Letest Update

Compound Interest with short tricks and MCQs

Here are some tricks and formulas for Compound Interest:

Compound Interest is an important topic for CUET CLAT and IPMAT.

Here are some important Short tricks and formulae that help you to sharpen your preparation 

Tricks:


1. Rule of 72: To find the number of years required to double your investment, divide 72 by the rate of interest.

Example: If the rate of interest is 8%, your investment will double in 9 years (72/8 = 9).

 

2. Power of Compounding: Compounding frequency affects the interest earned. More frequent compounding results in higher interest.

 

3. Interest on Interest: Compound interest earns interest on both principal and accrued interest.

 

Formulas:

1. Compound Interest (CI): CI = P [(1 + r/n)^(nt) - 1]

2. Amount (A): A = P (1 + r/n)^(nt)

3. Rate (r): r = (CI / P) × (1 / t)

4. Time (t): t = log(A/P) / log(1 + r/n)

5. Present Value (PV): PV = A / (1 + r/n)^(nt)

6. Future Value (FV): FV = PV × (1 + r/n)^(nt)

 

Special Formulas:

 

1. Compound Interest with Periodic Payments: CI = ∑[PMT × ((1 + r/n)^(nt) - 1) / r]

2. Continuous Compounding: A = P × e^(rt)

3. Annual Percentage Yield (APY): APY = (1 + r/n)^(n) - 1

 

Important Concepts:

 

1. Compounding Frequency: Annually, Semi-annually, Quarterly, Monthly, Daily.

2. Interest Rate Types: Nominal Rate, Effective Rate.

3. Time Value of Money: Present Value, Future Value.

 

Practice Questions:

 

1. Find the compound interest on ₹10,000 at 12% per annum for 3 years, compounded quarterly.

 

2. What is the amount if ₹20,000 is invested at 15% per annum for 5 years, compounded annually?

 

3. A person deposits ₹5,000 in a bank at 10% per annum for 2 years, compounded semi-annually. What is the compound interest?

 

Short Tricks:

 

1. Compound Interest (CI) formula: CI = P [(1 + r/n)^(nt) - 1]

2. When interest is compounded annually, n = 1.

3. When interest is compounded half-yearly, n = 2.

4. To find CI, first find the amount using the formula A = P (1 + r/n)^(nt)

5. CI = A - P

 

Important Formulas:

 

1. Amount (A) = P (1 + r/n)^(nt)

2. Compound Interest (CI) = P [(1 + r/n)^(nt) - 1]

3. Rate (r) = (CI / P) × (1 / t)

4. Time (t) = log(A/P) / log(1 + r/n)

 

MCQs with Solutions:

 

CLAT Previous Year Questions:

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

A) ₹2,100

B) ₹2,200

C) ₹2,300

D) ₹2,400

 

Answer: B) ₹2,200

 

Solution: CI = 10,000 [(1 + 0.10/1)^(1*2) - 1] = ₹2,200

 

1. A person invests ₹20,000 at 12% per annum for 3 years, compounded half-yearly. What is the amount?

 

A) ₹29,512

B) ₹30,192

C) ₹30,912

D) ₹31,512

 

Answer: B) ₹30,192

 

Solution: A = 20,000 (1 + 0.12/2)^(2*3) = ₹30,192

 

IPMAT Previous Year Questions:

 

1. What is the rate of interest if ₹15,000 yields ₹22,500 in 2 years, compounded annually?

A) 12%

B) 15%

C) 18%

D) 20%

 

Answer: B) 15%

 

Solution: r = (CI / P) × (1 / t) = (7,500 / 15,000) × (1 / 2) = 0.15 or 15%

 

1. A company borrows ₹50,000 at 10% per annum for 4 years, compounded annually. What is the compound interest?

 

A) ₹21,000

B) ₹23,000

C) ₹25,000

D) ₹27,000

 

Answer: B) ₹23,000

 

Solution: CI = 50,000 [(1 + 0.10/1)^(1*4) - 1] = ₹23,000

 

CUET Previous Year Questions:

 

1. What is the amount if ₹8,000 is invested at 12% per annum for 3 years, compounded half-yearly?

 

A) ₹11,392

B) ₹11,592

C) ₹11,792

D) ₹12,192

 

Answer: B) ₹11,592

 

Solution: A = 8,000 (1 + 0.12/2)^(2*3) = ₹11,592

 

1. A person deposits ₹12,000 in a bank at 10% per annum for 2 years, compounded annually. What is the compound interest?

 

A) ₹2,400

B) ₹2,600

C) ₹2,800

D) ₹3,000

 

Answer: B) ₹2,600

Solution: CI = 12,000 [(1 + 0.10/1)^(1*2) - 1] = ₹2,600

 

1. What is the rate of interest if ₹20,000 yields ₹27,500 in 2 years, compounded annually?

 

A) 12%

B) 15%

C) 18%

D) 20%

 

Answer: B) 15%

 

Solution: r = (CI / P) × (1 / t) = (7,500 / 20,000) × (1 / 2) = 0.15 or 15%

 

1. A company invests ₹30,000 at 12% per annum for 4 years, compounded half-yearly. What is the amount?

 

A) ₹47,032

B) ₹48,032

C) ₹49,032

D) ₹50,032

 

Answer: B) ₹48,032

 

Solution: A = 30,000 (1 + 0.12/2)^(2*4) = ₹48,032


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