Compound Interest Class 9 ICSE — Maths Chapter 2
Compound interest class 9 ICSE maths starts with one idea: interest earned in a period is added to the principal, and the next period’s interest is calculated on the new total. This chapter, Chapter 2 of the Class 9 ICSE Mathematics book, teaches compound interest without using the formula. You apply the repeated simple interest method period by period until the final amount is found. It also relates compound interest to simple interest, and covers yearly, half-yearly and fractional periods.
Download Compound Interest Without Using Formula Class 9 ICSE Mathematics Chapter 2 PDF
Download the Compound Interest Without Using Formula Class 9 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 16 pages, 6 sections, 28 questions.
What is inside Chapter 2
16 pages · 6 sections · 19 worked examples · 28 exercise questions
| Section | Title |
|---|---|
| 2.1 | INTRODUCTION |
| 2.2 | INTEREST (Simple Interest) |
| 2.3 | COMPOUND INTEREST (C.I.) |
| 2.4 | COMPOUND INTEREST AS A REPEATED SIMPLE INTEREST COMPUTATION WITH A GROWING PRINCIPAL |
| 2.5 | MORE ABOUT COMPOUND INTEREST |
| 2.6 | RELATION BETWEEN SIMPLE INTEREST (S.I.) AND COMPOUND INTEREST (C.I.) |
- EXERCISE 2 (A): 10 questions
- EXERCISE 2 (D): 18 questions
2.1 INTRODUCTION
When you borrow money from a bank, you must return it after a fixed period. You also pay some extra money for using the lender’s money. That arrangement defines the three core terms of this chapter.
- Principal is the money borrowed.
- Interest is the extra money paid for using the money.
- Amount is the total money paid back at the end of the period.
The amount is simply the principal plus the interest: A = P + I
Suppose you borrow ₹2,000 and repay ₹2,150 later. The principal is ₹2,000. The amount is ₹2,150. The interest is ₹150, the difference between the two. Every calculation in this chapter builds on this single relation, so it is worth fixing now.
2.2 INTEREST (Simple Interest)
Interest is simple when it is calculated on the original principal throughout the loan period. The rate stays fixed, and the principal never changes, no matter how long the loan runs. The rule is: I = \frac{P \times R \times T}{100}
Here P is the principal, R is the rate percent per annum, and T is the time in years. There is a convention worth remembering: when a problem says “interest” without any qualifier, it always means simple interest. The official CISCE website publishes the full Class 9 Mathematics syllabus and examination details.
Take ₹5,000 at 6% per annum for 3 years. Substituting into the rule: I = \frac{5000 \times 6 \times 3}{100} = 900 The interest is ₹300 per year. Because the principal stays at ₹5,000, the yearly interest never changes.
2.3 COMPOUND INTEREST (C.I.)
Money is lent at compound interest when the interest due at the end of a fixed period is not paid to the lender but added to the sum lent. The new total becomes the principal for the next period. The process repeats until the final amount is found. Compound interest is the difference between the final amount and the original principal: \text{C.I.} = A - P
A table in the chapter compares simple and compound interest on the same sum. Consider ₹2,000 at 10% per annum for 3 years. The pattern looks like this:
| Year | Simple interest | Compound interest |
|---|---|---|
| 1 | ₹200 | ₹200 |
| 2 | ₹200 | ₹220 |
| 3 | ₹200 | ₹242 |
Under simple interest, each year pays ₹200. Under compound interest, the yearly interest grows: ₹200, then ₹220, then ₹242. The first year is equal for both. From the second year onward, compound interest pulls ahead, and the gap widens every year.
2.4 COMPOUND INTEREST AS A REPEATED SIMPLE INTEREST COMPUTATION WITH A GROWING PRINCIPAL
This is the method section of the chapter. Each period uses the same simple interest rule, but the principal changes. The amount at the end of one period becomes the principal for the next period. That is the meaning of “a growing principal”.
The conversion period is the time after which the principal changes. Compounded yearly means the conversion period is one year. Compounded half-yearly means it is six months, so the principal changes twice a year. Before starting any calculation, identify the conversion period — it decides the time value T used in the interest formula.
Work through an example: find the compound interest on ₹12,000 at 7% per annum for 2 years.
First year: I_1 = \frac{12000 \times 7 \times 1}{100} = 840 Amount at the end of the first year = ₹12,000 + ₹840 = ₹12,840.
Second year: the principal is now ₹12,840. I_2 = \frac{12840 \times 7 \times 1}{100} = 898.80 Amount at the end of the second year = ₹12,840 + ₹898.80 = ₹13,738.80.
