The formula
SI = P × R × T ÷ 100, where P is the principal, R the annual rate in percent and T the time in years. The amount is A = P + SI = P(1 + RT ÷ 100). Interest grows by the same amount each year, so it is linear in time.
Worked examples
Example 1. SI on 8,000 at 6% for 3 years = 8,000 × 6 × 3 ÷ 100 = 1,440.
Example 2. A sum becomes 6,300 in 4 years and 7,200 in 7 years at simple interest. The extra 900 is 3 years of interest, so 300 a year. The interest for 4 years is 1,200, so the principal is 6,300 − 1,200 = 5,100. The rate is 300 ÷ 5,100 ≈ 5.88%.
Example 3. At what rate will a sum double itself in 12.5 years? Interest equals the principal: P = P × R × 12.5 ÷ 100, so R = 8%.
Example 4. A sum of 5,000 is lent for 8 months at 9% a year. Time = 8 ÷ 12 = 2/3 year. SI = 5,000 × 9 × (2/3) ÷ 100 = 300.
Example 5. A person invests 12,000, part at 5% and the rest at 8%, and earns 780 in a year. If x is at 5%, then 0.05x + 0.08(12,000 − x) = 780; 0.05x + 960 − 0.08x = 780; 0.03x = 180; x = 6,000. So 6,000 at each rate.
Common traps
- Not converting months or days to years.
- Mixing SI and amount: check whether the question asks for interest or the total.
- Quarterly or half-yearly rates: if the rate is given per half-year, adjust the time.
- Confusing simple with compound in "interest compounded" questions.
Speed tips
- Interest in one year is P × R ÷ 100: compute that first and multiply by years.
- A sum doubles in 100 ÷ R years at simple interest; it triples in 200 ÷ R years.
- For two rates on one sum, use the weighted average.
A practice routine
- Day 1: direct SI questions; ten problems with months and days converted.
- Day 2: amount and rate-finding questions.
- Day 3: doubling, tripling and split-investment problems.
- Day 4: a timed set of 12 mixed questions at 50 seconds each.
Where it appears
Simple interest appears in SSC CGL, banking, railway mathematics and MAT Mathematical Skills. Next, read compound interest, which builds on it, and revise percentage.
Practice tests below are published by institutes and educators on TestMint.
