Introduction to Simple Interest

Simple Interest · 20 min

Aptitude · Simple Interest

Rent on money, charged only on what you first borrowed

Simple interest is the one interest rule where the sum being charged never changes. Get that single sentence right and the whole chapter — including the reverse questions that hide the principal — becomes one multiplication and one subtraction.

Set a principal, rate and time, then walk the arithmetic →
Interest is rent you pay for using someone else’s money. In simple interest that rent is always worked out on the original sum, never on the sum as it grows.

01 The idea

One sum, one rate, and a total that grows in equal jumps

You borrow ₹1000 from a friend and he asks for 10% interest per year. Ten percent of ₹1000 is ₹100, so after one year you hand back ₹1100. Nothing surprising yet.

The question that decides the whole chapter is what happens in year two. Simple interest answers it the boring way: the second year is charged on the same ₹1000, so it is ₹100 again. Not ₹110. The sum the rate is applied to never moves.

That is why the money grows in equal jumps — ₹1100, ₹1200, ₹1300 — a straight line rather than a curve. Compound interest is the version where the second year is charged on ₹1100, and the gap between the two chapters is exactly that one decision.

Almost every question you will meet gives you three of the four quantities — principal, rate, time, interest — and asks for the fourth. So the work is never really about the formula. It is about reading which three you were handed.

In simple interest, one year’s interest is a fixed number. Work out that one number, multiply it by the years, and you are done.
PrincipalThe original sum borrowed or invested, written P. It is the only sum interest is ever charged on in this chapter.
Rate per annumThe percentage charged for one year, written R. “Per annum” means per year, and the rate is always per year unless the question says otherwise.
AmountPrincipal plus interest, written A — the total that actually changes hands at the end. Interest alone is the extra money only.

02 Worked example

₹1000 at 10% for 3 years, worked twice over

This one example carries the rest of the lesson — the formula in section 03, the console, and the cheat sheet all come back to it. The numbers are deliberately small enough to check in your head.

1
Name the three givensPrincipal ₹1000, rate 10% per annum, time 3 years. The question asks for the interest and the amount.P = 1000    R = 10% per annum    T = 3 years
2
Work out one year of interestTen percent of ₹1000. This is the number the rest of the question is built on.10% of 1000 = 1000 × 10 / 100 = 100
3
Charge that same figure in every yearYear one earns ₹100. Year two is charged on ₹1000 again, so it also earns ₹100. So does year three.100 + 100 + 100 = 3 × 100 = 300
4
Check it against the formulaThe formula is the three steps above compressed onto one line. It must agree, and it does.SI = P × R × T / 100 = 1000 × 10 × 3 / 100 = 300
5
Add the interest back for the amountThe interest is ₹300. The amount — what you actually repay — is the principal plus that interest.A = 1000 + 300 = ₹1300

Notice what did not happen: the second year was never charged on ₹1100. Had it been, the interest would have run ₹100, ₹110, ₹121 and the total would have been ₹331 instead of ₹300. That difference is the entire content of the compound interest chapter, and it is why examiners are so fond of asking for both.

03 The method

One formula, and the percentage shortcut that beats it

Every direct question in this chapter comes out of the first box. The second box is how you should actually answer it under time pressure, and it is the habit worth building now.

SI = P × R × T / 100  and  A = P + SI. The 100 is there only because R is written as a percentage rather than as a fraction.
The shortcut worth memorising: simple interest is just (R × T)% of the principal. At 10% for 3 years that is 30% of ₹1000, which is ₹300 — no formula written down. Better still, the amount is (100 + R × T)% of the principal, so 130% of ₹1000 = ₹1300.
Time as written in the questionTime to substituteWhy students lose the mark
6 months6/12 = 0.5 yearSubstituting 6 gives twelve times the right answer
2 years 6 months2.5 yearsThe months have to join the years, not replace them
3 years 9 months3.75 years9/12 is 0.75, not 0.9
2 years 8 months8/3 yearsKeep it as a fraction — 2.667 rounds badly
219 days219/365 = 0.6 yearUse 365 unless the question names a different year
292 days292/365 = 0.8 yearThese are chosen to be exact; if yours is not, re-read

05 Cheat sheet

Every direct case on one page

Each row is the same formula rearranged. You do not need to memorise six formulas — you need to recognise which quantity is missing, then make it the subject.

