⬇ Download PDF

Unit 2 · Topic 04 · Comparing Quantities

Simple Interest

Hook

Zara put ₹5,000 in a savings account at 8% per year. After 3 years, Kabir guessed she'd earn ₹1,200 — 8% of 5,000, times 3.

Zara worked it out formally and got the same number, but only because she used the right formula, not a guess.

She then asked him what would happen if the rate were per MONTH instead of per year — and his answer for THAT changed completely.

Watch the Lessons

The Story

Zara deposited ₹5,000 in a savings account earning 8% simple interest per year, and wanted to know her interest after 3 years. She used the formula: Simple Interest = (Principal × Rate × Time)/100, where Rate is the annual percentage and Time is in years. SI = (5000 × 8 × 3)/100 = 120000/100 = ₹1,200.

"Notice the interest is the SAME amount every year," she told Kabir. "Year 1 earns ₹400 (5000×8/100), year 2 earns another ₹400, year 3 earns another ₹400 — always calculated on the original ₹5,000, never on a growing balance. That's what makes it SIMPLE interest."

Kabir asked what her total amount (principal plus interest) would be after 3 years. Amount = Principal + SI = 5000 + 1200 = ₹6,200. He wrote a shortcut: Amount = P(1 + RT/100).

Zara then posed a reverse problem: if a loan of ₹8,000 accrues ₹960 interest over 2 years, what's the rate? Rearranging SI = PRT/100 to solve for R: R = (SI × 100)/(P × T) = (960 × 100)/(8000 × 2) = 96000/16000 = 6% per year.

Kabir tried a units trap next: a loan of ₹10,000 at 12% per year for 6 months. He almost used T=6 directly, but Zara stopped him — Time must be in YEARS to match the annual rate, so 6 months = 0.5 years. SI = (10000 × 12 × 0.5)/100 = 60000/100 = ₹600, not the much bigger number he'd have gotten using T=6 by mistake.

"Every simple interest problem is really the same formula rearranged," Kabir said by the end: "SI equals P times R times T, over 100 — and Time always has to be measured in years to match an annual rate, converting months or days first if needed."

The simple interest formulaSI = (P × R × T) / 100
Interest equals Principal times Rate times Time, divided by 100.

So What Just Happened?

Simple Interest (SI) = (Principal × Rate × Time)/100, where Principal (P) is the initial sum, Rate (R) is the annual percent, and Time (T) is in years.

Under simple interest, the same interest amount is earned every year, always calculated on the ORIGINAL principal, never on a growing balance — this is what distinguishes it from compound interest.

Total Amount = Principal + Simple Interest = P + (PRT/100) = P(1 + RT/100).

The formula can be rearranged to find any one quantity given the other three: R = (SI×100)/(P×T), T = (SI×100)/(P×R), P = (SI×100)/(R×T). Time must always be converted to years if given in months or days.

Interest is the same every year under SIYr1: ₹400Yr2: ₹400Yr3: ₹400
₹5,000 at 8% per year earns exactly ₹400 in year 1, year 2, and year 3.

Remember This

  • SI = (P × R × T)/100 — Principal times annual Rate times Time in years, over 100.
  • Amount = Principal + SI = P(1 + RT/100).
  • Simple interest earns the SAME amount every year, always on the original principal.
  • Time must always be in years — convert months (÷12) or days (÷365) before using the formula.
  • Rearrange the formula to solve for R, T, or P when SI and the other two quantities are known.
Time must be in years6 months = 6/12 years = 0.5 years
6 months converts to 0.5 years before entering the formula.

Try It Yourself

Find the simple interest on ₹12,000 at 9% per year for 4 years, then find the total amount.

A loan of ₹6,000 accrues ₹720 interest over 2 years. Rearrange the formula to find the annual rate.

Word Bank

Principal
The original sum of money invested or borrowed, before any interest.
Rate
The annual percentage at which interest is charged or earned.
Time
The duration over which interest accrues, always measured in years for the SI formula.
Simple Interest
Interest calculated only on the original principal, the same amount every period.
Amount
The total sum after adding interest to the principal: Amount = Principal + Interest.

Questions

Loading questions…