Question 1

A person deposits ₹10,000 in a savings account at 4% simple interest per annum. If he withdraws the entire amount after 2.5 years, what is the total amount he receives?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100 with T = 2.5 years. Step 2: SI = (10000 × 4 × 2.5) / 100 = (10000 × 10) / 100 = 100000 / 100 = ₹1,000. Step 3: Total Amount = Principal + SI = 10000 + 1000 = ₹11,000. Therefore, the total amount received is ₹11,000.

Question 2

A principal of ₹10,000 is invested at 5% per annum compound interest. What is the compound interest earned in 3 years?

Accepted Answer

Step 1: Calculate amount using A = P(1 + r/100)^n = 10000(1.05)^3. Step 2: (1.05)^3 = 1.157625, so A = 10000 × 1.157625 = ₹11,576.25. Step 3: Compound Interest = A - P = 11,576.25 - 10,000 = ₹1,576.25.

Question 3

Arun invested ₹15,000 at 5% simple interest per annum. After how many years will the total amount become ₹18,750?

Accepted Answer

Step 1: Calculate SI from the difference: SI = Amount - Principal = 18750 - 15000 = ₹3,750. Step 2: Use SI = (P × R × T) / 100, rearranged to find T: T = (SI × 100) / (P × R). Step 3: Substitute: T = (3750 × 100) / (15000 × 5) = 375000 / 75000 = 5 years. Therefore, the time period is 5 years.

Question 4

A sum becomes ₹4,840 in 2 years at 10% per annum compound interest. What is the principal?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 4840 = P(1.10)^2 = P × 1.21. Step 3: P = 4840/1.21 = ₹4,000. Therefore, the principal is ₹4,000.

Question 5

Priya borrowed ₹12,000 at 9% simple interest per annum. If she paid ₹16,320 to clear the debt, how many years did she borrow the money for?

Accepted Answer

Step 1: Calculate SI from the difference: SI = Amount - Principal = 16320 - 12000 = ₹4,320. Step 2: Use SI = (P × R × T) / 100, rearranged to find T: T = (SI × 100) / (P × R). Step 3: Substitute: T = (4320 × 100) / (12000 × 9) = 432000 / 108000 = 4 years. Therefore, the time period is 4 years.

Question 6

A sum of ₹8,000 is invested at 10% per annum compound interest. What will be the amount after 2 years?

Accepted Answer

Step 1: Use the compound interest formula A = P(1 + r/100)^n. Step 2: A = 8000(1 + 10/100)^2 = 8000(1.1)^2 = 8000 × 1.21 = ₹9,680. Therefore, the amount after 2 years is ₹9,680.

Question 7

₹2,000 is invested at 20% per annum compound interest. What will be the amount after 1.5 years, if interest is compounded half-yearly?

Accepted Answer

Step 1: When compounded half-yearly, rate per half-year = 20/2 = 10% and number of periods n = 1.5 × 2 = 3. Step 2: A = P(1 + r/100)^n = 2000(1.10)^3. Step 3: (1.10)^3 = 1.331, so A = 2000 × 1.331 = ₹2,662.

Question 8

The simple interest on a certain sum for 6 years at 7% per annum is ₹2,520. What is the principal amount?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged to find P: P = (SI × 100) / (R × T). Step 2: Substitute: P = (2520 × 100) / (7 × 6) = 252000 / 42 = ₹6,000. Therefore, the principal is ₹6,000.

Question 9

A sum of ₹5,000 is invested at 10% per annum for 2 years. What is the difference between the compound interest and simple interest earned?

Accepted Answer

Step 1: Calculate Simple Interest using SI = (P × R × T) / 100 = (5000 × 10 × 2) / 100 = ₹1,000. Step 2: Calculate Compound Interest using A = P(1 + R/100)^T = 5000(1.1)^2 = 5000 × 1.21 = ₹6,050, so CI = 6050 - 5000 = ₹1,050. Step 3: Difference = CI - SI = 1050 - 1000 = ₹50.

Question 10

A principal amounts to ₹2,420 in 2 years at 10% per annum compound interest. What is the simple interest on the same principal at the same rate for the same period?

Accepted Answer

Step 1: Find principal using A = P(1 + R/100)^T. 2420 = P(1.1)². 2420 = P × 1.21. P = 2420/1.21 = ₹2,000. Step 2: Calculate SI = (P × R × T)/100 = (2000 × 10 × 2)/100 = ₹400.