What is missingUse thisYou were given
Simple interestSI = P·R·T/100P, R and T
AmountA = P(1 + R·T/100)P, R and T
Principal, from the interestP = 100·SI/(R·T)SI, R and T
Principal, from the amountP = 100·A/(100 + R·T)A, R and T
RateR = 100·SI/(P·T)SI or A, plus P and T
TimeT = 100·SI/(P·R)SI or A, plus P and R
Anything, fastSI = (R·T)% of PThe shortcut worth defaulting to
Per annum means per yearA rate is always for one year unless the question says otherwise, so time must be in years before it goes into the formula.
Interest is not the amountInterest is the extra money; the amount is principal plus interest. Read the last line of the question again before you pick an option.
Sanity-check against the principalAt any sensible rate and time, interest well over the principal means R and T were multiplied when one of them should have been divided.

06 Where & why

Where this actually shows up

Simple interest is rarely the hard question in a paper. It is the question you are expected to finish in under thirty seconds so you have time for the ones that pay.

TCS NQT · Infosys
One direct question, options far apart

Almost always P, R, T given and SI or the amount wanted. The percentage shortcut answers it without writing the formula down, which is the point of drilling it.

Bank PO · SSC CGL
The reverse question

The amount is given and the principal is wanted. Reading the amount as (100 + R·T)% of the principal turns it into one division.

Every later chapter
The base that compound interest, instalments and partnership sit on

Compound interest is defined by how it differs from this. Instalment and partnership questions both reduce to simple interest on a changing principal.

Interviews
The one-line explanation

“Why is it called simple?” is a real question, and the answer is that the base never changes. Being able to say that cleanly reads as understanding rather than memorising.

If a question mentions interest and you cannot immediately tell whether it is simple or compound, look for the word simple or for a phrase like “interest is added to the principal each year”. When neither appears, exam convention is simple interest.

07 Interview questions

What interviewers and examiners actually ask

Ten questions in the order they escalate — definition first, then the reasoning, then the comparison that separates a student who understood from one who memorised.

What is simple interest, in one sentence?
Interest calculated only on the original principal for the whole period, never on the interest already earned. So one year’s interest is a fixed number, and the total is that number times the years. The formula SI = P·R·T/100 is just that sentence written down.
Why is there a 100 in the formula?
Because the rate is quoted as a percentage rather than a fraction. A rate of 10% really means the fraction 10/100, so dividing by 100 converts the percentage back into the fraction you actually multiply by. If you wrote the rate as 0.1, the 100 would disappear.
What does “per annum” mean, and why does it matter so much?
It means per year. It matters because the rate and the time must be in the same unit, and the rate is almost always yearly. If the question gives 6 months, you substitute 0.5, not 6 — substituting 6 makes the answer twelve times too large, which is the single most common error in the chapter.
How is simple interest different from compound interest?
Simple interest always charges the original principal, so the money grows in equal steps and forms a straight line. Compound interest charges the principal plus the interest so far, so the steps get bigger and the growth curves upward. On ₹1000 at 10% for 3 years that is ₹300 against ₹331 — and the gap widens fast with time.
For one year, do simple and compound interest differ?
No, they are identical for the first period, because there is no earlier interest to compound yet. They only separate from the second period onward. That is worth knowing because it is the sanity check on a lot of comparison questions.
The interest and the amount — which is which?
Interest is the extra money alone; the amount is the principal plus that interest. So on ₹1000 earning ₹300, the interest is ₹300 and the amount is ₹1300. Examiners set options containing both numbers deliberately, so the last line of the question decides which you pick.
Give me the fastest way to do a direct question.
Multiply rate by time to get one percentage, then take that percentage of the principal. At 8% for 3 years the interest is 24% of the principal, full stop. For the amount, use (100 + R·T)% instead — 124% of the principal — which skips the addition too.
The amount is given and the principal is not. How do you get it?
Read the amount as a percentage of the principal. If the rate is 7% for 5 years, the interest is 35% of the principal, so the amount is 135% of it. Then 135% corresponds to the given amount, so divide: principal = amount × 100 / 135. On an amount of ₹54,000 that gives ₹40,000.
How would you find the rate if you were only told a sum grew from ₹6400 to ₹8320 in 5 years?
Take the interest first: 8320 − 6400 = ₹1920. As a share of the principal that is 1920/6400 = 30%, and that 30% covers all 5 years. So the yearly rate is 30/5 = 6%. Finding the total percentage first and dividing by the years is faster and safer than substituting into the formula.
When would money actually be lent at simple interest in the real world?
Rarely, for anything long-term — almost all real deposits and loans compound, so this is more a teaching model than a description of a bank. It does show up in short-term instruments where the term is under one compounding period, and in some fixed-rate instalment schemes. Say that honestly rather than claiming it is what banks do; interviewers notice.

