Simple and Compound Interest Tricks: The Short Answer
Simple interest (SI) is charged only on the original principal: SI = P × R × T ÷ 100. Compound interest (CI) is charged on the principal plus the interest already added: Amount = P(1 + R/100)ᵀ and CI = Amount − P. The tricks that save the most time are effective rate (10% CI for 2 years = 21%), the CI−SI difference formula P(R/100)², the "amount ratio" method for consecutive years, and the doubling rule for SI and CI.
Key takeaway for bank exams and SSC: IBPS and SBI Clerk and PO ask 1 to 2 SI and CI questions as arithmetic word problems (often in quantity comparison or data sufficiency), and SSC CGL and CHSL ask 1 to 2 in Tier 1. Learn the formula table, the effective-rate table and the four shortcuts below. Every answer here was computed in Python.
For the 2-, 3- and 4-year CI–SI difference shortcuts in more depth, see our SI and CI difference formula note.
Simple Interest Formula and Tricks
| Find | Formula |
|---|---|
| Simple interest | SI = P × R × T ÷ 100 |
| Amount | A = P + SI |
| Principal | P = 100 × SI ÷ (R × T) |
| Rate | R = 100 × SI ÷ (P × T) |
| Time | T = 100 × SI ÷ (P × R) |
Example 1: Find the SI on ₹8,000 at 5% per year for 3 years.
SI = 8,000 × 5 × 3 ÷ 100 = ₹1,200.
Example 2 (two amounts given): A sum becomes ₹6,600 in 2 years and ₹7,200 in 4 years at simple interest. Find the principal and the rate.
Interest for 2 years = 7,200 − 6,600 = 600, so ₹300 per year. Principal = 6,600 − 600 = ₹6,000. Rate = 300 ÷ 6,000 × 100 = 5%.
Example 3 (rate equals time): The SI on a sum is 9/16 of the sum, and the rate (in %) equals the time (in years). Find the rate.
R × R ÷ 100 = 9/16 → R² = 56.25 → R = 7.5% (and time = 7.5 years).
Compound Interest Formula and Tricks
| Compounding | Amount formula |
|---|---|
| Yearly | P(1 + R/100)ᵀ |
| Half-yearly | P(1 + R/200)²ᵀ |
| Quarterly | P(1 + R/400)⁴ᵀ |
| Different rates each year | P(1 + R₁/100)(1 + R₂/100)(1 + R₃/100) |
| Fraction of a year (e.g. 2½ years) | P(1 + R/100)² × (1 + (R/2)/100) |
Example 4: Find the CI on ₹10,000 at 10% per year for 2 years.
Amount = 10,000 × 1.1² = 12,100, so CI = ₹2,100.
Example 5 (half-yearly and quarterly): Find the CI on ₹10,000 at 10% per year for 1 year compounded half-yearly, and on ₹16,000 at 20% per year for 9 months compounded quarterly.
- Half-yearly: 5% for 2 periods → 10,000 × 1.05² = 11,025 → CI = ₹1,025.
- Quarterly: 5% for 3 periods → 16,000 × 1.05³ = 18,522 → CI = ₹2,522.
Example 6 (different rates): ₹5,000 is invested at 10% in the first year and 20% in the second year, compounded yearly. Find the amount.
5,000 × 1.1 × 1.2 = ₹6,600.
Example 7 (fraction of a year): Find the CI on ₹10,000 at 10% per year for 2½ years, compounded yearly.
Two full years at 10%, then half a year at 5%: 10,000 × 1.1² × 1.05 = 12,705. CI = ₹2,705. The exam convention is to apply a proportional rate (R/2 for half a year) to the part-year, not a fractional power such as 1.1 raised to 2.5.
Effective Rate of Compound Interest (Shortcut Table)
Effective rate for 2 years = 2R + R²/100; for 3 years = 3R + 3R²/100 + R³/10,000.
| Rate | 2-year effective | 3-year effective |
|---|---|---|
| 5% | 10.25% | 15.7625% |
| 10% | 21% | 33.1% |
| 15% | 32.25% | 52.0875% |
| 20% | 44% | 72.8% |
So CI on any sum at 10% for 2 years is 21% of the sum. On ₹10,000 that is ₹2,100 (Example 4) without any squaring.
Difference Between CI and SI Formula (2 and 3 Years)
| Time | CI − SI |
|---|---|
| 2 years | P × (R/100)² |
| 3 years | P × (R/100)² × (3 + R/100) |
Example 8: Find the difference between CI and SI on ₹5,000 at 8% for 2 years and for 3 years.
- 2 years: 5,000 × 0.0064 = ₹32
- 3 years: 5,000 × 0.0064 × 3.08 = ₹98.56
Compound Interest Consecutive Years Trick (Amount Ratio)
If a sum amounts to A₁ after n years and A₂ after (n + 1) years at CI, then rate = (A₂ − A₁) ÷ A₁ × 100.
Example 9: A sum amounts to ₹6,050 in 2 years and ₹6,655 in 3 years at compound interest. Find the rate and the principal.
Rate = 605 ÷ 6,050 × 100 = 10%. Principal = 6,050 ÷ 1.1² = ₹5,000.
Doubling and Tripling Rules for SI and CI
| Interest | If a sum doubles in T years … |
|---|---|
| Simple interest | Rate = 100 ÷ T. It becomes n times in (n − 1) × T years |
| Compound interest | It becomes 4 times in 2T, 8 times in 3T, 2ᵏ times in kT years |
Example 10: A sum doubles in 8 years at SI. Find the rate and when it will triple.
