📚 Tripura PSC – Quantitative Aptitude
Topic: Simple & Compound Interest
Why it matters
PSC exams routinely ask for quick mental calculations of interest. Mastering these concepts saves time and guarantees a solid foundation for related questions (e.g., present value, annuities, tax deductions on interest).
1️⃣ Simple Explanation
| Concept | Definition | When to Use |
|---|---|---|
| Simple Interest (SI) | Interest calculated only on the original principal. | Short‑term loans, savings accounts with annual interest. |
| Compound Interest (CI) | Interest calculated on the principal plus any accumulated interest. | Long‑term investments, loans with periodic compounding (monthly, quarterly). |
- SI grows linearly.
- CI grows exponentially (interest on interest).
2️⃣ Key Points & Formulas
| Quantity | Formula | Notes |
|---|---|---|
| Simple Interest | ( SI = \dfrac{P \times R \times T}{100} ) | (P)=principal, (R)=rate per annum, (T)=time in years |
| Total Amount (SI) | ( A = P + SI ) | (A)=amount after (T) years |
| Compound Interest | ( A = P \left(1 + \dfrac{R}{n}\right)^{nT} ) | (n)=compounding periods per year |
| Compound Interest (CI) | ( CI = A - P ) | |
| Annual Effective Rate (if compounding differs) | ( R_{\text{eff}} = \left(1+\dfrac{R}{n}\right)^n - 1 ) | Expressed as a percentage |
| Half‑Yearly, Quarterly, Monthly | Replace (n=2,4,12) respectively | |
| Time in Months | ( T_{\text{months}} = T_{\text{years}} \times 12 ) | Use when (T) is given in months |
| Present Value (PV) | ( PV = \dfrac{A}{\left(1+\dfrac{R}{n}\right)^{nT}} ) | For discounting future sums |
Quick Recap of Variables
| Symbol | Meaning |
|---|---|
| (P) | Principal (initial amount) |
| (R) | Annual nominal interest rate (in %) |
| (T) | Time period (in years or fractions of a year) |
| (n) | Compounding frequency per year |
| (A) | Amount after compounding |
| (SI) | Simple interest earned |
| (CI) | Compound interest earned |
3️⃣ Worked Examples
Tip: Convert every rate to decimal only once. Keep units consistent.
3.1 Simple Interest
Question:
A person deposited ₹50,000 in a savings account that offers 6 % simple interest per annum. What is the total amount after 3 years?
| Step | Calculation | Result |
|---|---|---|
| 1 | (SI = \dfrac{50,000 \times 6 \times 3}{100}) | (SI = 9,000) |
| 2 | (A = 50,000 + 9,000) | (A = 59,000) |
Answer: ₹59,000
3.2 Compound Interest (Annual)
Question:
₹12,000 is invested at 8 % per annum, compounded annually, for 4 years. Find the amount.
| Step | Calculation | Result |
|---|---|---|
| 1 | (A = 12,000 \left(1 + \dfrac{8}{100}\right)^{4}) | (A = 12,000 \times 1.08^{4}) |
| 2 | Compute (1.08^{4} = 1.36049) | |
| 3 | (A = 12,000 \times 1.36049 = 16,325.88) | ₹16,325.88 |
Answer: ₹16,325.88
3.3 Compound Interest (Quarterly)
Question:
₹20,000 is deposited at 6 % per annum, compounded quarterly, for 2 years. Find the compound interest earned.
| Step | Calculation | Result |
|---|---|---|
| 1 | (n = 4) (quarterly) | |
| 2 | (A = 20,000 \left(1 + \dfrac{6}{4 \times 100}\right)^{4 \times 2}) | |
| 3 | (A = 20,000 \left(1 + 0.015\right)^{8}) | |
| 4 | (1.015^{8} = 1.12660) | |
| 5 | (A = 20,000 \times 1.12660 = 22,532) | |
| 6 | (CI = A - P = 22,532 - 20,000 = 2,532) |
Answer: ₹2,532
3.4 Time in Months for Compound Interest
Question:
₹10,000 is invested at 5 % per annum, compounded monthly, for 18 months. Find the amount.
| Step | Calculation | Result |
|---|---|---|
| 1 | (n = 12) (monthly) | |
| 2 | (T = 18/12 = 1.5) years | |
| 3 | (A = 10,000 \left(1 + \dfrac{5}{12 \times 100}\right)^{12 \times 1.5}) | |
| 4 | (1 + \dfrac{5}{1200} = 1.0041667) | |
| 5 | Exponent = (18) | |
| 6 | (1.0041667^{ |