08 Practice problems

Six to work by hand

Do these on paper without the console. Reach for the percentage shortcut before the formula — the point is to build the habit, not to get the answer by any route.

A first direct one

Easy
Find the simple interest on ₹1000 at 6% per annum for 2 years, then state the amount.
Follow-up
Do it twice — once through the formula and once as “12% of the principal” — and check the two agree. From here on you should only need the second route.
Show the hint
Rate times time is 12, so the interest is 12% of ₹1000 before you write anything down.

Interest or amount?

Easy
₹5000 is invested at 4% per annum for 3 years. Give the amount at the end.
Follow-up
The question asks for the amount, not the interest, so ₹600 is a trap answer rather than the answer. Get there in one step using (100 + R·T)% instead of two.
Show the hint
Twelve percent growth means the amount is 112% of the principal.

The principal is hiding

Medium
The simple interest on a certain sum for 5 years at 8% per annum is ₹800. Find the sum.
Follow-up
You are given the interest and asked for the base it came from, so the percentage runs backwards. Resist substituting into the formula — the unitary route is one line.
Show the hint
The interest is 40% of the principal, and 40% corresponds to ₹800.

Only the amount is given

Medium
A sum amounts to ₹6600 in 2 years at 10% per annum simple interest. Find the principal.
Follow-up
Nothing here is the interest — ₹6600 already includes it. Splitting the amount into 100% plus the growth percentage is the whole method, and it generalises to every reverse question.
Show the hint
At 10% for 2 years the amount is 120% of the principal, so ₹6600 is 120%.

Days, not years

Medium
Find the simple interest on ₹14,600 for 219 days at 10% per annum, taking a year as 365 days.
Follow-up
The time has to become a fraction of a year before it can meet a per-annum rate. The numbers are chosen so that fraction is exact, so if yours is untidy you have divided the wrong way round.
Show the hint
219/365 is 0.6 of a year, so the interest is 6% of the principal.

When does the interest catch the principal?

Hard
A sum is lent at 8% per annum simple interest. (a) After how many years does the interest earned equal the principal itself? (b) At what rate would the interest instead equal the principal in exactly 8 years? (c) State the one condition, in terms of R and T only, under which the interest equals the principal — and say what the amount is at that moment.
Follow-up
Not one of the three parts needs a principal, because the principal cancels out of every equation you write. Spotting that is the point: it turns a rupees question into a question purely about R and T, which is exactly how the harder n-times questions are built.
Show the hint
Interest equals principal means (R × T)% of P equals P, so ask what R times T has to be.