Maths-7 Compound Interest : Questions and Step-by-Step Solutions for all Competitive Exams

Maths-7 Compound Interest : Questions and Step-by-Step Solutions for all Competitive Exams

What Is Compound Interest?

Compound Interest means you earn interest not just on the original money (called Principal)- but also on the interest you’ve already earned. It’s like your money is growing on its own every year-like a tree that grows more branches, and those branches grow even more leaves

The Formula

Compound Interest (CI) = A – P

Where:

• A = Total amount after interest
• P = Principal (original money)

To find A, we use:

A = P  (1 + R /100 )^T

Where:

• R = Rate of interest per year (%)
• T = Time in years

Example:

Ram puts ₹1,000 in a magic money box that gives 10% interest every year.

Let’s see how much money he has after 2 years.

Year 1:

• Interest = ₹1,000 × 10% = ₹100
• New total = ₹1,000 + ₹100 = ₹1,100

Year 2:

• Now interest is on ₹1,100
• Interest = ₹1,100 × 10% = ₹110
• New total = ₹1,100 + ₹110 = ₹1,210

So after 2 years, Ram has ₹1,210.
Compound Interest = ₹1,210 − ₹1,000 = ₹210

Key Difference from Simple Interest

• Simple Interest: Interest is always on the original amount.
• Compound Interest: Interest is on the original + interest earned before!

Practice Time

Try this:

You invest ₹500 at 5% interest for 2 years.
How much Compound Interest will you earn?

Formula of Compound Interest

If

• P = Principal (starting money)
• R = Rate of Interest per year (%)
• T = Time in years

Then,

and

Step-by-Step Example

Example 1:
Find the compound interest on ₹1000 for 2 years at 10% per year.

Step 1: Write the formula

Step 2: Substitute

Step 3: Find CI

✅ Answer: Compound Interest = ₹210

Example 2:

Find CI on ₹5000 for 3 years at 5% per year.

Step 1:

Step 2:

Step 3:

✅ Answer: ₹788.13

Difference Between Simple & Compound Interest

Easy Tip for Students

💡 When you see “compounded annually,” it means interest is added once per year.
💡 “Compounded half-yearly” means added twice per year.
💡 “Compounded quarterly” means added four times per year.

Compound Interest Worksheet

Section A: Very Easy (Basics)

1️⃣ ₹1000, 10%, 1 year
Amount = 1000 × (1 + 10/100) = 1000 × 1.1 = ₹1100
CI = 1100 − 1000 = ₹100 ✅

2️⃣ ₹500, 5%, 1 year
A = 500 × (1.05) = ₹525 → CI = ₹25 ✅

3️⃣ ₹2000, 10%, 2 years
A = 2000 × (1.1)² = 2000 × 1.21 = ₹2420
CI = 2420 − 2000 = ₹420 ✅

4️⃣ ₹1500, 8%, 2 years
A = 1500 × (1.08)² = 1500 × 1.1664 = ₹1749.60
CI = 1749.60 − 1500 = ₹249.60 ✅

5️⃣ ₹1000, 5%, 3 years
A = 1000 × (1.05)³ = 1000 × 1.157625 = ₹1157.63
CI = ₹157.63 ✅

Section B: Moderate (More Years)

6️⃣ ₹1200, 10%, 2 years
A = 1200 × (1.1)² = 1200 × 1.21 = ₹1452
CI = ₹252 ✅

7️⃣ ₹5000, 5%, 3 years
A = 5000 × (1.05)³ = 5000 × 1.157625 = ₹5788.13
CI = ₹788.13 ✅

8️⃣ ₹2000, 10%, 4 years
A = 2000 × (1.1)⁴ = 2000 × 1.4641 = ₹2928.20
CI = ₹928.20 ✅

9️⃣ ₹1500, 12%, 2 years
A = 1500 × (1.12)² = 1500 × 1.2544 = ₹1881.60
CI = ₹381.60 ✅

🔟 ₹4000, 5%, 3 years
A = 4000 × (1.05)³ = 4000 × 1.157625 = ₹4630.50
CI = ₹630.50 ✅

Section C: Application Problems

1️⃣ ₹2500, 8%, 2 years
A = 2500 × (1.08)² = 2500 × 1.1664 = ₹2916
CI = ₹416 ✅

2️⃣ ₹10000, 6%, 3 years
A = 10000 × (1.06)³ = 10000 × 1.191016 = ₹11910.16
CI = ₹1910.16 ✅

3️⃣ ₹800, 10%, 2 years
A = 800 × (1.1)² = 800 × 1.21 = ₹968
CI = ₹168 ✅

4️⃣ ₹4000, 9%, 2 years
A = 4000 × (1.09)² = 4000 × 1.1881 = ₹4752.4
CI = ₹752.4 ✅

5️⃣ ₹6000, 10%, 2 years
A = 6000 × (1.1)² = 6000 × 1.21 = ₹7260
CI = ₹1260 ✅

Section D: Challenge (Concept Booster)

6️⃣ ₹10000, 10%, 3 years
A = 10000 × (1.1)³ = 10000 × 1.331 = ₹13310
CI = ₹3310 ✅

7️⃣ ₹5000, 8%, 3 years
A = 5000 × (1.08)³ = 5000 × 1.259712 = ₹6298.56
CI = ₹1298.56 ✅

8️⃣ ₹2000, 12%, 2 years
A = 2000 × (1.12)² = 2000 × 1.2544 = ₹2508.80
CI = ₹508.80 ✅

9️⃣ ₹8000, 5%, 2 years
A = 8000 × (1.05)² = 8000 × 1.1025 = ₹8820
CI = ₹820 ✅

0️⃣ ₹10000 → ₹12100 in 2 years
A = P(1 + R/100)²
12100 = 10000(1 + R/100)²
(1 + R/100)² = 1.21 → 1 + R/100 = 1.1 → R = 10% ✅

Tip for Students:

• “Amount” means total money after adding interest.
• “Compound” means you earn interest on your previous interest too.
• Always convert the rate into decimal → (1 + R/100).
• Square or cube it based on years (2 years → square, 3 years → cube).