Total C.I. = final amount − original principal = ₹13,738.80 − ₹12,000 = ₹1,738.80. The same answer comes from adding the two yearly interests: ₹840 + ₹898.80. This method carries through the rest of the Class 9 ICSE Maths chapters, so practise it on paper.
The same method handles every variation in the chapter:
- Half-yearly compounding uses T = 1/2, so the denominator becomes 100 × 2.
- Fractional periods like 2½ years treat the full years normally, then the half year as a separate period.
- Successive rates apply each year’s rate to that year’s principal.
- Repayment problems subtract the amount repaid from the amount due; the balance becomes the next principal.
Three mistakes appear again and again. Using the annual rate for a half-yearly period doubles the interest. Forgetting to add interest to the principal before the next period breaks the chain. Subtracting the wrong principal when finding C.I. — the first-year principal instead of the original sum — inflates the answer. Check each of these before you finish.
Across the two exercises, two question types dominate: finding the rate from two consecutive interests, and loan repayment problems where part of the amount is paid back. Both use the same growing-principal method, so this section prepares you for most of the exercise questions.
2.5 MORE ABOUT COMPOUND INTEREST
On the same sum and at the same rate, the C.I. of any period is always more than the C.I. of the previous period. This holds for yearly and half-yearly compounding alike. The reason is the growing principal: each period’s interest is calculated on a larger base than the last.
That leads to the chapter’s key rule. The difference between the compound interests of two consecutive periods is the interest of one period on the C.I. of the preceding period. Rearranged, this gives a direct rate formula: \text{Rate} = \frac{\text{Difference in interests} \times 100}{\text{C.I. of preceding period} \times \text{Time}} \% The same idea works with amounts in place of interests.
Suppose the interests of two consecutive years are ₹2,000 and ₹2,160. The difference is ₹160. That is one year’s interest on ₹2,000. So the rate is (160 × 100) / (2,000 × 1) = 8%.
2.6 RELATION BETWEEN SIMPLE INTEREST (S.I.) AND COMPOUND INTEREST (C.I.)
Two fixed relations connect the two kinds of interest. First, simple interest on a fixed sum at a fixed rate is the same every year. Second, compound interest for the first year equals simple interest for that first year, on the same sum and at the same rate.
The second relation is a shortcut. It lets you read the first year’s C.I. straight from S.I. data. If the S.I. on a sum is ₹750 in 3 years, then the S.I. per year is ₹250, and the first year’s C.I. is also ₹250.
Two important results follow for any two consecutive conversion periods. If the C.I. of one period is ₹x, the next period’s C.I. is ₹x plus the interest on ₹x for one period. The same applies to amounts. These results let you find later-year interests without recomputing from the start — the approach the next chapter on compound interest using the formula extends further.
What to practise from Compound Interest Class 9 ICSE
- EXERCISE 2 (A) — 10 questions on basic amount and compound interest calculations, including yearly, half-yearly and fractional periods.
- EXERCISE 2 (D) — 18 questions covering rate finding, depreciation, repayment and successive year problems.
Compound Interest Class 9 ICSE frequently asked questions
How is compound interest class 9 ICSE calculated without using the formula?
You apply the simple interest rule I = \frac{P \times R \times T}{100} to each period separately. The amount at the end of one period becomes the principal for the next. Compound interest is the final amount minus the original principal.
What is the conversion period in this ICSE chapter on compound interest?
The conversion period is the time after which the principal changes. Compounded yearly means one year; compounded half-yearly means six months. The conversion period decides the time value used in the interest formula.
Why is the compound interest for the first year equal to simple interest in Class 9 ICSE Maths?
In the first period there is no previous interest to add. The principal is the original sum for both methods, and the same rate applies. So the first-year interest is identical under simple and compound interest.
How do I find the rate when the compound interest of two consecutive years is given in Class 9 ICSE Maths?
Subtract the earlier interest from the later one. That difference is one period’s interest on the earlier interest. Divide the difference by the earlier interest and multiply by 100.
What is the difference between compound interest and simple interest for 2 years in Class 9 ICSE?
Simple interest pays the same amount each year, so the 2-year figure is twice the first-year interest. Compound interest pays more in the second year because the second-year interest is calculated on the first-year amount. The difference is the interest earned on the first year’s interest.
Reference: ICSE Class 9 Mathematics textbook material, chapter 2: Compound Interest Without Using Formula — CISCE-aligned.
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