Unit 2 · Topic 04 · Comparing Quantities
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.
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."
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.
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.
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