Simple & Compound Interest
Quantitative Aptitude – SBI PO
Goal: Understand how money grows over time when you lend it or deposit it in a bank.
1️⃣ Simple Interest (SI)
What is it?
- Simple Interest is the extra money you earn (or owe) on the original amount, called Principal (P), for a certain time at a fixed rate.
Everyday Analogy
- Imagine you lend your friend ₹100 for 1 month at 10% per month.
After the month, you only get ₹10 extra (the interest), not more than that.
Formula
SI = (P × R × T) / 100
- P = Principal (original amount)
- R = Rate of interest per year (or per month, whatever unit you use)
- T = Time (in years or months, same unit as rate)
Tip: Keep the units consistent. If R is in % per year, T must be in years.
Tiny Example
| P | R | T | SI |
|---|---|---|---|
| ₹1,000 | 12% | 2 years | (1000×12×2)/100 = ₹240 |
- Total amount after 2 years: ₹1,000 + ₹240 = ₹1,240
2️⃣ Compound Interest (CI)
What is it?
- Compound Interest means the interest is added to the principal, and future interest is calculated on this new total.
It’s like a snowball: it gets bigger as it rolls.
Everyday Analogy
- You give a friend ₹100 at 10% per year.
After 1 year, they give you ₹10 back (interest).
The next year, you earn 10% on ₹110, not just on ₹100.
The interest “compounds” or grows.
Formula
A = P × (1 + R/100)ⁿ
CI = A – P
- A = Amount after n years
- n = Number of compounding periods (years, months, etc.)
- R = Rate per compounding period
Tiny Example
| P | R | n | A | CI |
|---|---|---|---|---|
| ₹1,000 | 12% | 2 years | 1000 × (1+12/100)² = ₹1,254.24 | ₹254.24 |
- Total after 2 years: ₹1,254.24
- Interest earned: ₹254.24 (more than simple interest)
3️⃣ Key Differences at a Glance
| Feature | Simple Interest | Compound Interest |
|---|---|---|
| Interest basis | Only on original Principal | On Principal plus previous interest |
| Growth pattern | Linear (straight line) | Exponential (curving upward) |
| Formula | SI = PRT/100 | A = P(1+R/100)ⁿ |
4️⃣ Quick Calculation Tips
| Situation | How to Compute |
|---|---|
| You know total amount (A) and need rate (R) | Rearrange CI formula: |
R = 100 × ((A/P)^(1/n) – 1) |
|
| You need time (T) for SI | T = (SI × 100) / (P × R) |
| You need time (n) for CI | n = log(A/P) / log(1 + R/100) |
| Use a calculator | Most calculators have a log key for CI time. |
5️⃣ Practice Problems (Try Before You Check!)
- SI: ₹5,000 is invested at 8% per year for 3 years. How much interest do you earn?
- CI: ₹10,000 is deposited at 6% per year, compounded annually, for 4 years. What is the total amount?
- Rate: ₹2,000 grows to ₹2,500 in 5 years under compound interest. Find the annual rate (rounded to 2 decimals).
(Answer them, then scroll down for solutions!)
6️⃣ Answers & Explanations
-
SI
SI = (5000 × 8 × 3)/100 = ₹1,200
You earn ₹1,200 after 3 years. -
CI
A = 10000 × (1+6/100)^4 = 10,000 × 1.2625 = ₹12,625
Total amount = ₹12,625. -
Rate
A/P = 2500/2000 = 1.25
1.25 = (1 + R/100)^5
Take 5th root: (1.25)^(1/5) ≈ 1.0447
R/100 = 0.0447 → R ≈ 4.47%
Annual rate ≈ 4.47%.
7️⃣ Why It Matters for SBI PO
- Speed & Accuracy: Quick mental calculations or simple use of a calculator.
- Common Questions: Often ask for the amount, interest, time, or rate.
- Time‑Saving Trick: Memorize the SI formula; for CI, focus on the “(1+R/100)” part.
8️⃣ Final Checklist
- ✅ Know the difference between simple and compound interest.
- ✅ Practice converting between SI, CI, and total amount.
- ✅ Use consistent units (years, months, etc.) when plugging into formulas.
- ✅ Check your calculator for the log function if needed.
Happy studying! 🚀