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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