Simple & compound interest

📚 Simple & Compound Interest – Study Notes

(For Village Development Officers – Quantitative Aptitude)

1. What is Interest?

• Interest is the extra amount you get (or owe) for lending or borrowing money.
• Think of it as a small bonus you receive for letting someone use your money, or the extra cost you pay if you borrow.

2. Simple Interest (SI)

2.1. Definition

• The extra amount added only to the original amount (the principal).
• It does not grow on itself over time.

2.2. Everyday Analogy

• Imagine you give a friend 10 ₹ in a jar.
• After 3 months, you get back 10 ₹ + 2 ₹ (the interest).
• That 2 ₹ is always calculated from the 10 ₹ only, no matter how long you keep it.

2.3. Formula

SI = (Original Amount × Rate × Time) / 100

• Original Amount = the money you lent.
• Rate = yearly percentage (e.g., 5 % per year).
• Time = number of years (or a fraction of a year).

2.4. Quick Steps

1. Multiply Original Amount × Rate × Time.
2. Divide the result by 100.
3. That gives you the interest.
4. Add it to the Original Amount to get the Total Return.

2.5. Tiny Example

3. Compound Interest (CI)

3.1. Definition

• Interest is calculated on the original amount AND on the interest that has already accumulated.
• It grows exponentially over time.

3.2. Everyday Analogy

• Think of a plant that gets water.
• First week you add 10 ₹ water.
• Next week you add the same 5 % not only to the original 10 ₹ but also to the 0.5 ₹ you added last week.
• The plant grows faster each week.

3.3. Formula

CI = Original Amount × ( (1 + Rate/100)^Time – 1 )

• ^ = “to the power of”.
• If you want the Total Amount (Original + Interest):

  Total = Original Amount × (1 + Rate/100)^Time
  

3.4. Quick Steps

1. Convert the rate into a decimal: Rate/100.
2. Add 1 to it: 1 + Rate/100.
3. Raise this to the power of Time: (1 + Rate/100)^Time.
4. Subtract 1 to get the interest factor.
5. Multiply by the Original Amount to get the interest.
6. Add to the Original Amount for the total.

3.5. Tiny Example

4. Key Differences at a Glance

5. Practice Problems (Quick Solve)

1. Question: If you lend ₹500 at 4 % per year for 3 years, what is the simple interest?
   Solution:
   SI = (500 × 4 × 3) / 100 = ₹60
   Total = ₹560

2. Question: The same loan is compounded yearly. What is the total amount after 3 years?
   Solution:
   Total = 500 × (1 + 4/100)^3 = 500 × 1.124864 = ₹562.44

3. Question: How long will it take ₹2,000 to become ₹3,000 at 5 % simple interest?
   Solution:
   SI = (2000 × 5 × T)/100 = 100T
   Set 100T = 1000 → T = 10 years

4. Question: Same amount, 5 % compound interest. Find the time.
   Solution:
   3000 = 2000 × (1 + 0.05)^T → 1.5 = 1.05^T
   Take log: T ≈ log(1.5)/log(1.05) ≈ 8.1 years

6. Quick Tips for Exams

7. Summary

• Simple Interest: One‑time bonus on the original amount.
• Compound Interest: Bonus that keeps adding to itself, making