Simple Interest

Module 15 — Lesson 0015 · In Depth · 35 min

Interest is rent on money. Simple interest charges rent only on the original principal — never on accumulated interest. So growth is linear (AP), not compounding (GP) — the bridge between Profit/Loss and Compound Interest.

1. The Core Variables

Symbol Meaning Note
P Principal — original sum 100% base
R Rate per year (per annum %)
T Time — duration Must be in years; months ÷12
SI Simple interest — extra earned/paid
A Amount — final total A = P + SI

2. The Fundamental Formulas — The Golden Equation

SI = (P × R × T) / 100

This single formula solves 90% of basic questions. All derived forms are rearrangements:

Find Formula
Principal P = (100 × SI) / (R × T)
Rate R = (100 × SI) / (P × T)
Time T = (100 × SI) / (P × R)
Amount A = P + SI = P[1 + RT/100]
Why linear: SI adds the same interest each year (PR/100). After n years, SI = n×PR/100 — an AP with difference PR/100. Compound interest multiplies — a GP. That distinction decides which formula to use.

3. Advanced Concept: The "Times" Logic (Doubling/Tripling)

"A sum doubles in 10 years — find rate." Translate "times" to SI:

Shortcut: If a sum becomes N times itself in time T:

R × T = 100 × (N − 1)

Worked: Sum triples (N=3) in 24 years → R×24=100×2 → R=8.33%.
Doubles in 10 years → R×10=100 → R=10%. Check: SI=PRT/100 =P×10×10/100=P → A=2P ✓.

4. Advanced Concept: Two Amounts, Two Times

Scenario: "Amounts to $800 in 3 years and $900 in 4 years." In SI, yearly interest is constant — the increase from year 3 to 4 is exactly one year's SI.

  1. 1-year SI: (A₂ − A₁)/(T₂ − T₁)
  2. Total SI for T₁: 1-year SI × T₁
  3. Principal: A₁ − Total SI(T₁)
  4. Rate: R = (100×SI)/(P×T)
Worked: 800 in 3y, 900 in 4y → 1-year SI=(900−800)/(4−3)=100.
Total SI for 3y =300 → P=800−300=500.
Rate =100×100/(500×1)=20%. Check: SI=500×20×3/100=300 → A=800 ✓; for 4y SI=400 → A=900 ✓.

5. Fractional Interest Problems

"SI is 1/5 of principal" → let P = x, then SI = x/5. Substitute into x/5 = xRT/100 → x cancels → RT =20. If T or R is given, the other follows without needing P.

This cancellation is the point — when SI is a fraction of P, P drops out and you get a relation between R and T only.

6. Comparison and Difference

Difference between interests from two schemes/people:

Worked: P=1000, T=2, rates 8% vs 10% → ΔSI=1000×2×2/100=40. Check: 160 vs 200 diff 40 ✓.

7. Summary of Variables

Symbol Meaning
P Principal
A Amount (P+SI)
SI Simple interest
N Times multiple (doubles=2, triples=3)

Golden equation: SI = ?

Time in months → convert to years by?

Sum doubles in 10y → rate?

Sum triples in 24y → rate?

Amounts to 800 in 3y and 900 in 4y → 1-year SI?

In that case, principal P = ?

SI is 1/5 of P → relation?

ΔSI same P,T, rates differ by 2% (P=1000,T=2) → ΔSI?

Notes

SI :- Basics :-

Interest ⇒ rent on money ; SI on P only → linear (AP), not GP

SI ⇒ PRT/100 ; must T in years (months/12)

A ⇒ P+SI = P[1+RT/100] ; P,R,T ⇒ 100×SI/(product of other two)

Times Logic :-

Doubles→A=2P→SI=P ; Triples→SI=2P ; N times→SI=(N−1)P

Shortcut ⇒ R×T=100(N−1) (eg triples in 24y→R=8.33%)

Two Amounts / Fractional :-

Two amounts ⇒ 1y SI=(A₂−A₁)/(T₂−T₁) ; then P=A₁−T₁×1y ; then R

(eg 800 in3y,900 in4y→1y=100→P=500→R=20%)

Fraction ⇒ SI=x×fraction → cancel P → RT relation (eg 1/5→RT=20)

Comparison :-

ΔSI ⇒ P×T×ΔR/100 (same P,T) ; else difference of PRT/100s

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