
Interest compounded semi‑annually	`n = 2`
Quarterly	`n = 4`
Monthly	`n = 12`
Daily	`n = 365`
Discount on a future amount	`PV = A / (1 + r) * T` (simple discount)

3. Worked Example

Problem

A person deposits ₹10,000 in a bank that pays 8 % per annum compounded quarterly for 3 years.
What will be the maturity amount? What is the compound interest earned?

Step‑by‑step

Identify variables
- Principal P = ₹10,000
- Annual rate r = 8 % = 0.08 (decimal)
- Time T = 3 years
- Compounding frequency n = 4 (quarterly)
Compute the factor
[ (1 + r/n)^{nT} = \left(1 + \frac{0.08}{4}\right)^{4 \times 3} = \left(1 + 0.02\right)^{12} = 1.02^{12} ]
Calculate 1.02^12
- Using a calculator: 1.02^12 ≈ 1.268241.
Find the maturity amount A
[ A = P \times 1.268241 = 10,000 \times 1.268241 ≈ ₹12,682.41 ]
Find the compound interest earned
[ CI = A - P = 12,682.41 - 10,000 = ₹2,682.41 ]

Answers

Quantity	Value
Maturity Amount (`A`)	₹12,682.41
Compound Interest (`CI`)	₹2,682.41

Quick Check

Formula used: A = P × (1 + r/n)^(nT)
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