Simple & Compound Interest: Complete Notes, Formulas, Examples, and Practice Questions

 

Simple & Compound Interest: Complete Notes, Formulas, Examples, and Practice Questions

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1. Basic Formulas

A. Simple Interest (SI)

• Definition: Interest calculated only on the original principal for the entire period.

• Formula:

  $$\text{SI}=\frac{P\times R\times T}{100}$$

  Where:

  • $P$ = Principal (initial amount)

  • $R$ = Rate of interest per annum (%)

  • $T$ = Time (in years)

• Amount (A):

  $$A=P+SI$$

B. Compound Interest (CI)

• Definition: Interest calculated on the principal plus all previously earned interest.

• Formula (compounded annually):

  $$A=P{(1+\frac{R}{100})}^T$$$$\text{CI}=A-P$$

• Compounded n times per year:

  $$A=P{(1+\frac{R}{100n})}^{nT}$$

• Compounded half-yearly:

  $$A=P{(1+\frac{R}{200})}^{2T}$$

• Compounded quarterly:

  $$A=P{(1+\frac{R}{400})}^{4T}$$

• Compounded monthly:

  $$A=P{(1+\frac{R}{1200})}^{12T}$$

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2. Difference Between SI and CI

Feature	Simple Interest (SI)	Compound Interest (CI)
Calculation Base	Only on original principal	On principal + accumulated interest
Growth	Linear	Exponential
Formula	$SI=\frac{P\times R\times T}{100}$	$CI=P(1+\frac{R}{100}{)}^T-P$
Amount after n years	$A=P+SI$	$A=P(1+\frac{R}{100}{)}^T$
Example (2 years, ₹1000, 10%)	₹200	₹210
Common Uses	Short-term loans, simple bank deposits	Savings, loans, investments, population growth, etc.
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3. Installments and Growth Applications

A. Installments (EMI)

• For repaying a loan in equal installments (EMI), the formula is based on CI concepts.

• Installment formula (annual):

  $$\text{Installment}=\frac{P\times R\times (1+R{)}^n}{(1+R{)}^n-1}$$

  Where $R$ is the rate per period (as a decimal), $n$ is the number of periods.

B. Growth/Depreciation

• Population/Bacteria Growth:

  $$\text{Future Value}=P{(1+\frac{R}{100})}^T$$

• Depreciation:

  $$\text{Future Value}=P{(1-\frac{R}{100})}^T$$

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4. Examples

Example 1 (Simple Interest):
Find SI on ₹4,000 at 7% for 2 years.

$$SI=\frac{4000\times 7\times 2}{100}=\text{₹}560$$

Example 2 (Compound Interest):
Find CI on ₹4,000 at 7% for 2 years (compounded annually).

$$\begin{gathered} A=4000\times (1+0.07{)}^2=4000\times 1.1449=\text{₹}4,579.6 \\ CI=4579.6-4000=\text{₹}579.6 \end{gathered}$$

Example 3 (Difference between SI and CI):
For ₹10,000 at 10% for 2 years:
SI = ₹2,000; CI = ₹2,100; Difference = ₹100

Example 4 (Installment):
A loan of ₹12,000 at 10% CI to be paid in 2 equal annual installments.
Let each installment be ₹x:

$$x\mathrm{/}(1+0.1{)}^2+x\mathrm{/}(1+0.1)=12,000$$

(Solve for x)

Example 5 (Growth):
Population of a town is 20,000, growing at 5% per year. Find population after 3 years.

$$20,000\times (1.05{)}^3=20,000\times 1.157625=23,152.5$$

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5. Practice Questions (with answers for first 20)

Questions 1–20 (with answers)

