Interest Class 6 ICSE — Maths Chapter 11
The Interest Class 6 ICSE chapter teaches simple interest, the extra money paid for using borrowed money. You learn the meaning of principal, rate, time and amount, then one central formula. That formula gives interest directly, and you can rearrange it to find principal, rate or time. This page explains each section in the book’s order, with worked patterns and the chapter PDF for practice.
Download Interest Class 6 ICSE Mathematics Chapter 11 PDF
Download the Interest Class 6 ICSE Mathematics chapter PDF to revise offline or print for practice. It is the full chapter as printed in the book — 6 pages, 6 sections, 28 questions.
What is inside Chapter 11
6 pages · 6 sections · 15 worked examples · 28 exercise questions
| Section | Title |
|---|---|
| 11.1 | BASIC CONCEPT |
| 11.2 | CALCULATING INTEREST |
| 11.3 | INVERSE PROBLEMS ON SIMPLE INTEREST |
| 11.4 | WHEN PRINCIPAL IS REQUIRED |
| 11.5 | WHEN RATE IS REQUIRED |
| 11.6 | WHEN TIME IS REQUIRED |
- EXERCISE 11 (A): 5 questions
- EXERCISE 11 (B): 8 questions
- REVISION EXERCISE (Chapter 11): 15 questions
11.1 BASIC CONCEPT
Section 11.1 defines the three terms this chapter builds on. Interest is the additional money you pay for using borrowed money. The borrowed money itself is the principal, also called the sum. The total money you return is the amount.
These three link by one relation: amount equals principal plus interest. In symbols:
A = P + I
The section also defines rate percent. It is the interest on ₹100 for one year. For example, 6% per annum means ₹6 interest on ₹100 for one year. A rate can also be given per month or semi-annually. Time is the period for which the money is borrowed or lent.
A monthly rate converts to a yearly rate by multiplying by 12. A semi-annual rate doubles for a yearly rate. Try this pattern with your own numbers. If a lender quotes 3% per month, the yearly rate is 3\% \times 12 = 36\% per annum. If the rate is 5% semi-annually, the yearly rate is 2 \times 5\% = 10\% per annum.
11.2 CALCULATING INTEREST
Interest depends on three factors: the principal (P), the rate of interest (R) and the time (T). Change any one, and the interest changes.
The chapter gives one formula for simple interest:
I = \frac{P \times R \times T}{100}
The 100 appears because the rate is a percentage, an amount per hundred.
Here is a worked pattern with fresh numbers. Find the interest on ₹1,200 at 5% per annum for 4 years. Substitute into the formula:
I = \frac{1,200 \times 5 \times 4}{100} = \frac{24,000}{100} = ₹240
So the interest is ₹240.
The book stresses one unit rule. When the rate is per month, the time must be in months. When the rate is per year, the time must be in years. A common mistake in this ICSE chapter is mixing them — taking a monthly rate with a time in years. The fix is to convert the time to months first, or to convert the monthly rate to a yearly rate by multiplying by 12. Both routes give the same answer.
11.3 INVERSE PROBLEMS ON SIMPLE INTEREST
The same formula works backwards. If you know the interest, rate and time, you can find any missing piece. Section 11.3 rewrites the interest formula for each case.
For the principal:
P = \frac{100 \times I}{R \times T}
For the rate:
R\% = \frac{100 \times I}{P \times T}\%
For the time:
T = \frac{100 \times I}{P \times R}
Each form comes from the same interest formula, just solved for a different letter. Notice 100 \times I appears in every rearrangement. Memorise one pattern, and the others follow. The table below collects all four forms so you can see the pattern at a glance.
| To find | Formula | You know |
|---|---|---|
| Interest I | I = \frac{P \times R \times T}{100} | P, R, T |
| Principal P | P = \frac{100 \times I}{R \times T} | I, R, T |
| Rate R\% | R\% = \frac{100 \times I}{P \times T}\% | I, P, T |
| Time T | T = \frac{100 \times I}{P \times R} | I, P, R |
11.4 WHEN PRINCIPAL IS REQUIRED
Sometimes a question gives you the amount, not the interest. The phrase “amounts to” means A = P + I, so you must find the interest before the principal. Section 11.4 shows two routes.
