Compound Interest Class 10 ICSE — A. Das Gupta Chapter 1
Compound interest class 10 ICSE opens the A. Das Gupta Mathematics book with the formulas that run through all of commercial mathematics. The chapter defines the principal, the rate, and the time, then builds the amount formula step by step. You will learn annual and half yearly compounding, plus the two practical applications: population growth and depreciation. The Class 10 ICSE Maths collection also covers the later chapters that build on these ideas.
Download Compound Interest Class 10 ICSE Mathematics Chapter 1 PDF
Download the Compound Interest Class 10 ICSE Mathematics chapter PDF from the A. Das Gupta textbook to revise offline or print for practice. It is the full chapter as printed in the book — 25 pages, 3 sections, 60 questions.
What is inside Chapter 1
25 pages · 3 sections · 60 exercise questions
| Section | Title |
|---|---|
| 1 | Formulae |
| 1 | When Interest is Reckoned Annually |
| 2 | When Interest is Reckoned Half-yearly (or Semi-annually) |
- EXERCISE 1 (A): 14 questions
- EXERCISE 1(B): 31 questions
- EXERCISE 1 (C): 15 questions
1 Formulae
This section fixes the notation used for the whole chapter. Principal P is the money invested or borrowed. Rate R is the interest per cent per annum, and time n is the number of years.
The amount after n years is given by the core formula:
A = P \left(1 + \frac{R}{100}\right)^n
Compound interest is the amount minus the principal. This simplifies to the bracket form \text{C.I.} = P \left[katex display="true"]\left(1 + \frac{R}{100}\right)^n - 1 \right[/katex]. The bracket form is useful because it gives the interest directly without a separate subtraction step.
Why does the factor (1 + R/100) repeat n times? Each year the interest is added to the principal, so the next year’s interest is calculated on a larger base. This is the difference between compound and simple interest, and it is why the amount grows faster than a straight line.
Worked pattern: take P = 20000, R = 5\%, n = 2. Then A = 20000 \times \left(\frac{21}{20}\right)^2 = 20000 \times \frac{441}{400} = 22050. So \text{C.I.} = 22050 - 20000 = 2050.
1 When Interest is Reckoned Annually
This section applies the annual formula in four situations. The first is a uniform rate for the whole period, which is the basic formula from the previous section.
The second situation uses two successive rates, R_1\% and R_2\%. The amount becomes A = P \left(1 + \frac{R_1}{100}\right) \left(1 + \frac{R_2}{100}\right). The third situation extends this to three successive rates with a third bracket, R_1\%, R_2\% and R_3\%.
The fourth situation is an incomplete period, say 2 years 7 months. The completed years compound normally, while the fractional months earn simple interest on the amount at the end of the completed years. The formula becomes A = P \left(1 + \frac{R}{100}\right)^2 \left(1 + \frac{\frac{7}{12}R}{100}\right).
| Case | Formula |
|---|---|
| Uniform rate | A = P \left(1 + \frac{R}{100}\right)^n |
| Two successive rates | A = P \left(1 + \frac{R_1}{100}\right) \left(1 + \frac{R_2}{100}\right) |
| Three successive rates | A = P \left(1 + \frac{R_1}{100}\right) \left(1 + \frac{R_2}{100}\right) \left(1 + \frac{R_3}{100}\right) |
| Incomplete period | A = P \left(1 + \frac{R}{100}\right)^2 \left(1 + \frac{\frac{7}{12}R}{100}\right) |
Worked pattern: Rs 10000 at 10% for 2 years. Then A = 10000 \times \left(\frac{11}{10}\right)^2 = 12100. The compound interest is 12100 - 10000 = 2100.
The common mistake is compounding a fractional year as a full period. The fractional months must be treated as simple interest on the amount at the end of the completed years. That keeps the answer accurate and matches how banks actually credit interest.
2 When Interest is Reckoned Half-yearly (or Semi-annually)
When interest is compounded half yearly, the rate is halved and the time is doubled. The rate becomes \frac{R}{2}\% per half year, and n years become 2n half years. The amount formula becomes A = P \left(1 + \frac{R}{2 \times 100}\right)^{2n}.
