In this article
Simple interest questions appear in almost every banking, SSC, railway and state exam. They’re easy marks — if you can solve them quickly. These shortcuts and patterns will help you answer in seconds instead of minutes.
The one formula
SI = P × R × T ÷ 100
Amount (A) = P + SI
- P — principal (the money lent or borrowed)
- R — rate of interest per year (%)
- T — time in years
₹12,000 at 8.5% for 3 years: SI = 12,000 × 8.5 × 3 ÷ 100 = ₹3,060. Amount = ₹15,060.
Rearrange instead of memorising
Every other formula comes from rearranging the main one:
| Find | Formula |
|---|---|
| Principal | P = SI × 100 ÷ (R × T) |
| Rate | R = SI × 100 ÷ (P × T) |
| Time | T = SI × 100 ÷ (P × R) |
Shortcut 1: doubling and tripling time
Money doubles when SI equals P. Setting SI = P in the formula gives:
Time to double = 100 ÷ R years
- At 10%: doubles in 10 years.
- At 8%: doubles in 12.5 years.
More generally, to become n times the principal, SI must be (n − 1) × P:
Time to become n times = (n − 1) × 100 ÷ R
Exam question: “A sum becomes 3 times in 16 years at SI. In how many years will it become 5 times?”
Tripling needs SI = 2P in 16 years, so P earns 1P every 8 years.
Five times needs SI = 4P → 4 × 8 = 32 years.
Shortcut 2: interest per year is constant
Under SI, the interest every year is the same. That makes “amount after x years and y years” questions easy.
A sum amounts to ₹6,800 in 3 years and ₹7,600 in 5 years.
Interest for 2 years = 7,600 − 6,800 = ₹800 → ₹400 per year.
Interest for 3 years = ₹1,200 → Principal = 6,800 − 1,200 = ₹5,600.
Rate = 400 × 100 ÷ 5,600 ≈ 7.14%.
Shortcut 3: convert time units first
The formula needs time in years:
- Months → divide by 12 (9 months = 0.75 years)
- Days → divide by 365 (73 days = 0.2 years)
Date-range questions (e.g. “from 5 January to 18 March”) usually count one end date but not the other. Count the days in each month carefully: Jan 26 (6–31), Feb 28, Mar 18 = 72 days.
Shortcut 4: rate changes over time
If the rate is 6% for the first 2 years, 8% for the next 3 and 10% after that, just add the year-rates:
SI = P × (R₁T₁ + R₂T₂ + R₃T₃) ÷ 100
SI vs CI: the difference trick
For 2 years at rate R on principal P (CI compounded yearly):
CI − SI = P × (R ÷ 100)²
₹10,000 at 10% for 2 years: difference = 10,000 × 0.01 = ₹100. This one-liner saves a lot of time in exams.
Common traps
- Interest vs amount — the question may ask for the total amount, not just the interest.
- Rate per annum vs per month — “1% per month” means 12% per annum.
- Mixed units — months and years in the same question.
- Rounding too early — keep fractions until the final step.
Check your answers
While practising, verify your answers with our Simple Interest Calculator — enter principal, rate and time in years, months or days to get the interest and total amount instantly. It’s a quick way to catch calculation slips before exam day.
Free toolTry the Simple Interest CalculatorFind the interest and total amount using the simple interest formula.Frequently asked questions
What is the difference between SI and CI in exam questions?
For the first year, SI and CI are equal (when CI is compounded yearly). From the second year, CI is higher because interest is earned on interest.
How many days are in a year for SI questions?
Use 365 days unless the question says otherwise. Count the start and end dates carefully — usually one of them is excluded.
How do I find the principal if only the amount is given?
Amount = P(1 + RT/100), so P = Amount ÷ (1 + RT/100). For example, ₹13,800 after 4 years at 4.5% gives P = 13,800 ÷ 1.18 ≈ ₹11,695.
Written by the Toolsopedia team. Spotted an error? Tell us and we’ll fix it.