Rate = 100 ÷ 8 = 12.5%. Tripling needs SI = 2P → 2 × 8 = 16 years.
Example 11: A sum doubles in 5 years at CI. In how many years will it become 8 times?
8 = 2³, so 3 × 5 = 15 years.
Compound Interest Instalment Questions (Bank Exam Favourite)
For a loan P repaid in n equal yearly instalments x at R% compound interest:
P = x/(1 + R/100) + x/(1 + R/100)² + … + x/(1 + R/100)ⁿ
Example 12: A loan of ₹2,100 at 10% CI is repaid in 2 equal annual instalments. Find each instalment.
2,100 = x/1.1 + x/1.21 = x × (1.1 + 1) ÷ 1.21 = x × 2.1 ÷ 1.21 → x = ₹1,210.
Check: after year 1, owe 2,310 − 1,210 = 1,100; after year 2, owe 1,210 − 1,210 = 0. ✔
Simple and Compound Interest Tricks (Quick Revision Table)
| Situation | Shortcut |
|---|---|
| SI | P × R × T ÷ 100 |
| CI amount | P(1 + R/100)ᵀ |
| Half-yearly | Halve the rate, double the time |
| Quarterly | Rate ÷ 4, time × 4 |
| 2-year effective CI rate | 2R + R²/100 |
| CI − SI, 2 years | P(R/100)² |
| CI − SI, 3 years | P(R/100)²(3 + R/100) |
| Amounts in consecutive years | R = (A₂ − A₁)/A₁ × 100 |
| SI doubles in T years | R = 100/T |
| CI doubles in T years | 2ᵏ times in kT years |
Common Mistakes in SI and CI Questions
- Using yearly rate for half-yearly compounding. Halve the rate and double the periods.
- Treating CI like SI over many years; interest grows each year.
- Applying the doubling rule of CI to SI. SI grows by equal amounts each year, so 4 times needs 3T years, not 2T.
- Forgetting to subtract P when the question asks for interest, not amount.
- Rounding 1.05³ or 1.1³ too early. Use 1.157625 and 1.331 exactly.
Simple and Compound Interest Questions for Bank Exams (Practice Set)
- Find the SI on ₹12,000 at 6% per year for 2½ years. Answer: ₹1,800.
- Find the CI on ₹15,000 at 10% for 2 years. Answer: ₹3,150. 21% of 15,000.
- Find the CI on ₹8,000 at 10% per year for 2 years, compounded half-yearly. Answer: ₹1,724.05. 8,000 × 1.05⁴ − 8,000.
- A sum doubles in 10 years at SI. In how many years will it become 4 times? Answer: 30 years. (4 − 1) × 10.
- A sum triples in 4 years at CI. In how many years will it become 27 times? Answer: 12 years. 27 = 3³ → 3 × 4.
- A sum amounts to ₹4,410 in 2 years and ₹4,630.50 in 3 years at CI. Find the rate and the principal. Answer: 5% and ₹4,000. 220.50 ÷ 4,410 = 5%; 4,410 ÷ 1.1025.
- Find the difference between CI and SI on ₹8,000 at 5% for 2 years. Answer: ₹20. 8,000 × 0.0025.
- Find the effective 2-year rate for 20% compound interest. Answer: 44%. 40 + 4.
- ₹6,000 is invested at 5% in year 1 and 10% in year 2 (compounded yearly). Find the amount. Answer: ₹6,930.
- A loan of ₹3,310 at 10% CI is repaid in 3 equal annual instalments. Find each instalment. Answer: ₹1,331.
For timed practice, take the SSC CGL Simple and Compound Interest Mock Test 02 and the IBPS Clerk Quant Mini Mock Test 03.
Simple and Compound Interest FAQs
What is the difference between simple and compound interest?
Simple interest is calculated only on the original principal every year. Compound interest is calculated on the principal plus the interest already earned, so it grows faster over time.
What is the formula for compound interest?
Amount = P(1 + R/100)ᵀ and CI = Amount − P. For half-yearly compounding use R/2 and 2T; for quarterly use R/4 and 4T.
What is the shortcut for CI for 2 years?
Effective rate = 2R + R²/100. At 10% this is 21%, so the CI for 2 years is 21% of the principal.
What is the formula for the difference between CI and SI for 2 years?
CI − SI = P × (R/100)². For 3 years, multiply further by (3 + R/100).
How many SI and CI questions come in bank exams?
Usually 1 to 2 in IBPS and SBI prelims, often inside arithmetic word problems, quantity comparison or data sufficiency. Mains papers use them in caselet DI.
How do you know when a sum doubles at compound interest?
If it doubles in T years, it becomes 4 times in 2T, 8 times in 3T and 16 times in 4T years, because each T years multiplies the amount by 2.
Practice Next
- Mock tests: SSC CGL Simple and Compound Interest Mock Test 02, IBPS Clerk Quant Mini Mock Test 03, SBI Clerk Quant Mini Mock Test 03 and IBPS PO Quant Sectional Mock Test 07.
- Related notes: SI and CI difference formula for 2, 3 and 4 years, percentage tricks for SSC CGL, profit and loss tricks for SSC CGL and average tricks for SSC CGL.
- Exam details: SBI Clerk 2026 notification and SSC CGL 2026.
- Browse all study notes.