Simple Compound Interest - Quick Revision
Simple Compound Interest - Quick Revision
Key Points (One-Liners)
- SI = (P×R×T)/100, always calculated on original principal only.
- CI = P[(1 + R/100)^T – 1], interest earns interest.
- For same R & T, CI > SI always (except T = 1 year).
- Half-yearly CI: rate becomes R/2, time becomes 2T.
- Quarterly CI: rate becomes R/4, time becomes 4T.
- Effective annual rate = (1 + r/n)^n – 1 (n = compounding freq.).
- If T = 1 year, SI = CI.
- Difference CI – SI for 2 yrs = P(R/100)^2.
- Difference CI – SI for 3 yrs = P(R/100)^2 (3 + R/100).
- Rate % = (100 × SI)/(P × T) (when SI known).
- Time (yr) = (100 × SI)/(P × R) (when SI known).
- CI shortcut: Amount after T yrs = P × (Growth multiplier)^T.
- Doubling time (approx.) = 72 ÷ R (Rule of 72).
- Installment SI: each installment = [P(100 + RT)]/(100T).
- CI loan repayment: present value of each installment.
| Formula/Rule |
Application |
| SI = (P R T)/100 |
Any simple-interest problem |
| Amount (SI) = P + SI = P(1 + RT/100) |
Maturity value under SI |
| CI = P[(1 + R/100)^T – 1] |
Compound interest once a year |
| Amount (CI) = P(1 + R/100)^T |
Maturity value under CI |
| Half-yearly A = P(1 + R/200)^(2T) |
Twice-a-year compounding |
| Quarterly A = P(1 + R/400)^(4T) |
Four-times-a-year compounding |
| Difference CI–SI (2 yr) = P(R/100)^2 |
Quick 2-year comparison |
| Installment (SI loan) x = 100P/(100T + RT(T-1)/2) |
Equal yearly repayment under SI |
| Effective rate = (1 + r/n)^n – 1 |
Compare schemes with different n |
Memory Tricks
- SI formula: “People Rarely Talk” → P R T in numerator.
- CI formula: “1-plus-R-rate-to-the-T” sounds like “One plus great tea”.
- Difference 2-yr CI–SI: “Pee-R-square” → P(R/100)^2.
- Half-yearly switch: “Rate halved, time doubled.”
- Rule of 72: “72 divided by rate gives doubling date—no calculator!”
Common Mistakes
| Mistake |
Correct Approach |
| Using annual rate & time directly for half-yearly CI |
Halve rate, double time (or use n=2) |
| Forgetting to subtract P to get CI; quoting Amount instead |
CI = Amount – P |
| Taking SI formula for CI when T > 1 year |
Check if interest is compounded; if yes, use CI formula |
| Mixing up 2-yr and 3-yr difference formulas |
2-yr: P(R/100)^2; 3-yr: P(R/100)^2(3+R/100) |
| Assuming CI = SI for T = 2 |
CI > SI for all T > 1; equal only when T = 1 |
Last Minute Tips
- Write formulas on rough sheet first; saves 30 s per question.
- Rate or Time missing? SI formula can be rearranged—no need to guess.
- Options far apart? Use rounded values & Rule of 72 to estimate.
- Doubling/tripling? Work in multiples: 2→(1+R/100)^T = 2.
- Always check compounding frequency—examiner’s favourite trap.
Quick Practice (5 MCQs)
1. Find CI on ₹4 000 at 10 % p.a. compounded half-yearly for 1 year.
**Ans:** ₹ 410
2. The difference between CI and SI on ₹5 000 for 2 yrs is ₹ 50. Find rate.
**Ans:** 10 %
3. A sum doubles in 8 yrs SI. Find rate.
**Ans:** 12.5 %
4. In how many years will ₹8 000 become ₹13 312 at 20 % p.a. CI?
**Ans:** 3 yrs
5. Equal annual installment to repay ₹10 000 in 3 yrs at 4 % SI is:
**Ans:** ₹3 600
BETA
