Ratio, Proportion & Commercial Maths (VI–VIII) • Topic 4 of 5

Simple Interest

When money (the Principal, P) is borrowed or lent, the extra charge paid for its use is interest. In simple interest the charge is computed only on the original principal, every year, so it is the same amount each year. The formula is SI = (P × R × T) / 100, where R is the rate percent per annum and T is the time in years; the total to be repaid is the Amount = P + SI. Three cautions decide most questions: the rate is per annum, so T must be in YEARS (6 months = 1/2 year, 8 months = 8/12 year); the interest is always on the original P, never on a growing balance (that is compound interest); and 'amount' is principal plus interest, not interest alone. PEDAGOGY: introduce SI through a familiar savings or borrowing story and a year-by-year table — Year 1 interest, Year 2 the same, and so on — so children see why 'simple' interest is a repeated equal addition before the formula is handed over. COMMON MISCONCEPTIONS: leaving time in months instead of converting to years; confusing the amount with the interest; and (a deeper one) assuming interest compounds. HOW TESTED: a direct SI computation with whole-number time, a question where time is given in months, and finding the amount or the unknown rate/principal by rearranging the formula.

✅ Solved examples

1. Find the simple interest on ₹2000 at 5% per annum for 3 years.
SI = (P × R × T) / 100 = (2000 × 5 × 3) / 100 = 30000 / 100 = ₹300.
2. Find the amount to be repaid on ₹1500 at 8% per annum for 2 years.
SI = (1500 × 8 × 2) / 100 = 24000 / 100 = ₹240. Amount = P + SI = 1500 + 240 = ₹1740.
3. Find the simple interest on ₹4000 at 10% per annum for 6 months.
6 months = 6/12 = 1/2 year. SI = (4000 × 10 × (1/2)) / 100 = (4000 × 10 × 0.5) / 100 = 20000 / 100 = ₹200.
4. At what rate percent per annum will ₹1000 give ₹150 as simple interest in 3 years?
R = (SI × 100) / (P × T) = (150 × 100) / (1000 × 3) = 15000 / 3000 = 5%.

✏️ Practice — try these, take hints as needed

1. Find the simple interest on ₹5000 at 4% per annum for 2 years.
Use SI = PRT/100.
5000 × 4 × 2, then ÷ 100.
₹400
2. Find the amount on ₹2500 at 6% per annum for 4 years.
First find SI = PRT/100.
Amount = P + SI.
₹3100 (SI = ₹600)
3. Find the simple interest on ₹6000 at 5% per annum for 9 months.
Convert 9 months to years: 9/12 = 3/4 year.
SI = PRT/100.
₹225
4. In what time will ₹800 amount to ₹920 at 5% per annum simple interest?
SI = Amount − P = 120.
Rearrange: T = (SI × 100)/(P × R).
3 years

📝 Topic test — 8 questions

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