Simple Interest: Concepts, Formulas, and Clear Examples

SI grows linearly: interest each year is same on original principal. $SI = \frac{PRT}{100}$, amount $A=P+SI$.

Contrast with CI when stem asks difference or which is better for same P,R,T.

Installment and half-year wording may still use SI unless compounding stated.

Core formula

Simple interest

$$SI = \frac{P \times R \times T}{100}$$

Amount

$$A = P + SI = P\left(1 + \frac{RT}{100}\right)$$

Example — 3 years 10%

$P=8000$, R=10, T=3. SI = $\frac{8000\cdot10\cdot3}{100}=2400$. A = 10400.

Find unknown

Rate

$$R = \frac{100\,SI}{PT}$$

Time

$$T = \frac{100\,SI}{PR}$$

Different time units

• T in years; if months, use $T/12$.
• Days: $T/365$ unless stem says 360-day year.

Two-rate split

• Split principal into parts at different rates; sum SI.

SI vs CI quick compare

• CI > SI for T>1 same rate.
• Year 1 interest equal.

Discount/true discount light

• Present value under simple interest rare; use $SI=PTR/100$ on face value if given.

Step-by-step method for exam questions

1. Note P, R%, T in consistent years.
2. Compute SI = PTR/100.
3. Add to P if amount needed.
4. Reverse formula if finding R or T.
5. Compare options; watch monthly rate traps.
6. Select answer.

Formula cheat sheet

Frequently asked questions

Half-yearly SI?

Unless compounding stated, SI still linear—half year T=0.5.

Principal doubles?

SI: T such that RT/100=1 → T=100/R years.

Different P each year?

Not standard SI—recheck problem type.

SI on SI?

That is CI, not SI.

Practice on this platform

Use 4 practice sets (10 MCQs, detailed solution after each answer) and 2 timed mocks (20 minutes) on this topic to convert formulas into speed and accuracy.