Simple Interest Formula and Tricks

📑 On this page

⚡ The short answer

Simple interest is charged only on the original principal, so it is the same every year. SI = P × R × T ÷ 100 and Amount = P + SI. Keep R and T in the same unit. The trap: CLAT asks for the amount and plants the interest, or the other way round.

🎬 The 30-second story

The 1.5% that wasn't

“₹12,000 laptop on pay-later at just 1.5%. Basically free.”

💻

Aarav

Aarav picks a 10-month plan. Simple interest, says the app.

“1.5% a month, Aarav. It's in the small print.”

🔍

Zoya

Zoya actually reads the terms.

“₹1,800 in interest? I budgeted ₹180!”

🧾

Aarav

Ten months later, the final bill.

“You paid 1.5% once in your head. They charged it ten times.”

📅

Zoya

₹180 a month × 10 months.

Tara's maths: SI = P × R × T ÷ 100, with R and T in the same unit: 12,000 × 1.5 × 10 ÷ 100 = ₹1,800. In yearly terms, 18% for 10/12 of a year gives the same ₹1,800.

What is simple interest, really?

Interest is rent for money. With simple interest, the rent is always worked out on the original sum, never on what has piled up. ₹20,000 at 9% a year costs ₹1,800 in Year 1, ₹1,800 in Year 2, ₹1,800 forever.

🟦 Picture the percent

9% simple interest: total interest as a share of the principal

Year 1

9% of P

Year 3

9 × 3 = 27% of P

Year 5

9 × 5 = 45% of P

Each year adds the same 9 squares, so total interest is R × T per cent of P. On ₹20,000, 45% is ₹9,000.

That picture is the whole topic. Every year adds the same slice, so simple interest grows in a straight line. Double the principal, the rate or the time, and the interest doubles.

What is the simple interest formula, and why does it work?

R% of P is P × R ÷ 100: one year's interest. Charge it for T years and multiply by T. Give CLAT any three of P, R, T and SI, and the fourth falls out of the same equation.

🧮 The formula

Building SI from one year's interest

💰

the sum borrowed or deposited

📊

R ÷ 100

rate per year, as a fraction

📅

time in years

🧾

SI = P × R × T ÷ 100

Amount A = P + SI = P(1 + RT/100)

To find	Use	Example
Interest	SI = P × R × T ÷ 100	₹5,000 at 6% for 3 years = ₹900
Principal	P = 100 × SI ÷ (R × T)	SI ₹900 at 6% for 3 years: P = ₹5,000
Rate	R = 100 × SI ÷ (P × T)	₹900 on ₹5,000 in 3 years: R = 6%
Time	T = 100 × SI ÷ (P × R)	₹900 on ₹5,000 at 6%: T = 3 years

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📌 Make R and T speak the same language

A yearly rate needs time in years: 8 months = 8/12 year, 146 days = 146/365 = 0.4 year. A monthly rate needs time in months. Mixing them is the single most common SI error, and the wrong answer is always in the options.

How do you solve simple interest questions step by step?

✍️ Worked example Warm-up ⏱ 30 sec

Interest for a few months

Meher parks ₹8,000 of her fest prize money at 7.5% a year simple interest for 8 months. How much interest does she earn?

1
Rate is per year, so time must be in years: 8 months = 8/12 = 2/3 year.
2
SI = 8,000 × 7.5 × 2/3 ÷ 100.
3
8,000 × 7.5 ÷ 100 = 600 a year; two-thirds of 600 = 400.

Answer: ₹400

⚡ The exam-hall shortcut

Find one year's interest first (₹600), then take the fraction of the year. Two clean steps, no decimals.

✍️ Worked example CLAT level ⏱ 50 sec

Two amounts, find P and R

At simple interest, a sum grows to ₹14,880 in 3 years and to ₹16,800 in 5 years. Find the sum and the rate.

