Kit Library / Mathematics / Arithmetic & Financial Mathematics
⚡ Topic Learning KitShared by a Veda learner · Generated with Veda AI
Veda Bites are swipeable micro-lessons — each one teaches exactly one idea. The bites below come from this kit — swipe through them in the app.
💡 Key Idea
Interest never compounds here.
In simple interest, the interest each period is calculated only on the original principal — never on interest already earned.
↳ Simple interest is linear: same interest every period, because the base never changes.
➗ Formula
One formula powers every SI problem.
↳ Memorise SI = PRT/100 — every other SI formula is derived from it.
📖 Definition
Know these four words cold.
↳ Every SI problem gives you three of P, R, T, SI, A — solve for the missing one.
⚙️ Process
Four steps, zero confusion.
↳ Standardise units before substituting — most mistakes happen at the conversion step.
✏️ Example
See the formula in action.
↳ Equal interest every year is the signature of simple interest.
⚠️ Common Mistake
Months are not years.
↳ Always convert time to years before using the formula.
⚖️ Comparison
Same rate, very different totals.
↳ SI grows in a straight line; CI curves upward — the gap widens with time.
One formula, four rearrangements.
↳ Don't memorise three formulas — just rearrange SI = PRT/100.
🧠 Memory Trick
Say it like a word: P-R-T.
Chant "P-R-T over 100" — Principal × Rate × Time, all divided by 100. The three letters in order match the formula's numerator.
↳ PRT/100 — three letters, one denominator, zero confusion.
🌍 Real World
It's in your bank, your loan, your EMI.
↳ Short-term and flat-rate loans almost always use simple interest.
⭐ Important Fact
How fast does money double?
At 10% p.a. simple interest, money doubles in exactly 10 years — because SI = P when R·T = 100.
↳ Under SI, doubling time = 100 ÷ R years.
🎯 Exam Tip
These question types repeat every year.
↳ Recognise the pattern first, then pick the rearranged formula.
Turn fractions into one equation.
When a question says *"SI is 1/4 of the principal"*, write $\frac{SI}{P} = \frac{RT}{100}$ and substitute the fraction directly.
↳ SI/P = RT/100 is the master ratio for all 'fraction of principal' problems.
🚫 Warning
SI never compounds — resist the urge.
↳ If you're adding interest back to P, you've switched to CI by mistake.
❓ Did You Know
Rates are always yearly by default.
The phrase "per annum" (p.a.) means *per year*. If a rate is quoted without a time unit, it is assumed to be annual — so T must always be in years to match.
↳ Rate and time must share the same unit — usually years.
Simple interest is interest calculated only on the original principal, never on accumulated interest. It uses the formula SI = (P × R × T) / 100 and is the foundation for understanding loans, deposits, and basic financia…
Full explanation, worked examples & memory tricks in the app
All 17 questions, laddered from warm-up to topper-level, each with its answer and the reasoning behind it.
Q1. Simple interest is calculated on which amount?
BeginnerA · The original principal only
Simple interest is charged only on the original principal $P$; it never earns interest on interest, which is what makes it 'simple'.
Q2. Which formula gives the simple interest?
BeginnerB · $SI = \frac{P \times R \times T}{100}$
The rate is a percentage, so it is divided by 100: $SI = \frac{P \times R \times T}{100}$.
Q3. In the formula $SI = \frac{P \times R \times T}{100}$, what unit must $T$ be in?
BeginnerD · Years
The rate is per annum (per year), so time must be expressed in years before substituting.
Q4. The 'amount' in a simple interest problem equals:
BeginnerD · $P + SI$
The amount is what you finally have or repay: principal plus simple interest, $A = P + SI$.
Q5. Find the simple interest on ₹8,000 at 6% per annum for 3 years.
BeginnerA · ₹1,440
$SI = \frac{8000 \times 6 \times 3}{100} = \frac{144000}{100} = ₹1{,}440$.
Q6. Which of these is the best real-life use of simple interest?
BeginnerA · A short-term moneylender loan
Simple interest is the standard method for short-term loans, moneylender loans and simple savings schemes; long-term products usually use compound interest.
Q7. Simple interest is computed only on the principal using $SI = \frac{P \times R \times T}{100}$, where $T$ must be in years.
BeginnerA · True
Simple interest is computed only on the principal using $SI = \frac{P \times R \times T}{100}$, where $T$ must be in years.
Q8. A sum of ₹5,000 is lent at 10% per annum for 6 months. What is the simple interest?
IntermediateA · ₹250
Six months is $T = 0.5$ years, so $SI = \frac{5000 \times 10 \times 0.5}{100} = ₹250$. Plugging in $T = 6$ would wrongly give ₹3,000.
Q9. ₹1,200 is earned as interest on ₹10,000 in 2 years. What is the rate per annum?
IntermediateD · 6%
$R = \frac{100 \times SI}{P \times T} = \frac{100 \times 1200}{10000 \times 2} = 6\%$ per annum.
Q10. Why does the formula divide by 100?
IntermediateA · Because the rate is a percentage, so $R\% = \frac{R}{100}$
The rate $R$ is given as a percent, and $R\% = \frac{R}{100}$ converts it into a decimal multiplier.
Q11. If the principal and rate stay the same but the time is doubled, the simple interest:
IntermediateB · Doubles
$SI$ is directly proportional to $T$ when $P$ and $R$ are fixed, so doubling the time doubles the interest.
Q12. Rearrange $SI = \frac{P \times R \times T}{100}$ to make $P$ the subject.
IntermediateC · $P = \frac{100 \times SI}{R \times T}$
Multiply both sides by 100 and divide by $R \times T$: $P = \frac{100 \times SI}{R \times T}$.
Q13. ₹10,000 is invested at 10% per annum. Compare the total interest after 3 years under simple and compound interest. Which statement is correct?
AdvancedC · Simple gives ₹3,000; compound gives ₹3,310
Simple interest adds a fixed ₹1,000 each year (total ₹3,000). Compound interest earns on the growing balance: ₹1,000 + ₹1,100 + ₹1,210 = ₹3,310.
Q14. A student computes interest on ₹5,000 at 10% for 6 months as $\frac{5000 \times 10 \times 6}{100} = ₹3{,}000$. What went wrong?
AdvancedC · Time was used in months instead of years
The formula needs $T$ in years. Six months is $0.5$ years, giving $SI = \frac{5000 \times 10 \times 0.5}{100} = ₹250$, not ₹3,000.
Q15. A sum earns ₹480 as simple interest in one year at 8% per annum. What is the principal?
AdvancedC · ₹6,000
$P = \frac{100 \times SI}{R \times T} = \frac{100 \times 480}{8 \times 1} = ₹6{,}000$.
Q16. Which statement about simple interest is FALSE?
AdvancedB · The principal grows each year as interest is added to it
In simple interest the principal stays fixed; interest is never added to it. That is why each year's interest is identical — the other three statements are true.
Q17. A principal amount of ₹15,000 is invested at a rate of 12% per annum for a period of 4 years. After this period, the total amount is reinvested at the same rate for another 2 years. What is the total simple interest earned over the entire period?
AdvancedD · ₹4,800
To find the total simple interest earned, we first calculate the interest for the first 4 years: \(SI_1 = \frac{15000 \times 12 \times 4}{100} = ₹7,200\). Then, for the next 2 years, the interest is: \(SI_2 = \frac{15000 \times 12 \times 2}{100} = ₹3,600\). The total interest is…
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