1. Find SI on ₹5,000 at 8% for 3 years.
   Ans: ₹1,200

2. Find CI on ₹5,000 at 8% for 3 years (compounded annually).
   Ans: ₹1,299.52

3. What is the difference between SI and CI on ₹2,000 at 10% for 2 years?
   Ans: ₹20

4. If SI on a sum for 2 years at 5% is ₹200, find the principal.
   Ans: ₹2,000

5. Find the amount after 2 years on ₹3,000 at 6% CI (compounded annually).
   Ans: ₹3,381.80

6. If ₹1,500 amounts to ₹1,800 in 4 years at SI, find the rate.
   Ans: 5%

7. Find CI on ₹10,000 at 10% for 2 years (compounded annually).
   Ans: ₹2,100

8. Find SI on ₹7,000 at 12% for 5 years.
   Ans: ₹4,200

9. Find the principal if SI is ₹600 at 10% for 3 years.
   Ans: ₹2,000

10. Find the amount after 3 years on ₹2,500 at 8% CI (compounded annually).
    Ans: ₹3,149.12

11. If CI on ₹4,000 for 2 years is ₹824, find the rate.
    Ans: 10%

12. Find SI on ₹2,400 at 9% for 2 years.
    Ans: ₹432

13. Find CI on ₹2,400 at 9% for 2 years.
    Ans: ₹453.36

14. Find the difference between SI and CI on ₹1,200 at 10% for 2 years.
    Ans: ₹12

15. If ₹8,000 amounts to ₹10,000 in 5 years at SI, find the rate.
    Ans: 5%

16. Find CI on ₹6,000 at 5% for 3 years (compounded annually).
    Ans: ₹946.50

17. Find SI on ₹6,000 at 5% for 3 years.
    Ans: ₹900

18. If the rate is 8% and SI for 4 years is ₹640, find the principal.
    Ans: ₹2,000

19. Find the amount after 2 years on ₹2,000 at 10% CI (compounded annually).
    Ans: ₹2,420

20. If the population of a city is 50,000 and grows at 4% per year, what will it be after 2 years?
    Ans: 54,080

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Questions 21–100 (Practice Only)