1
The principal is the same in both, so the gap is pure interest: 16,800 − 14,880 = ₹1,920 for 2 years.
2
One year's interest = 1,920 ÷ 2 = ₹960.
3
3 years' interest = 3 × 960 = ₹2,880, so P = 14,880 − 2,880 = ₹12,000.
4
R = 960 ÷ 12,000 × 100 = 8%.

Answer: Sum ₹12,000, rate 8% a year

⚡ The exam-hall shortcut

Back-check: ₹960 a year on ₹12,000 gives ₹14,880 after 3 years and ₹16,800 after 5.

✍️ Worked example Tricky ⏱ 40 sec

"Becomes n times" questions

Kabir's deposit triples in 16 years at simple interest. In how many years would it become 5 times itself?

1
Triples means P becomes 3P, so the interest is 2P, not 3P.
2
2P of interest in 16 years means P of interest every 8 years. (Rate = 200 ÷ 16 = 12.5%.)
3
5 times means interest of 4P: 4 × 8 = 32 years.

Answer: 32 years

⚡ The exam-hall shortcut

Interest is (n − 1)P: 2 parts in 16 years, so 4 parts take 32. The trap, 16 × 5 ÷ 3 ≈ 26.7, treats the principal as interest.

What are the fastest simple interest shortcuts for CLAT?

✓Total % = R × T. 9% for 5 years is 45% of P. One multiplication, then one percentage.
✓Becomes n times in T years: (n − 1) × 100 = R × T. Doubles at 8%? 100 ÷ 8 = 12.5 years.
✓Same rate, same interest: P × T stays fixed. ₹9,000 for 20 years earns what ₹12,000 earns in 15 years. That is inverse proportion.
✓Two amounts given: the gap is the interest for the gap in years. Work out one year's interest, then backtrack to P.
✓Split at two rates: find the average rate and use the alligation cross.

Zoya splits ₹20,000 between a 6% and a 10% scheme and earns ₹1,500 a year. Her average rate is 1,500 ÷ 20,000 = 7.5%. The cross gives the split.

✖️ The alligation cross

Splitting ₹20,000 between 6% and 10% to earn 7.5% overall

6% scheme : 10% scheme = 5 : 3

Ratio 5 : 3: ₹12,500 at 6% and ₹7,500 at 10%. Check: ₹750 + ₹750 = ₹1,500.

🎛️ Try it yourself — change any number

Try it: ₹20,000 at 9% for 5 years

Principal (₹) Rate per year (%) Years (8 months = 0.6667) Compounding per year (for the CI line only)

Simple interest

9,000

Compound interest

10,772.48

CI − SI

1,772.48

SI = P×R×T/100; CI = P(1 + R/100)⁵ − P

As set: SI ₹9,000, or 45% of P. Double the years and SI doubles exactly. The CI line shows compounding would earn ₹10,772.48. Set years to 1 and the two match.

How does simple interest hide in a CLAT caselet?

CLAT won't write "find the SI". It writes a paragraph: Kabir needs ₹60,000 for 2 years. A cooperative offers 11% a year simple. A lender wants "just 1.25% a month", simple. His uncle asks ₹500 a month as interest. A bank offers 10% compounded annually. First, put every rate on a per-year basis.

Source	Stated as	Per year	Interest, 2 years
Cooperative	11% a year, simple	11%	₹13,200
Lender	1.25% a month, simple	15%	₹18,000
Uncle	₹500 a month	₹6,000 = 10%	₹12,000
Bank	10% a year, compound	10% on a growing sum	₹12,600

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📊 The data

What each ₹60,000 loan costs Kabir over 2 years

Cooperative, 11% SI

₹13,200

Lender, 1.25%/month SI · smallest-looking rate, costliest loan

₹18,000

Uncle, ₹500/month · cheapest

₹12,000

Bank, 10% compound

₹12,600

The lender's 1.25% becomes 30% of ₹60,000 over 24 months. Uncle and bank both charge 10%, but compounding adds ₹600.

