One Formula, Four Different Questions
Learn to identify principal, rate, time and amount, use the simple interest formula, handle time given in months or days, and rearrange the formula to find any missing quantity.
Can one formula answer every simple interest question?
Yes. has four letters, and any question gives you three of them and asks for the fourth — so the only skill is rearranging it.
That makes this the most self-contained chapter in the syllabus. This page covers everything in the ICSE Class 7 Mathematics chapter on simple interest: the quantities and the formula, calculating interest and amount, finding a missing quantity, and word problems.
That makes this the most self-contained chapter in the syllabus. This page covers everything in the ICSE Class 7 Mathematics chapter on simple interest: the quantities and the formula, calculating interest and amount, finding a missing quantity, and word problems.
Formula
What do principal, rate, time and amount mean?
- Principal (P) — the sum of money borrowed, lent or deposited.
- Rate (R) — the interest charged on ₹100 for one year, written as a percentage per annum.
- Time (T) — the period of the loan or deposit, in years.
- Interest (SI) — the extra money paid for the use of the principal.
- Amount (A) — the principal together with the interest.
The two formulae are:
Worked example. ₹5000 is deposited at 8 percent per annum for 3 years.
A recurring deposit at a bank works on the same idea, and "per annum" on any loan document means exactly this rate.
The word simple matters, and it is what separates this chapter from later ones. The interest is calculated on the original principal every year, so it is the same each year — ₹400 a year in the example above. It is never added to the principal, which is what compound interest would do.
- Rate (R) — the interest charged on ₹100 for one year, written as a percentage per annum.
- Time (T) — the period of the loan or deposit, in years.
- Interest (SI) — the extra money paid for the use of the principal.
- Amount (A) — the principal together with the interest.
The two formulae are:
Worked example. ₹5000 is deposited at 8 percent per annum for 3 years.
A recurring deposit at a bank works on the same idea, and "per annum" on any loan document means exactly this rate.
The word simple matters, and it is what separates this chapter from later ones. The interest is calculated on the original principal every year, so it is the same each year — ₹400 a year in the example above. It is never added to the principal, which is what compound interest would do.
How do you calculate interest when the time is in months or days?
Convert the time to years first, because the formula's is in years.
Worked example, months. ₹4000 at 10 percent for 9 months. Here year:
Worked example, months again. ₹6000 at 12 percent for 8 months, so :
Worked example, days. ₹7300 at 5 percent for 73 days, so :
And for mixed periods, 2 years 6 months is years.
Forgetting the conversion is the commonest single error in the chapter. Using for nine months would give ₹3600 instead of ₹300 — twelve times too much, and obviously impossible since the interest would nearly equal the principal.
Worked example, months. ₹4000 at 10 percent for 9 months. Here year:
Worked example, months again. ₹6000 at 12 percent for 8 months, so :
Worked example, days. ₹7300 at 5 percent for 73 days, so :
And for mixed periods, 2 years 6 months is years.
Forgetting the conversion is the commonest single error in the chapter. Using for nine months would give ₹3600 instead of ₹300 — twelve times too much, and obviously impossible since the interest would nearly equal the principal.
How do you find the principal, rate or time?
Rearrange the same formula, so that whichever letter is unknown stands alone:
Finding the rate. The interest on ₹6000 for 3 years is ₹900:
Finding the time. ₹2500 at 8 percent earns ₹600 in
Finding the principal. A sum earns ₹1260 in 3 years at 7 percent:
The pattern is easy to see once written out: the 100 always moves to the top, and the two quantities you know move to the bottom.
Every answer can then be checked by substituting back. Putting , and into the original formula gives , which matches — a single line that confirms the rearrangement was done correctly.
Finding the rate. The interest on ₹6000 for 3 years is ₹900:
Finding the time. ₹2500 at 8 percent earns ₹600 in
Finding the principal. A sum earns ₹1260 in 3 years at 7 percent:
The pattern is easy to see once written out: the 100 always moves to the top, and the two quantities you know move to the bottom.