21. Find SI on ₹2,500 at 6% for 4 years.

22. Find CI on ₹2,500 at 6% for 4 years (compounded annually).

23. What is the difference between SI and CI on ₹3,000 at 8% for 2 years?

24. If SI on a sum for 3 years at 7% is ₹315, find the principal.

25. Find the amount after 3 years on ₹5,000 at 5% CI (compounded annually).

26. If ₹4,000 amounts to ₹5,000 in 5 years at SI, find the rate.

27. Find CI on ₹8,000 at 10% for 2 years (compounded annually).

28. Find SI on ₹12,000 at 9% for 2 years.

29. Find the principal if SI is ₹720 at 12% for 2 years.

30. Find the amount after 2 years on ₹1,800 at 10% CI (compounded annually).

31. If CI on ₹5,000 for 2 years is ₹1,050, find the rate.

32. Find SI on ₹3,600 at 8% for 5 years.

33. Find CI on ₹3,600 at 8% for 5 years.

34. Find the difference between SI and CI on ₹2,000 at 12% for 2 years.

35. If ₹2,500 amounts to ₹3,000 in 4 years at SI, find the rate.

36. Find CI on ₹7,000 at 6% for 3 years (compounded annually).

37. Find SI on ₹7,000 at 6% for 3 years.

38. If the rate is 10% and SI for 5 years is ₹1,500, find the principal.

39. Find the amount after 3 years on ₹4,000 at 9% CI (compounded annually).

40. If the population of a town is 80,000 and grows at 5% per year, what will it be after 2 years?

41. Find CI on ₹9,000 at 8% for 2 years (compounded half-yearly).

42. Find CI on ₹10,000 at 12% for 3 years (compounded quarterly).

43. Find SI on ₹5,500 at 7% for 2 years.

44. Find CI on ₹5,500 at 7% for 2 years.

45. What is the difference between SI and CI on ₹6,000 at 9% for 2 years?

46. If SI on a sum for 2 years at 5% is ₹400, find the principal.

47. Find the amount after 2 years on ₹7,000 at 8% CI (compounded annually).

48. If ₹3,000 amounts to ₹3,600 in 4 years at SI, find the rate.

49. Find CI on ₹2,000 at 15% for 2 years (compounded annually).

50. Find SI on ₹2,000 at 15% for 2 years.

51. Find CI on ₹8,000 at 6% for 3 years (compounded annually).

52. Find SI on ₹8,000 at 6% for 3 years.

53. If the rate is 9% and SI for 3 years is ₹1,080, find the principal.

54. Find the amount after 3 years on ₹2,500 at 12% CI (compounded annually).

55. If the population of a city is 30,000 and grows at 6% per year, what will it be after 2 years?

56. Find CI on ₹1,200 at 10% for 2 years (compounded annually).

57. Find SI on ₹1,200 at 10% for 2 years.

58. What is the difference between SI and CI on ₹1,500 at 8% for 2 years?

59. If SI on a sum for 4 years at 6% is ₹240, find the principal.

60. Find the amount after 4 years on ₹2,000 at 5% CI (compounded annually).

61. If ₹2,000 amounts to ₹2,400 in 4 years at SI, find the rate.

62. Find CI on ₹5,000 at 5% for 2 years (compounded annually).

63. Find SI on ₹5,000 at 5% for 2 years.

64. If the rate is 7% and SI for 3 years is ₹420, find the principal.

65. Find the amount after 2 years on ₹6,000 at 8% CI (compounded annually).

66. If the population of a town is 60,000 and grows at 3% per year, what will it be after 2 years?

67. Find CI on ₹2,500 at 12% for 2 years (compounded half-yearly).

68. Find CI on ₹4,000 at 8% for 3 years (compounded quarterly).

69. Find SI on ₹3,000 at 10% for 4 years.

70. Find CI on ₹3,000 at 10% for 4 years.

71. What is the difference between SI and CI on ₹5,000 at 6% for 2 years?

72. If SI on a sum for 3 years at 8% is ₹480, find the principal.

73. Find the amount after 3 years on ₹7,000 at 9% CI (compounded annually).

74. If ₹4,000 amounts to ₹5,000 in 5 years at SI, find the rate.

75. Find CI on ₹3,600 at 7% for 2 years (compounded annually).

76. Find SI on ₹3,600 at 7% for 2 years.

77. If the rate is 10% and SI for 2 years is ₹400, find the principal.

78. Find the amount after 2 years on ₹2,000 at 12% CI (compounded annually).

79. If the population of a city is 45,000 and grows at 4% per year, what will it be after 2 years?

80. Find CI on ₹1,500 at 12% for 2 years (compounded annually).

81. Find SI on ₹1,500 at 12% for 2 years.

82. What is the difference between SI and CI on ₹2,000 at 8% for 2 years?

83. If SI on a sum for 5 years at 6% is ₹600, find the principal.

84. Find the amount after 5 years on ₹2,000 at 5% CI (compounded annually).

85. If ₹2,500 amounts to ₹3,000 in 4 years at SI, find the rate.

86. Find CI on ₹5,000 at 7% for 3 years (compounded annually).

87. Find SI on ₹5,000 at 7% for 3 years.

88. If the rate is 9% and SI for 2 years is ₹360, find the principal.

89. Find the amount after 2 years on ₹4,000 at 10% CI (compounded annually).

90. If the population of a town is 70,000 and grows at 5% per year, what will it be after 2 years?

91. Find CI on ₹6,000 at 8% for 2 years (compounded half-yearly).

92. Find CI on ₹7,000 at 6% for 3 years (compounded quarterly).

93. Find SI on ₹7,000 at 6% for 3 years.

94. Find CI on ₹7,000 at 6% for 3 years.

95. What is the difference between SI and CI on ₹8,000 at 7% for 2 years?

96. If SI on a sum for 4 years at 8% is ₹640, find the principal.

97. Find the amount after 4 years on ₹3,000 at 6% CI (compounded annually).

98. If ₹5,000 amounts to ₹6,000 in 5 years at SI, find the rate.

99. Find CI on ₹2,000 at 9% for 2 years (compounded annually).

100. Find SI on ₹2,000 at 9% for 2 years.

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Practice these formulas and questions to master simple and compound interest, their differences, installment concepts, and growth applications for all competitive exams.