Question 11

₹6,000 is invested at 15% per annum compound interest. What is the difference between the compound interest and simple interest for 2 years?

Accepted Answer

Step 1: Compound Interest: A = 6000(1.15)^2 = 6000 × 1.3225 = ₹7,935. CI = 7,935 - 6,000 = ₹1,935. Step 2: Simple Interest: SI = (6000 × 15 × 2)/100 = ₹1,800. Step 3: Difference = CI - SI = 1,935 - 1,800 = ₹135.

Question 12

Rajesh deposits ₹5,000 in a bank at a simple interest rate of 8% per annum. How much interest will he earn after 3 years?

Accepted Answer

Step 1: Use the Simple Interest formula: SI = (P × R × T) / 100. Step 2: Substitute values: SI = (5000 × 8 × 3) / 100 = 120000 / 100 = ₹1,200. Therefore, the interest earned is ₹1,200.

Question 13

The compound interest on ₹6,400 at 12.5% per annum for 1 year, compounded half-yearly, is:

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 12.5% ÷ 2 = 6.25% per half-year. Step 2: Number of half-years in 1 year = 2. Step 3: Amount = 6400(1 + 6.25/100)^2 = 6400(1.0625)^2 = 6400 × 1.12890625 = ₹7,225. Step 4: Compound Interest = 7225 - 6400 = ₹825.

Question 14

A principal amount becomes ₹10,648 in 1 year at 8% per annum compound interest, compounded half-yearly. What is the principal?

Accepted Answer

Step 1: For half-yearly compounding, rate per half-year = 8% ÷ 2 = 4% per half-year. Step 2: Number of half-years in 1 year = 2. Step 3: Amount = P(1 + r/100)^n → 10,648 = P(1.04)^2 = P × 1.0816. Step 4: P = 10,648 ÷ 1.0816 = ₹10,000.

Question 15

₹5,000 becomes ₹6,050 in 2 years at compound interest. What is the rate of interest per annum?

Accepted Answer

Step 1: Use A = P(1 + r/100)^n. Step 2: 6050 = 5000(1 + r/100)^2. Step 3: (1 + r/100)^2 = 6050/5000 = 1.21. Step 4: 1 + r/100 = √1.21 = 1.1. Step 5: r/100 = 0.1, so r = 10% per annum.

Question 16

₹12,000 is invested at 10% per annum compound interest, compounded quarterly. What is the amount after 9 months?

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 10% ÷ 4 = 2.5% per quarter. Step 2: Number of quarters in 9 months = 3 quarters. Step 3: Amount = 12000(1 + 2.5/100)^3 = 12000(1.025)^3 = 12000 × 1.076890625 = ₹12,922.68 ≈ ₹12,923.

Question 17

A sum of ₹20,000 is invested at 20% per annum compound interest, compounded quarterly. What will be the interest earned in the first quarter?

Accepted Answer

Step 1: For quarterly compounding, rate per quarter = 20% ÷ 4 = 5% per quarter. Step 2: Interest for first quarter = (20000 × 5)/100 = ₹1,000. Step 3: Note: In the first quarter, compound interest equals simple interest because there is no prior compounding. Amount after Q1 = 20000 + 1000 = ₹21,000.

Question 18

A sum of ₹8,000 earns ₹2,400 as simple interest in 5 years. What is the rate of interest per annum?

Accepted Answer

Step 1: Use SI = (P × R × T) / 100, rearranged to find R: R = (SI × 100) / (P × T). Step 2: Substitute: R = (2400 × 100) / (8000 × 5) = 240000 / 40000 = 6% per annum. Therefore, the rate is 6% p.a.

Question 19

A sum of ₹10,000 is invested at 8% per annum for 2 years. By how much does the compound interest exceed the simple interest?

Accepted Answer

Step 1: SI = (10000 × 8 × 2) / 100 = ₹1,600. Step 2: A = 10000(1.08)² = 10000 × 1.1664 = ₹11,664. Step 3: CI = 11664 - 10000 = ₹1,664. Step 4: Excess = CI - SI = 1664 - 1600 = ₹64.

Question 20

The difference between compound interest and simple interest on ₹6,000 for 2 years is ₹60. What is the rate of interest per annum?

Accepted Answer

Step 1: For 2 years, difference = P × R² / 10000. Step 2: 60 = 6000 × R² / 10000. Step 3: 60 = 0.6 × R². Step 4: R² = 100. Step 5: R = 10% per annum.

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