Simple & compound interest: Quantitative Aptitude Notes for Lakshadweep TET (Teacher Eligibility)

Lakshadweep TET – Quantitative Aptitude

Topic: Simple & Compound Interest

Goal – Understand the fundamentals, memorize the key formulas, and be able to solve typical TET‑style questions quickly.

1. Simple Explanation

Concept	What it means	When it is used
Simple Interest (SI)	Interest calculated only on the original principal for the entire period.	Short‑term loans, savings accounts with flat rate, TET exam questions that ask for “simple interest.”
Compound Interest (CI)	Interest is added to the principal at regular intervals, so the next period’s interest is earned on a larger amount (principal + previous interest).	Long‑term savings, bank deposits, loans with compounding, typical TET questions involving “compound interest.”

Rule of thumb:

If the interest is calculated once at the end of the whole period → Simple.

If the interest is calculated repeatedly (annually, monthly, quarterly etc.) → Compound.

2. Key Points & Formulas

Item	Formula	Variables (as used in TET)	Notes
Simple Interest (SI)	`SI = P × R × T / 100`	`P` = principal, `R` = annual rate (%), `T` = time (years)	Use when interest is not added to the principal.
Maturity Value (Simple)	`A = P + SI`	`A` = amount after `T` years	Same as `A = P (1 + R T / 100)`
Compound Interest (CI)	`A = P (1 + R / n)^(nT)`	`n` = number of compounding periods per year	Most common form; if `n = 1` it reduces to simple interest.
Interest earned (CI)	`CI = A – P`	`A` = maturity value, `P` = principal	Gives total interest earned over the period.
Effective Annual Rate (EAR)	`EAR = (1 + R/n)^n – 1`	`EAR` = effective yearly rate	Useful for comparing rates with different compounding frequencies.
Time for doubling (Rule of 72)	`T ≈ 72 / R`	`T` in years	Approximation; works best for rates between 6–10 %.
Continuous compounding (optional)	`A = P e^(rT)`	`r` = annual rate expressed in decimal	Not usually required in TET but good to know.

3. Worked Example

Problem

A sum of ₹50 000 is invested at 8 % per annum compounded quarterly. How much will be the amount after 3 years?

Step‑by‑Step Solution

Identify variables
- P = 50,000
- R = 8 % → R/100 = 0.08
- n = 4 (quarterly compounding)
- T = 3 years
Plug into the compound amount formula

[ A = P \left(1 + \frac{R}{n}\right)^{nT} ] [ A = 50{,}000 \left(1 + \frac{0.08}{4}\right)^{4 \times 3} ]
Compute inside the parentheses

[ 1 + \frac{0.08}{4} = 1 + 0.02 = 1.02 ]
Compute exponent

[ nT = 4 \times 3 = 12 ]
Raise to the power

[ 1.02^{12} \approx 1.26824 ]
Multiply by principal

[ A \approx 50{,}000 \times 1.26824 = 63{,}412 ]
Result
- Amount after 3 years ≈ ₹63,412
- Interest earned = ₹63,412 – ₹50,000 = ₹13,412

Answer – ₹63 412 (approx.)

4. Quick Revision Summary

Topic	Formula	Quick Tips
Simple Interest	`SI = PRT/100`	Think of it as “flat” – no compounding.
Simple Maturity	`A = P(1 + RT/100)`	Add SI to P.
Compound Interest	`A = P(1 + R/n)^(nT)`	Replace n = 1 → simple interest.
Compound Interest Earned	`CI = A – P`	Total earned over the period.
Effective Rate	`EAR = (1 + R/n)^n – 1`	Compare different n’s.
Rule of 72	`T ≈ 72/R`	Quick doubling time estimate.
Continuous	`A = P e^(rT)`	Rarely needed; remember e ≈ 2.71828.

Practice Checklist

Identify whether the problem deals with simple or compound interest.
Determine the compounding frequency n (annual, semi‑annual, quarterly, monthly).
Plug values into the correct formula.
Simplify step‑by‑step, double‑check exponents.
Round to the nearest rupee or paise as required.

Good luck with your Lakshadweep TET preparation! Keep revisiting these formulas until they become second nature.