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Madhyamik Mathematics Suggestion – Compound Interest and Compound Growth | Chapter 6

15 Sept 2026 0 views
Madhyamik Mathematics • Chapter 6

Compound Interest and Compound Growth — চক্রবৃদ্ধি সুদ ও সমাহার বৃদ্ধি বা হ্রাস

This chapter deals with Compound Interest, compound amount, changing principal, periodic interest calculation, growth and depreciation. The chapter is an important part of Madhyamik Mathematics and includes objective, short-answer and descriptive problems.

Chapter Focus: Compound Interest, Compound Amount, annual rate, changing principal, compound growth, depreciation and mathematical problems involving different compounding periods.

What is Compound Interest?

In simple interest, interest is calculated on the original principal. In compound interest, the interest earned during a period is added to the principal. In the next period, interest is calculated on this increased amount.

Therefore, the principal does not remain fixed throughout the entire calculation. It changes after every compounding period.

Compound Amount = P(1 + r/100)n

Here, P represents the initial principal, r represents the annual rate and n represents the number of compounding periods when the rate is applicable for each period.

Compound Interest and Compound Amount

Term Meaning
Principal The original amount of money invested or borrowed.
Interest The additional amount calculated on the principal or accumulated amount.
Compound Amount The total amount after adding compound interest to the principal.
Compound Interest The difference between the final compound amount and the original principal.
Growth An increase in a quantity over time at a specified rate.
Depreciation A decrease in value over time at a specified rate.

MCQ — Multiple Choice Questions

Question 1. At an annual rate of 5%, what will be the compound interest on ₹5,000 for 2 years?

(a) ₹512.50
(b) ₹515.50
(c) ₹510.50
(d) ₹52,050
Answer: (a) ₹512.50

Question 2. In compound interest, the rate of interest for each year is:

(a) Always equal
(b) Always unequal
(c) May be equal or unequal
(d) None of these
Answer: (a) Always equal

Question 3. If the compound interest on a sum for 2 years is ₹105 and the simple interest is ₹100, the rate of interest is:

(a) 5%
(b) 8%
(c) 9%
(d) 10%
Answer: (d) 10%

Question 4. In compound interest:

(a) The principal never changes every year
(b) The principal changes every year
(c) The principal may or may not change
(d) None of these
Answer: (b) The principal changes every year

Question 5. The original source contains a question comparing the simple interest for 2 years with compound interest for 2 years when interest is compounded annually.

Source note: The mathematical expression/options for this question are supplied as an image in the original article, so the exact option text cannot be reliably reproduced from the extracted source.

True or False

1. In compound interest, interest is earned on interest.
Answer: True
2. In compound interest, interest is periodically added to the principal, causing the principal amount to increase progressively.
Answer: True
3. As the number of interest periods increases, compound interest decreases.
Answer given in source: True
4. Banks generally provide both simple interest and compound interest.
Answer given in source: False
5. For a particular period, simple interest is greater than compound interest.
Answer given in source: False
6. In compound interest, the interest rate for every period must always remain the same.
Answer given in source: False
Source-based note: The True/False answers above are reproduced according to the supplied source. Some statements may require careful interpretation depending on the compounding convention used.

Fill in the Blanks

1. The source asks about the value of a machine when it continues to be used for a long period.

Answer: Depreciation

2. At an annual rate of ______%, the compound amount of ₹1,000 after 2 years is ₹1,210.

Answer: 10%

3. In compound interest, the annual interest rate for each year is ________.

Answer given in source: Equal or unequal, both are possible

4. The source states that as the rate of interest increases, compound interest becomes ________.

Answer given in source: Less

5. A decrease in something at a fixed rate over time is called ________.

Answer: Uniform-rate decrease or depreciation

6. A fixed-rate increase of something over time is called ________.

Answer: Growth

Short Answer Questions — 2 Marks

Question 1: Different Rates in Two Years

The compound interest rate is 6% in the first year and 4% in the second year. Find the compound amount of ₹22,000 after two years.

Source note: The original page provides the detailed working as an image. The question text is readable, but the source's solution image is not available as extractable text.
Method: First calculate the first year's amount using 6%. Then apply the second year's 4% rate to the amount obtained after the first year.

Question 2: Long-Term Compound Interest

Find the compound interest on ₹50,000 at an annual rate of 10% for 22 years.

Source note: The original source supplies the numerical solution as an image. Therefore, the exact source working has not been reconstructed here.

Question 3: Half-Yearly Compounding

The source asks for the compound interest when interest is compounded every 6 months, using an annual rate and a principal of ₹20,000.

Source note: The extracted source text has lost several numerical values in this question. The original page presents the complete expression as an image, so missing values have not been invented.

Question 4: Depreciation of a Machine

The value of a machine decreases by 10% every year. If its present value is ₹1,62,000, find its value 2 years ago.

Approach: For a yearly decrease, the amount after each year becomes 90% of the previous amount. To determine an earlier value, work backwards using the same percentage factor.
Present Value = Previous Value × 0.90 × 0.90

Long Answer Questions — 5 Marks

The source contains six important descriptive problems from the চক্রবৃদ্ধি সুদ ও সমাহার বৃদ্ধি বা হ্রাস chapter. These questions are particularly useful for practising multi-step calculations.