⚠️ When the answer is "cannot be determined"

SI links four quantities. Given only the interest and the time, with no rate, the principal is not fixable, however tempting the numbers. And check the word simple: interest "added to the account each year" is compound.

Interest or amount: which traps does CLAT set?

⚔️ Side by side

Two words that change the answer

🪙Interest

only the extra money

•SI = P × R × T ÷ 100
•"earns", "interest", "pays as interest"

💼Amount

principal plus interest

•A = P + SI = P(1 + RT/100)
•"amounts to", "becomes", "total received"

Test	Interest	Amount
₹5,000, 6%, 3 years	₹900	₹5,900
Grows with time?	From zero, in a straight line	From P, in a straight line
Equal for two people means	P × T equal (same rate)	P(1 + RT/100) equal

CLAT 2023 turned on the last row.

⚠️ Three more places marks leak

Months as decimals: 18 months is 1.5 years, not 1.8. Per-month rates: 2% a month is 24% a year. "n times": becoming 3 times means interest of 2P. Estimate first: near 10% for near 2 years means interest near 20% of P.

How CLAT asked it

📝 Asked in CLAT 2019 · Q59 Split investment at two rates

An employee of an organization invests a total of Rs 25,400 in two different schemes X and Y at a simple interest rate of 18% per annum and 10% per annum respectively. If a total of Rs. 6460 has been earned as simple interest in 2 years, what amount was invested in Scheme Y?

ARs. 8,625

BRs. 16,775

CRs. 12,240

DRs. 10,930

Reveal answer + reasoning

Answer: B

There is no official key for 2019; this is our solution. Yearly interest = 6,460 ÷ 2 = ₹3,230. If all ₹25,400 earned 10%, that would be ₹2,540. The extra ₹690 comes from the 8% bonus on scheme X: X = 690 ÷ 0.08 = ₹8,625. So Y = 25,400 − 8,625 = ₹16,775.
Check: 8,625 × 18% × 2 = ₹3,105 and 16,775 × 10% × 2 = ₹3,355; total ₹6,460. About 60 seconds.

Why the others fail

A — That is the amount in scheme X, the 18% one. The question asks for Y.
C — If Y were ₹12,240, X would be ₹13,160, and two years' interest would be ₹7,185.60, not ₹6,460.
D — With Y = ₹10,930, X = ₹14,470 and the interest comes to ₹7,395.20. Too much.

📝 Asked in CLAT 2023 · Q138 Same amount, how many years

… Also, in urban areas the average earnings of men (₹ 9,000) are significantly higher than women (₹ 5,700) even in casual employment. … The average monthly earning for the SC/ST workers in casual work is ₹ 8,000 below the corresponding figure of ₹ 8,600 for the non-SC/ST. [Note: Values have been approximated to the nearest hundred]

Of those in casual employment, if a man's average earnings was deposited at a rate of 16% simple interest for 20 years, in how many years at the same rate of simple interest a SC/ST worker must deposit their average earnings to earn the same amount as a man in 20 years?

A24 years

B22.5 years

C21 years

D23.2 years

Reveal answer + reasoning

Answer: D

Casual-work figures: man ₹9,000, SC/ST worker ₹8,000. The key reads "the same amount" as principal plus interest.
Man: 9,000 × (1 + 16 × 20 ÷ 100) = 9,000 × 4.2 = ₹37,800.
SC/ST worker: 8,000 × (1 + 0.16t) = 37,800, so t = 3.725 ÷ 0.16 = 23.28 years. Nearest option: 23.2 years.
Read as the same interest, 9,000 × 20 = 8,000 × t gives 22.5 years (option B). The key took "amount" literally. About 75 seconds.

Why the others fail

A — Fits neither reading; a rough round-up.
B — Equal interest, not equal amount. A careful but wrong reading of "amount".
C — Uses the non-SC/ST figure of ₹8,600: 9,000 × 20 ÷ 8,600 ≈ 21. Wrong worker.