The book notes that the simple interest and compound interest for the first unit of time are always equal. This holds because the first interest payment is identical in both methods. The difference appears only from the second period onwards, when compound interest works on the increased amount.
Worked pattern: Rs 5000 at 8% per annum compounded half yearly for 1 year. Here R/2 = 4\% and 2n = 2. So A = 5000 \times \left(1 + \frac{4}{100}\right)^2 = 5000 \times \frac{26}{25} \times \frac{26}{25} = 5408. The compound interest is 5408 - 5000 = 408.
Population growth and decrease
Population growth uses the same compounding idea. If a population grows at r\% per annum, then (Population after n years) = Present Population \times \left(1 + \frac{r}{100}\right)^n. The backwards form gives the population n years ago: (Population n years ago) \times \left(1 + \frac{r}{100}\right)^n = Present Population.
Two successive growth rates r_1\% and r_2\% give (Population after 2 years) = Present Population \times \left(1 + \frac{r_1}{100}\right) \times \left(1 + \frac{r_2}{100}\right). The formula extends to more than 2 years. A regular decrease uses a minus sign instead of plus.
When birth rate and death rate are both given, subtract the death rate from the birth rate to get the net annual growth. For example, a birth rate of 11.7% and a death rate of 4.2% give a net growth of 7.5% per year.
Depreciation
Depreciation is population growth with a minus sign. If a machine’s value depreciates at r\% per annum, then (Value after n years) = Present Value \times \left(1 - \frac{r}{100}\right)^n. The backwards form is (Value n years ago) \times \left(1 - \frac{r}{100}\right)^n = Present Value.
Worked pattern: a machine worth Rs 20000 depreciates at 10% per annum. After 2 years its value is 20000 \times \left(\frac{9}{10}\right)^2 = 20000 \times \frac{81}{100} = 16200. The machine lost Rs 3800 over two years.
For the population and depreciation sections, the full ICSE Class 10 books list shows how this chapter connects to the rest of the syllabus. You can verify the official exam scope on the CISCE website.
What to practise from Compound Interest Class 10 ICSE
- EXERCISE 1 (A) — 14 questions: annual compounding, successive rates and incomplete periods.
- EXERCISE 1(B) — 31 questions: half yearly compounding, finding the rate, time or principal, and the difference between compound interest and simple interest.
- EXERCISE 1 (C) — 15 questions: population growth and depreciation.
Work through 1(A) first to fix the annual formulas, then move to 1(B) for the half yearly and reverse problems. Finish with 1(C), where the same compounding idea is applied to real-world growth and decay.
Compound Interest Class 10 ICSE frequently asked questions
What is the compound interest class 10 icse formula for amount and compound interest?
The amount is A = P \left(1 + \frac{R}{100}\right)^n and the compound interest is \text{C.I.} = P \left[katex display="true"]\left(1 + \frac{R}{100}\right)^n - 1 \right[/katex]. Subtract the principal from the amount to get the interest directly.
How is compound interest different from simple interest for the same principal and rate?
Simple interest stays fixed on the original principal each year. Compound interest is recalculated on the growing amount, so it is larger from the second period onward. The first period’s interest is identical in both methods.
How do you find the rate of interest when only the compound interest is given?
Write the compound interest formula with P and n known, then solve for R. Compare A/P with a known power of (1 + R/100) and read off the rate.
How is compound interest calculated when interest is compounded half yearly?
Halve the rate and double the time. Use A = P \left(1 + \frac{R}{2 \times 100}\right)^{2n}, then subtract the principal to get the interest.
What is the difference between population growth and depreciation in this chapter?
Population growth uses a plus sign in (1 + r/100)^n, so the amount rises. Depreciation uses a minus sign, (1 - r/100)^n, so the value falls each year.
Reference: ICSE Class 10 Mathematics textbook material, chapter 1: Compound Interest — CISCE-aligned.
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