Compound Interest and Uniform Rate of Increase or Decrease
Multiple Choice Questions (MCQ)
1.What is the formula to calculate compound interest (CI) after n years at r% rate with principal P?
A. CI = P × r × n
B. CI = P × (1 + r100)ⁿ
C. CI = P × [(1 + r100)ⁿ – 1]
D. CI = P + (r × n)
Answer: C. CI = P × [(1 + r100)ⁿ – 1]
2.If ₹10,000 is compounded annually at 5% for 3 years, what will be the amount?
A. ₹11,500
B. ₹11,576.25
C. ₹11,650
D. ₹11,000
Answer: B. ₹11,576.25
3.A value decreases at 10% per year for 2 years. If the initial value is ₹20,000, the value after 2 years is:
A. ₹18,000
B. ₹17,000
C. ₹16,200
D. ₹15,000
Answer: C. ₹16,200
4.What happens when the compounding frequency increases?
A. Interest decreases
B. Interest remains same
C. Interest becomes zero
D. Interest increases
Answer: D. Interest increases
5.If a population grows uniformly at 4% annually, and the current population is 5,000, what will it be after 3 years (approx.)?
A. 5,400
B. 5,500
C. 5,624
D. 6,000
Answer: C. 5,624
Short Answer Questions (SAQ)
1. Write the formula to find the final amount when interest is compounded semi-annually.
Answer: A=P(1+r2100)2n
2. State one difference between compound interest and simple interest.
Answer: Compound interest is calculated on both principal and accumulated interest, while simple interest is calculated only on the principal.
3. If a quantity increases by 5% each year, what is the multiplier used in the formula?
Answer: The multiplier is (1+5100) = 1.05
Long Answer Questions (LAQ)
1. A sum of ₹12,000 is compounded annually at 6% for 2 years. Find the amount and compound interest.
Answer: Given: P = ₹12,000, r = 6%, n = 2
Amount:
A = 12000 × (1+6100)2 = 12000 × (1.06)2 = 12000 × 1.1236 = ₹13,483.20
Compound Interest:
CI = A − P = 13,483.20 − 12,000 = ₹1,483.20
2. A car costs ₹5,00,000 and depreciates by 12% annually. What will be its value after 2 years?
Answer: Given: Original value = ₹5,00,000, r = 12%, n = 2
New Value:
= 500000 × (1−12100)2 = 500000 × (0.88)2 = 500000 × 0.7744 = ₹3,87,200
Answer: The car’s value after 2 years will be ₹3,87,200.