Compound Interest Class 9 ICSE — Arun Chapter 3

Compound Interest Class 9 ICSE is the chapter that takes the simple interest idea and makes it work on itself. This Arun Deep chapter shows how interest earned in one period becomes part of the principal for the next. You learn two paths to the answer: the year by year method and the direct amount formula A = P\left(1 + \frac{r}{100}\right)^n. Both lead to the same result.

Download Compound Interest Class 9 ICSE Mathematics Chapter 3 PDF

Download the Compound Interest Class 9 ICSE Mathematics chapter PDF from the Arun Deep textbook to revise offline or print for practice. It is the full chapter as printed in the book — 6 pages, 1 sections, 15 questions.

What is inside Chapter 3

6 pages · 1 sections · 15 exercise questions

• Exercise 3-A: 7 questions
• Exercise 3-B: 8 questions

3 Compound Interest

The chapter opens with a summary block called Points to Remember. It sets down the two formulas every question in the exercises builds on.

Simple interest is the older idea. Interest is charged only on the original principal, never on interest already earned. The formula is:

\text{S.I.} = \frac{\text{Principal} \times \text{Rate} \times \text{Time}}{100} = \frac{\text{Prt}}{100}

Here P is the principal (the sum lent or borrowed), r is the rate per annum, and t is the time in years. The amount after simple interest is P + S.I.

The chapter then moves to compound interest, which works differently. Interest is added to the principal at the end of each period, and the next period’s interest is calculated on this larger sum. The direct formula for the amount is:

A = P \left(1 + \frac{r}{100}\right)^n

where A is the amount, r is the rate per annum, and n is the number of periods. Compound interest itself is then:

\text{C.I.} = A - P = P \left[katex display="true"]\left(1 + \frac{r}{100}\right)^n - 1 \right[/katex]

The key point is what n measures. The chapter’s formula note says n is the period in years, half-years, or quarters. That single sentence drives every half yearly and quarterly question in the exercises.

Annual compounding: the year by year method

When n is small, the direct formula can hide what is happening. The year by year method shows it. You compute the interest for one year, add it to the principal, and that new sum becomes the principal for the next year.

Here is the pattern with fresh numbers. Suppose you invest Rs. 40000 at 10% per annum for 2 years, compounded annually.

The textbook works every question this way in Exercise 3-A. Exercise 3-B switches to the direct formula. Both give the same answer. You can browse the rest of the Class 9 ICSE Maths book list to see how this chapter fits the year.

Simple interest versus compound interest

Why does compound interest come out higher? Because each year’s interest earns interest of its own the next year. Simple interest never does; it is always calculated on the original principal.

Try Rs. 12000 at 10% for 2 years. Simple interest is \frac{12000 \times 10 \times 2}{100} = 2400. Compound interest is 12000 \times (1.1)^2 - 12000 = 14520 - 12000 = 2520. The difference is Rs. 120, which is exactly the interest earned on the first year’s interest of Rs. 1200.

Half yearly and quarterly compounding

When compounding happens more than once a year, both the rate and the period must be converted. The rule is simple: divide the rate by the number of periods per year, and multiply the number of years by that same number.

• Half yearly: rate becomes \frac{r}{2}, period becomes 2n.
• Quarterly: rate becomes \frac{r}{4}, period becomes 4n.

Take Rs. 50000 at 8% p.a. compounded half yearly for 1 year. The rate becomes 4% per half-year and the period becomes 2 half-years. First half-year interest is \frac{50000 \times 4 \times 1}{100} = 2000. Second half-year interest is \frac{52000 \times 4 \times 1}{100} = 2080. Total interest is Rs. 4080.

The quarterly version works the same way. Rs. 15625 at 16% p.a. for 9 months becomes 4% per quarter over 3 quarters. Worked quarter by quarter, the total interest is Rs. 1951.

Changing rates across years

When the rate differs from year to year, the amount formula extends to one factor per year:

A = P \left(1 + \frac{r_1}{100}\right)\left(1 + \frac{r_2}{100}\right)

For Rs. 20000 at 10% for the first year and 12% for the second, the amount is 20000 \times \frac{110}{100} \times \frac{112}{100} = 24640. Compound interest is Rs. 4640.

There is no shortcut to a single rate. Each year’s factor is separate because the rate itself changes. The next chapter on expansions continues this algebraic work in the Arun Deep Class 9 Maths series.

Fractional periods

When the time is not a whole number of years, the chapter splits the period. The whole years use the standard formula. The remaining fraction is handled as simple interest on the amount at the end of the whole years.

For Rs. 30000 at 10% for 2\frac{1}{2} years, the amount is 30000 \times (1.1)^2 \times (1.05) = 38115. The first part compounds for 2 full years. The half-year factor uses half the annual rate.

The common mistake is to use the fractional part as a whole year. A student who treats 2\frac{1}{2} years as 2.5 in the exponent gets a different, wrong answer. The same error appears when a period is given in months. Convert months to a fraction of a year before applying the formula.

What to practise from Compound Interest Class 9 ICSE

This Class 9 ICSE chapter has two exercise blocks, and they train different skills.

• Exercise 3-A (7 questions): the year by year method. You compute interest period by period, converting the rate for half yearly and quarterly compounding.
• Exercise 3-B (8 questions): the amount formula applied directly. You use it for changing rates across years and for fractional periods.

Both blocks end the same way. Compound interest equals amount minus principal.

The chapter also has one summary section, Points to Remember, which collects both formulas at the top. For official syllabus details, check the CISCE website.

Compound Interest Class 9 ICSE frequently asked questions

What is compound interest class 9 ICSE?

Compound interest is interest calculated on the principal plus any interest already earned. Each period’s interest joins the principal, and the next period’s interest is computed on that larger sum. The chapter gives the amount formula A = P\left(1 + \frac{r}{100}\right)^n and defines compound interest as A − P.

How do you find compound interest when it is compounded half yearly?

Divide the annual rate by 2 and double the number of periods. For Rs. 32500 at 12% p.a. compounded half yearly for 1 year, the rate becomes 6% and the period becomes 2 half-years. Work the interest half-year by half-year on the growing principal.

What is the difference between simple interest and compound interest?

Simple interest is always calculated on the original principal. Compound interest is calculated on the principal plus accumulated interest. For the same rate and time beyond one year, compound interest is always higher.

How do you find compound interest for two and a half years?

Compound the whole years with the standard formula, then treat the half-year as simple interest on the resulting amount. For 2\frac{1}{2} years at 12%, the amount is P\left(1 + \frac{12}{100}\right)^2 \left(1 + \frac{12}{2 \times 100}\right).

Why is compound interest more than simple interest for the same rate and time?

Because it charges interest on interest. The first year’s interest becomes part of the principal for the second year, so the second year’s interest is larger. Simple interest never does this; it is always on the original sum.

Reference: ICSE Class 9 Mathematics textbook material, chapter 3: Compound Interest — CISCE-aligned.

More from this book

• Chapter 4: Expansions
• Chapter 19: Mean and Median of Ungrouped Data
• Chapter 20: Parimeter and Area of Plane Figures