💥 Myth vs fact

Myth vs fact

🙅 Myth

1.5% interest is always small.

Tap to bust it →

✅ Fact

Check the unit. 1.5% a month is 18% a year.

🙅 Myth

If a sum triples in 16 years, it becomes 6 times in 32.

Tap to bust it →

✅ Fact

Interest doubles, not the multiple: 2P becomes 4P, so it is 5 times in 32 years.

🙅 Myth

"Amount" and "interest" mean the same thing.

Tap to bust it →

✅ Fact

Amount = principal + interest. CLAT 2023 hinged on it.

🙅 Myth

Simple interest and compound interest are never equal.

Tap to bust it →

✅ Fact

They are equal for exactly one compounding period. After that, CI is bigger.

Can you do these five?

🎯 Quick quiz

Five simple interest checks

0 / 5

Zoya lends Rohan ₹4,500 at 8% a year simple interest for 2 years 6 months.

Q1. How much interest does Rohan pay?

Meher's ₹6,000 becomes ₹7,440 in 3 years at simple interest.

Q2. What is the rate per year?

A sum doubles in 12.5 years at simple interest.

Q3. What is the rate of interest?

Kabir's savings account pays simple interest. In 2 years, his deposit earned ₹1,200.

Q4. How much did he deposit?

Aarav splits ₹15,000 between a 5% scheme and an 8% scheme, both simple interest, and earns ₹1,020 a year.

Q5. How much is in the 8% scheme?

🎯 Simple interest in a nutshell

Interest only on the original principal, so it is the same every year.
SI = P × R × T ÷ 100; total interest is R × T per cent of P.
Amount = P + SI. Read whether CLAT wants interest or amount.
Match units: yearly rate with years, monthly rate with months.
Becoming n times means interest of (n − 1)P.

📎 Formula card

Interest: SI = P × R × T ÷ 100
Amount: A = P + SI = P(1 + RT/100)
Rearranged: P = 100·SI ÷ (RT); R = 100·SI ÷ (PT); T = 100·SI ÷ (PR)
n times in T years: (n − 1) × 100 = R × T; doubles in 100 ÷ R years
Two amounts given: one year's SI = (A₂ − A₁) ÷ (T₂ − T₁)
Same rate, same interest: P₁ × T₁ = P₂ × T₂
Time conversions: months ÷ 12; days ÷ 365 (73 days = 1/5 year)

Frequently asked questions

What is the formula for simple interest?

Simple interest = P × R × T ÷ 100, where P is the principal, R the rate per year and T the time in years. The amount you get back is P + SI. For example, ₹5,000 at 6% a year for 3 years earns ₹900 in interest, so the amount is ₹5,900.

How do you calculate simple interest for months or days?

Convert the time into the rate's unit. With a yearly rate, divide months by 12 and days by 365. So ₹8,000 at 7.5% a year for 8 months is 8,000 × 7.5 × 8/12 ÷ 100 = ₹400. With a monthly rate, keep the time in months.

In how many years does a sum double at simple interest?

A sum doubles when the interest equals the principal, that is, 100% of P. Since total interest is R × T per cent, the time is 100 ÷ R years. At 8% it doubles in 12.5 years. To become n times, the interest must be (n − 1) × 100%, so T = (n − 1) × 100 ÷ R.

What is the difference between simple and compound interest?

Simple interest is charged only on the original principal, so it is the same every year. Compound interest is charged on the principal plus interest already added, so it grows faster. They match for the first period only. ₹20,000 at 9% for 5 years earns ₹9,000 simple but ₹10,772.48 compound.

Is simple interest asked in CLAT?

Yes. CLAT 2019 asked a direct question on splitting ₹25,400 between 18% and 10% schemes. CLAT 2023 put simple interest inside an earnings passage, asking how many years a smaller deposit needs to reach the same amount at 16%. Expect it inside a caselet, often mixed with percentages.