Question 1: Doubling and Fourfold Growth

If a sum of money becomes double in n years at a fixed annual compound interest rate, determine in how many years it will become four times.

Step 1: If the original principal is P, then after n years the amount is 2P.
Step 2: The same growth factor that changes P to 2P, when applied for another n years, changes 2P to 4P.
Answer: The money will become four times in 2n years.

Question 2: Difference Between Compound Interest and Simple Interest

If the difference between compound interest and simple interest on a certain sum for 3 years at an annual rate of 10% is ₹30, find the principal.

Important: The source gives this problem as a long-answer question and provides the detailed solution through an image.

For a 3-year calculation, first write the compound amount using the compound-interest formula and then subtract the simple interest from the compound interest. The resulting difference is equated to ₹30 and the original principal is obtained.

The exact numerical working from the source image is not reproduced because it is not available as searchable text.

Question 3: Quarterly Compound Interest

Find the compound interest on ₹10,000 for 9 months at an annual compound interest rate of 8%, when interest is compounded every 3 months.

Step 1: Since interest is compounded every 3 months, there are four compounding periods in one year.
Step 2: The rate for each 3-month period is one-fourth of the annual rate.
Step 3: Nine months contain three such compounding periods.
Amount = 10000 × (1 + 8/400)3
Method: Calculate the compound amount using the three quarterly periods and then subtract ₹10,000 to obtain the compound interest.

Question 4: Different Interest Rates in Three Years

Find the compound interest on ₹40,000 for 3 years when the annual rates for the first, second and third years are respectively 4%, 5% and 6%.

First year: Amount = 40,000 × 1.04
Second year: The amount obtained after the first year is increased by 5%.
Third year: The amount after the second year is increased by 6%.
Final Amount = 40000 × 1.04 × 1.05 × 1.06
Final step: Compound Interest = Final Amount − ₹40,000.

Question 5: Half-Yearly Compounding

The source asks a compound-interest problem involving a principal, annual rate of 4%, half-yearly compounding and a compound amount of ₹6,632.55.

Source note: The extracted text of the original question is malformed and several values are mixed together. The complete mathematical expression is provided through an image in the source. Therefore, an exact numerical answer has not been invented.

Question 6: Finding the Number of Years

At an annual compound interest rate of 8%, determine after how many years ₹40,000 will become a compound amount of ₹46,656.

46656 = 40000 × (1 + 8/100)n
Step 1: The growth factor is 1.08.
Step 2: The required equation is 46656 / 40000 = 1.08n.
Answer approach: Compare the accumulated amount with successive powers of 1.08 to identify the required number of years.

Compound Growth and Depreciation

Compound growth is not limited to money. The same mathematical idea can be used when a quantity increases or decreases at a fixed percentage rate over time.

Growth

If a quantity increases by a fixed percentage every year, each year's increase is calculated from the amount available at the beginning of that period. This produces compound growth.

Growth Amount = P(1 + r/100)n

Depreciation or Decrease

When the value of an object decreases by a fixed percentage every year, the remaining value becomes the base for the next year's reduction. This is known as depreciation or compound decrease.

Reduced Value = P(1 − r/100)n
Situation Multiplier Basic Form
Growth 1 + r/100 P(1 + r/100)n
Decrease 1 − r/100 P(1 − r/100)n

Important Points to Remember

  • In compound interest, interest is added to the principal after each compounding period.
  • The principal therefore changes from period to period.
  • Compound amount includes both the original principal and compound interest.
  • When compounding is quarterly, the annual rate is divided into four periods.
  • When compounding is half-yearly, the annual rate is divided into two periods.
  • Growth uses an increasing multiplier.
  • Depreciation uses a decreasing multiplier.
  • Always identify the compounding period before applying the formula.

Quick Revision Table

Topic What You Should Practise
Compound Interest Annual compound-interest calculations
Compound Amount Finding the final accumulated value
Different Rates Applying a different rate in each year
Quarterly Compounding Changing annual rate and number of periods
Half-Yearly Compounding Calculating interest twice a year
Compound Growth Finding increased values over several periods
Depreciation Finding reduced values over time
SI and CI Difference Problems comparing simple and compound interest

How to Prepare Chapter 6

Start with the basic meaning of compound interest and understand why the principal changes after every compounding period. Then practise annual, half-yearly and quarterly calculations separately.

After mastering the formula-based questions, move to problems involving different rates in different years, compound growth, depreciation and the difference between simple and compound interest.

Exam Tip: In every compound-interest problem, identify four things first: Principal, Rate, Time and Compounding Period. This makes the calculation much easier and helps prevent mistakes.

More Madhyamik Mathematics Resources

Madhyamik Suggestion 2027 — All Subjects Explore subject-wise WBBSE Class 10 important questions and revision resources. WBBSE Class 10 Madhyamik 2027 Guide Explore syllabus, exam preparation and useful Class 10 study resources.
Source-based note: This article has been substantially rewritten and reorganised for a cleaner Cademy-style reading experience. The supplied source contains several image-based solutions and a few malformed extracted equations. Those parts have been clearly identified instead of filling missing information with unsupported content.

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