Every answer can then be checked by substituting back. Putting , and into the original formula gives , which matches — a single line that confirms the rearrangement was done correctly.
How do you find a sum that grows to a given amount?
When a question gives the amount rather than the interest, the interest is not known directly — so use the combined relation:
Worked example. What sum grows to ₹7000 in 4 years at 10 percent per annum?
Here , so
Check: , and . Correct.
Another. A sum becomes ₹5220 in 3 years at 8 percent. Since :
Difference of amounts. If ₹2000 is lent at 9 percent and ₹3000 at 6 percent, both for 2 years, the total interest is
The trap is treating the amount as the interest. In the first example, dividing ₹7000 by the rate and time as though it were interest would give a nonsensical principal — the ₹7000 already contains the principal, which is why the factor is needed.
Worked example. What sum grows to ₹7000 in 4 years at 10 percent per annum?
Here , so
Check: , and . Correct.
Another. A sum becomes ₹5220 in 3 years at 8 percent. Since :
Difference of amounts. If ₹2000 is lent at 9 percent and ₹3000 at 6 percent, both for 2 years, the total interest is
The trap is treating the amount as the interest. In the first example, dividing ₹7000 by the rate and time as though it were interest would give a nonsensical principal — the ₹7000 already contains the principal, which is why the factor is needed.
Exam tip
Exam tip: converting time to years on the first line
Simple interest questions are formula work, so the marks are in the setting out.
List P, R, T with their values before substituting, and convert the time to years right there: *T = 9 months = year.* That conversion line is the one examiners look for.
Write the formula before the numbers. earns a mark on its own even if the arithmetic slips.
Read whether the question wants the interest or the amount, and add when it wants the amount. Answering with SI when A was asked loses the final mark.
When the amount is given, use rather than treating A as the interest.
And check by substituting back into the original formula — one line, and it catches every rearrangement error.
List P, R, T with their values before substituting, and convert the time to years right there: *T = 9 months = year.* That conversion line is the one examiners look for.
Write the formula before the numbers. earns a mark on its own even if the arithmetic slips.
Read whether the question wants the interest or the amount, and add when it wants the amount. Answering with SI when A was asked loses the final mark.
When the amount is given, use rather than treating A as the interest.
And check by substituting back into the original formula — one line, and it catches every rearrangement error.
Did you know
Why is the interest the same every year?
Because simple interest is always calculated on the original principal, which never changes.
On ₹5000 at 8 percent, the first year earns ₹400. The second year earns ₹400 again — not 8 percent of ₹5400 — because the ₹400 already earned is set aside rather than added to the principal.
So the total grows in equal steps: ₹400, ₹800, ₹1200. That straight-line growth is exactly what makes the formula so simple, and it is the one feature that distinguishes it from the compound interest met in later classes.
On ₹5000 at 8 percent, the first year earns ₹400. The second year earns ₹400 again — not 8 percent of ₹5400 — because the ₹400 already earned is set aside rather than added to the principal.
So the total grows in equal steps: ₹400, ₹800, ₹1200. That straight-line growth is exactly what makes the formula so simple, and it is the one feature that distinguishes it from the compound interest met in later classes.
Key takeaways
Simple interest: quick revision
- Principal is the sum, rate is the percent per annum, time is in years, and the amount is .
- , and the interest is the same every year because it is always on the original principal.
- Convert time first: or , so 9 months is year.
- Rearrange for the unknown — , , — with the 100 always moving to the top.
- When the amount is given, use , so ₹7000 in 4 years at 10 percent comes from a principal of ₹5000.
- Always substitute your answer back into the original formula as a check.
You will remember all of this far better after answering five questions on it than after reading it twice.
- , and the interest is the same every year because it is always on the original principal.
- Convert time first: or , so 9 months is year.
- Rearrange for the unknown — , , — with the 100 always moving to the top.
- When the amount is given, use , so ₹7000 in 4 years at 10 percent comes from a principal of ₹5000.
- Always substitute your answer back into the original formula as a check.
You will remember all of this far better after answering five questions on it than after reading it twice.