60-second revision
- SI = P × R × T/100; amount = P + SI. SI is the same every year.
- At SI a sum becomes n times when R × T = (n - 1) × 100 (doubles when R × T = 100).
- CI amount = P(1 + R/100)^T; compound interest = amount - P.
- Half-yearly: use R/2 and 2T; quarterly: use R/4 and 4T.
- CI - SI for 2 years = P(R/100)²; for 3 years = P(R/100)²(3 + R/100).
- At CI, if a sum becomes x times in n years, it becomes x^k times in kn years.
- Two-year CI at R% = 2R + R²/100 % (10% gives 21%, 20% gives 44%).
Simple interest
Interest is charged only on the original principal. SI = P × R × T/100, where R is the yearly rate in % and T is time in years. Example: Rs 5,000 at 9% per annum for 3 years earns 5,000 × 9 × 3/100 = Rs 1,350; amount Rs 6,350.
| To find | Formula |
|---|---|
| Principal | P = 100 × SI/(R × T) |
| Rate | R = 100 × SI/(P × T) |
| Time | T = 100 × SI/(P × R) |
| Rate to make it n times | R × T = (n - 1) × 100 |
Example: a sum triples in 10 years at SI. Interest = 2P, so R × 10 = 200 and R = 20%.
Time in months or days must be converted to years: 9 months = 3/4 year, 73 days = 1/5 year (365-day year).
Compound interest
Interest is added to the principal at the end of each period, and the next period's interest is charged on the new total. Amount A = P(1 + R/100)^T, and CI = A - P. Example: Rs 5,000 at 8% for 2 years gives 5,000 × 1.08 × 1.08 = Rs 5,832, so CI = Rs 832.
| Compounded | Rate per period | Number of periods |
|---|---|---|
| Yearly | R | T |
| Half-yearly | R/2 | 2T |
| Quarterly | R/4 | 4T |
Example: Rs 8,000 at 20% per annum compounded half-yearly for 1 year means 10% for 2 periods: 8,000 × 1.1 × 1.1 = Rs 9,680.
Different rates in different years: multiply the factors. Rs 10,000 at 10% in year 1 and 20% in year 2 becomes 10,000 × 1.1 × 1.2 = Rs 13,200.
Compound interest as successive percentages
| Rate | 2-year CI % | 3-year CI % |
|---|---|---|
| 5% | 10.25% | 15.7625% |
| 10% | 21% | 33.1% |
| 20% | 44% | 72.8% |
The two-year figure is 2R + R²/100 (the a + b + ab/100 rule from percentages). Use it to get CI in one step.
Difference between CI and SI
- For 2 years: CI - SI = P(R/100)². Rs 20,000 at 5%: 20,000 × 1/400 = Rs 50.
- For 3 years: CI - SI = P(R/100)²(3 + R/100). Rs 10,000 at 10%: 10,000 × 0.01 × 3.1 = Rs 310 (CI 3,310 - SI 3,000).
- For 1 year, compounded yearly, CI and SI are equal.
Growth by multiples, and depreciation
- Multiples at CI: if a sum doubles in 5 years, it becomes 4 times in 10 years and 8 times in 15 years.
- Depreciation uses (1 - R/100): a Rs 50,000 machine losing 10% a year is worth 50,000 × 0.9 × 0.9 = Rs 40,500 after 2 years.
- Effective annual rate for R% compounded half-yearly = (1 + R/200)² - 1. For 8% it is 8.16%.
Test yourself: 10 questions, 60 s each
Every answer is explained. Free, no sign-up.
Start the quiz