Simple Interest: ICSE Class 7 Complete Guide

A father of a seventh grader called me last month. He had lent ten thousand rupees to a friend for eighteen months at some rate, and when the friend returned the money he had added 'a little extra'. Neither of them could agree on whether the extra was fair. The father came to me for help, and after we worked through the simple interest formula together, he got his answer in ninety seconds. 'I wish they had taught me this in school,' he said.

That is the gift of simple interest. It is the first glimpse of how money grows over time, the logic that underpins every bank loan, fixed deposit, recurring deposit and even the penalty on a late phone bill. ICSE Class 7 Selina introduces it as the third chapter of the commercial maths trilogy, right after percentage and profit loss discount. If your child can do percent confidently, simple interest is just one small step away.

This guide walks through the single formula, every variation of question ICSE examiners ask, and the one specific trick with months and days that catches students off guard in almost every school test.

Simple interest problems use four terms. Get them right and half the chapter is done.

* Principal (P): the sum of money borrowed or deposited. This is the starting amount.
* Rate of interest (R): the percent charged per year. For example, $10\%$ per annum means ten rupees per hundred per year.
* Time (T): the duration for which the money is borrowed or deposited, expressed in years.
* Simple Interest (SI): the extra money earned (or paid) after the time period ends.

And one more:

* Amount (A): the total money returned at the end. $A = P + SI$.

The rate is always per year (per annum) unless the question says otherwise. The time must always be expressed in years. This is the most common source of errors, as we will see below.

Problem: Find the simple interest on Rs 5000 at $8\%$ per annum for 3 years.

Solution:

$P = 5000$, $R = 8$, $T = 3$.

The simple interest is Rs 1200.

Total amount after 3 years $= P + SI = 5000 + 1200 = 6200$.

Problem: Rohit invested some money at $6\%$ per annum simple interest for 5 years and earned Rs 900 as interest. Find the principal.

Solution:

$SI = 900$, $R = 6$, $T = 5$.

The principal was Rs 3000.

Check: $SI = \frac{3000 \times 6 \times 5}{100} = 900$. Matches.

Problem: A sum of Rs 4000 earned Rs 800 simple interest in 4 years. Find the rate percent.

Solution:

$P = 4000$, $SI = 800$, $T = 4$.

The rate is $5\%$ per annum.

Check: $SI = \frac{4000 \times 5 \times 4}{100} = 800$. Matches.

Problem: In how many years will Rs 5000 earn Rs 1250 as simple interest at $5\%$ per annum?

Solution:

$P = 5000$, $SI = 1250$, $R = 5$.

The time required is 5 years.

Here is the ICSE speciality. Selina often gives the time in months or days instead of years, and students forget to convert.

To convert:

* Months to years: divide by 12. So 6 months $= \frac{6}{12} = 0.5$ years.
* Days to years: divide by 365. So 73 days $= \frac{73}{365} = 0.2$ years.

Worked example 5: Find the simple interest on Rs 6000 at $10\%$ per annum for 9 months.

Solution:

$P = 6000$, $R = 10$, $T = \frac{9}{12}$ years $= 0.75$ years (or use the fraction directly).

The simple interest is Rs 450.

Notice how I absorbed the 12 into the denominator. Whenever time is in months, you can just multiply the denominator by 12 and keep the months in the numerator. Same answer, slightly cleaner arithmetic.

Worked example 6: Find the simple interest on Rs 2000 at $4\%$ per annum from 1st April 2026 to 30th September 2026.

Solution: First count the days.
April: 30 days
May: 31
June: 30
July: 31
August: 31
September: 30

Total = 183 days. But in ICSE convention, you usually exclude the first day and include the last, or vice versa. Check what your textbook says. Selina typically uses the 'excluding first, including last' rule, which gives 182 days. To keep the example simple, let us use 180 days so the arithmetic is clean.

$T = \frac{180}{365}$ years.

The simple interest is approximately Rs 39.45.

Some textbooks use 360 days in a year (called banker's interest). Selina uses 365. Always read the question carefully to see which convention applies.

Occasionally the question tells you the amount returned at the end and asks you to find the interest. Just subtract.

Example: A sum of Rs 4000 grows to Rs 4600 in 3 years at simple interest. Find the rate.

Solution:
$SI = A - P = 4600 - 4000 = 600$.

The rate is $5\%$ per annum.

This kind of question is common in ICSE school tests because it checks whether the student remembers the amount formula.

Six errors that keep students losing easy marks on this chapter.

1. Forgetting to divide by 100. Writing $SI = P \times R \times T$ and getting an answer that is a hundred times too big.

2. Not converting months to years. Using $T = 9$ for 9 months instead of $T = \frac{9}{12}$.

3. Using the amount in the formula. Substituting $A$ where $P$ should go. The formula uses principal, not amount.

4. Sloppy unit handling in days. Using 365 when the textbook expects 360, or vice versa. Read the chapter's convention first.

5. Wrong rearrangement. Writing $P = \frac{SI \times R \times T}{100}$ instead of $P = \frac{SI \times 100}{R \times T}$. A practice is to memorise all four versions separately.

6. Missing the final 'rupee' label. Writing '$SI = 1200$' without the rupee sign. Always label your final answer with the correct unit.

* $SI = \frac{PRT}{100}$ is the one formula for the entire chapter.
* $A = P + SI$ gives the total amount returned at the end.
* Rate is per year and time must be in years.
* Months to years: divide by 12. Days to years: divide by 365 (or 360 if your textbook says so).
* Rearrange the formula to find P, R or T when the other three are given.
* Always check your answer by substituting back into the original formula.
* Watch the units. Label the final answer with rupees or the time unit as appropriate.