When the interest is given directly, use the principal formula:
P = \frac{100 \times I}{R \times T}
For example, if the interest on a loan is ₹90 at 5% per annum for 3 years, then P = \frac{100 \times 90}{5 \times 3} = ₹600.
The unitary method starts by assuming a principal of ₹100. Compute the interest on ₹100, add it to get the amount, then scale up. Suppose a sum amounts to ₹2,300 in 2 years at 7.5% per annum. On ₹100, the interest is \frac{100 \times 7.5 \times 2}{100} = ₹15, so the amount is ₹115. Then the principal is \frac{100}{115} \times 2,300 = ₹2,000.
The algebraic method does the same work with a letter. Let the principal be x. Write the interest in terms of x, then solve x + interest = amount. For the same sum, interest = \frac{x \times 7.5 \times 2}{100} = \frac{3x}{20}. Then x + \frac{3x}{20} = 2,300, giving \frac{23x}{20} = 2,300, so x = ₹2,000.
11.5 WHEN RATE IS REQUIRED
Section 11.5 applies the rate form of the formula. The rate is always a percentage, so the percent sign stays in the answer.
R\% = \frac{100 \times I}{P \times T}\%
Use this pattern with new numbers. Find the rate if the interest on ₹450 is ₹90 in 5 years. Substitute:
R\% = \frac{100 \times 90}{450 \times 5}\% = \frac{9,000}{2,250}\% = 4\%
The rate is 4% per annum. Carry the percent sign through every step, or you may drop it from the final answer.
11.6 WHEN TIME IS REQUIRED
The time form of the formula gives the answer in years, since the rate is usually per annum.
T = \frac{100 \times I}{P \times R}
Use this pattern with new numbers. Find the time for the interest on ₹1,200 to reach ₹180 at 6% per annum. Substitute:
T = \frac{100 \times 180}{1,200 \times 6} = \frac{18,000}{7,200} = 2\frac{1}{2} \text{ years}
The chapter also covers sums that double or triple themselves. The method assumes the principal is ₹100. For a doubling sum, the amount is 2 \times ₹100 = ₹200, so the interest is amount minus principal, ₹200 - ₹100 = ₹100. Then:
T = \frac{100 \times 100}{100 \times 5} = 20 \text{ years}
So a sum doubles in 20 years at 5% per annum. For a tripling sum, repeat the same steps with amount = 3 × ₹100. For related work with percentages, see the Profit and Loss chapter.
What to practise from Interest Class 6 ICSE
This chapter’s practice is spread across two exercises and one revision set. All three blocks belong to the Class 6 ICSE Maths syllabus, which you can confirm on the official CISCE website.
- EXERCISE 11 (A) — 5 questions on finding simple interest, including rates given in paise per rupee.
- EXERCISE 11 (B) — 8 questions on inverse problems for principal, rate and time.
- REVISION EXERCISE (Chapter 11) — 15 questions mixing all the patterns from the chapter.
One conversion appears in Exercise 11 (A): 5 paise per rupee equals 5%. A rate stated in paise per rupee converts directly to a percentage. For more chapters, browse the Class 6 Maths hub.
Interest Class 6 ICSE frequently asked questions
How do I find the principal in Interest Class 6 ICSE problems?
Use the principal formula P = \frac{100 \times I}{R \times T} when the interest is given. If the question says “amounts to”, find the interest first from A = P + I, then apply the formula or the unitary method.
What is the difference between principal, interest and amount?
Principal is the borrowed money. Interest is the extra money paid for using it. Amount is the total you return, given by A = P + I.
Why must time be in months when the rate is per month?
Because the rate is stated per month, the formula needs matching units. If you use a time in years with a monthly rate, the answer is wrong. Convert the time to months first, or convert the rate to per annum by multiplying by 12.
How do I solve a sum that triples itself question?
Assume the principal is ₹100. For a tripling sum the amount is ₹300, so the interest is ₹200. Then put I = 200, P = 100 and the given rate into T = \frac{100 \times I}{P \times R}.
How do I convert paise per rupee into a percentage?
Paise per rupee means paise on every ₹1. Since ₹1 is one-hundredth of ₹100, the percentage equals the same number. So 5 paise per rupee is 5%, and 12 paise per rupee is 12%.
Reference: ICSE Class 6 Mathematics textbook material, chapter 11: Interest — CISCE-aligned.