Maharashtra TET – Quantitative Aptitude
Topic: Simple & Compound Interest
Target Audience: Candidates preparing for the Maharashtra Teacher Eligibility Test (TET).
Duration of the topic: 10‑12 minutes of focused study.
1. Simple Explanation
| Concept | What it is | When it is used | Formula |
|---|---|---|---|
| Simple Interest (SI) | Interest earned only on the principal amount, not on previously earned interest. | Short‑term loans, deposits, or any situation where interest is calculated once. | SI = P × R × T / 100 |
| Compound Interest (CI) | Interest earned on the principal plus on any interest that has been added to the account (i.e., interest is reinvested). | Long‑term savings, investments, loans where interest is added periodically. | CI = P × (1 + R/100)ⁿ – P (per compounding period) |
- P – Principal (initial amount)
- R – Annual rate of interest (in %)
- T – Time period (in years for SI; number of compounding periods for CI)
- n – Number of compounding periods in a year (e.g., 4 for quarterly, 12 for monthly)
- A – Amount after interest (A = Principal + Interest)
2. Key Points to Remember
| # | Key Point | Quick Tip |
|---|---|---|
| 1 | SI is linear – Interest increases proportionally with time. | Use the straight‑line formula SI = PRT/100. |
| 2 | CI is exponential – Interest grows faster over time. | Small changes in rate or compounding frequency produce large differences. |
| 3 | Compounding frequency matters – More frequent compounding → higher CI. | 4× (quarterly) > 2× (semi‑annual) > 1× (annual). |
| 4 | Effective annual rate (EAR) | EAR = (1 + R/n)ⁿ – 1 (use when rate is quoted nominally). |
| 5 | Time unit consistency | Convert all terms to the same unit (years or days) before plugging into the formula. |
| 6 | Partial periods | Use the formula for partial years: SI = P × R × (t/365) / 100 for days. |
| 7 | Compound interest on a deposit | A = P × (1 + r)^n where r = R/100 and n = number of periods. |
| 8 | Loan repayment | For an EMI loan, use the amortization formula (not covered in basic TET). |
| 9 | Common shortcuts |
- For SI,
SI = P × R × T / 100. - For CI,
A = P × (1 + R/100)^T(if compounding once per year). | |
3. Worked Example
Problem (TET style):
A student deposits ₹10,000 in a bank that pays 8% per annum compounded semi‑annually. How much will he have after 3 years?
Solution Steps
-
Identify the variables
- Principal, ( P = ₹10,000 )
- Nominal rate, ( R = 8% ) per annum
- Compounding frequency, ( n = 2 ) (semi‑annual)
- Time, ( T = 3 ) years
-
Compute the per‑period rate
[ r = \frac{R}{n} = \frac{8}{2} = 4% = 0.04 ] -
Compute the total number of periods
[ N = n \times T = 2 \times 3 = 6 \text{ periods} ] -
Apply the compound interest formula
[ A = P \times (1 + r)^N ] [ A = 10,000 \times (1 + 0.04)^6 ] -
Calculate
[ (1 + 0.04)^6 = 1.04^6 \approx 1.2653 ] [ A \approx 10,000 \times 1.2653 = ₹12,653 ] -
Interpret
After 3 years, the student will have ₹12,653 in the account.
Quick Verification
- Simple Interest would have been:
( SI = 10,000 \times 8 \times 3 / 100 = ₹2,400 )
Amount would be ( 10,000 + 2,400 = ₹12,400 ) – slightly less than CI, confirming compounding advantage.
4. Quick Revision Summary
| Concept | Formula | Quick Check |
|---|---|---|
| SI | SI = P × R × T / 100 |
Linear – double time → double interest. |
| CI (annual) | A = P × (1 + R/100)^T |
Exponential – small rate → large growth over many years. |
| CI (n‑times per year) | A = P × (1 + R/(100·n))^(nT) |
More compounding → higher A. |
| Effective Rate | EAR = (1 + R/n)^n – 1 |
Use when comparing nominal rates. |
| Partial Periods | SI = P × R × (t/365) / 100 |
Convert days → years. |
- Remember:
- Keep units consistent.
- For quick mental math, round the per‑period rate (e.g., 4% ≈ 0.04).
- Use the “rule of 72” for rough CI doubling time:
Doubling Time ≈ 72 / R.
Final Tip for TET
- Practice: Solve at least 5 problems of each type (SI & CI) with varying compounding frequencies.
- Speed: Memorize the core formulas; for TET, you’ll often have 1–2 minutes per question.
- Accuracy: Double‑check units and rounding;