Question 1

Rajesh invests ₹8,000 at 10% per annum for 2 years. What is the difference between the compound interest and simple interest earned on this amount?

Accepted Answer

Step 1: Calculate Simple Interest (SI) using SI = (P × R × T) / 100
SI = (8,000 × 10 × 2) / 100 = 160,000 / 100 = ₹1,600

Step 2: Calculate Compound Interest (CI) using CI = P(1 + R/100)^T - P
Amount = 8,000(1 + 10/100)^2 = 8,000(1.1)^2 = 8,000 × 1.21 = ₹9,680
CI = 9,680 - 8,000 = ₹1,680

Step 3: Find the difference
Difference = CI - SI = 1,680 - 1,600 = ₹80

Alternatively, for 2 years: Difference = (P × R^2) / (100)^2 = (8,000 × 10 × 10) / 10,000 = ₹80

Therefore, the answer is ₹80.

Question 2

What is the compound interest on ₹8,000 at 10% per annum for 2 years, compounded annually?

Accepted Answer

Step 1: Use formula CI = P[(1 + r/100)^n - 1]. Step 2: CI = 8000[(1 + 10/100)^2 - 1] = 8000[(1.1)^2 - 1] = 8000[1.21 - 1] = 8000 × 0.21 = ₹1,680. Therefore, answer is ₹1,680.

Question 3

Rajesh invested ₹8,000 in a bank at 10% per annum compound interest, compounded annually. After 2 years, he withdrew half of the amount. The remaining amount was kept for another 1 year at the same rate. What is the final amount with Rajesh?

Accepted Answer

Step 1: Calculate amount after 2 years using CI formula A = P(1 + r/100)^n
A = 8,000 × (1 + 10/100)²
A = 8,000 × (1.1)²
A = 8,000 × 1.21
A = ₹9,680

Step 2: After 2 years, Rajesh withdraws half
Amount remaining = 9,680 ÷ 2 = ₹4,840

Step 3: This ₹4,840 is invested for 1 more year at 10% p.a.
A = 4,840 × (1 + 10/100)¹
A = 4,840 × 1.1
A = ₹5,324

Therefore, the final amount is ₹5,324

Question 4

A sum of ₹8,000 is invested at 10% per annum compounded half-yearly for 1 year. What is the compound interest earned?

Accepted Answer

Step 1: For half-yearly compounding, Rate per half-year = 10/2 = 5%, Number of periods = 1 × 2 = 2. Step 2: Amount = 8000 × (1 + 5/100)² = 8000 × (1.05)² = 8000 × 1.1025 = ₹8,820. Step 3: CI = 8820 − 8000 = ₹820. Common mistake: Using annual rate directly gives CI = 8000 × 10/100 = ₹800 (option a). Therefore, answer is ₹820.

Question 5

A sum of ₹16,000 is invested at 10% per annum compounded half-yearly. What is the compound interest accrued after 1.5 years?

Accepted Answer

Step 1: When compounded half-yearly, rate per period = 10/2 = 5%, and number of periods for 1.5 years = 1.5 × 2 = 3. Step 2: Amount = P × (1 + r/100)^n = 16000 × (1.05)^3. Step 3: (1.05)^3 = 1.157625. Step 4: Amount = 16000 × 1.157625 = ₹18,522. Step 5: CI = 18522 − 16000 = ₹2,522. Therefore, the answer is ₹2,522.

Question 6

A sum of money becomes ₹9,680 after 2 years at 10% per annum compound interest. If the same sum is invested at 12% per annum simple interest for 3 years, what will be the total interest earned?

Accepted Answer

Step 1: Find the Principal using the compound interest formula.
Using A = P(1 + r/100)^n
9,680 = P(1 + 10/100)²
9,680 = P(1.1)²
9,680 = P × 1.21
P = 9,680 ÷ 1.21 = ₹8,000

Step 2: Calculate simple interest on ₹8,000 at 12% p.a. for 3 years.
Simple Interest = (P × R × T) / 100
SI = (8,000 × 12 × 3) / 100
SI = 288,000 / 100
SI = ₹2,880

Step 3: Therefore, the total interest earned under simple interest is ₹2,880.

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