Simple and Compound Interest Formula Guide: Effective Rate Table, Difference and Half-Yearly Formulas for SSC
Rahul Kumar
SSC Exam Expert & Content Editor
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PDF Notes: Simple and Compound Interest Formula Guide: Effective Rate Table, Difference and Half-Yearly Formulas for SSC
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This simple and compound interest formula guide for SSC is a one-page sheet of every interest formula, plus a table of effective rates for 2 and 3 years that lets you solve CI questions in a few seconds. For the method and more practice, read the Simple and Compound Interest Tricks note.
Simple Interest
| Item | Formula |
|---|---|
| SI | P × R × T / 100 |
| Amount | P + SI |
| Principal | SI × 100 / (R × T) |
| Rate | SI × 100 / (P × T) |
| Time | SI × 100 / (P × R) |
| Sum doubles in T years | R = 100/T % |
| Sum becomes n times in T years | R = 100(n − 1)/T % |
Compound Interest
| Item | Formula |
|---|---|
| Amount | P(1 + R/100)^n |
| CI | Amount − P |
| Half-yearly | Rate R/2 and time 2n |
| Quarterly | Rate R/4 and time 4n |
| Different rates r1, r2, r3 in successive years | P(1 + r1/100)(1 + r2/100)(1 + r3/100) |
Difference of CI and SI
| Years | Formula |
|---|---|
| 2 years | P(R/100)² |
| 3 years | P R²(300 + R)/100³ |
Effective Rate Table (CI for 2 and 3 Years)
| Rate per year | CI for 2 years (% of P) | CI for 3 years (% of P) |
|---|---|---|
| 5% | 10.25% | 15.76% |
| 10% | 21% | 33.1% |
| 20% | 44% | 72.8% |
| 25% | 56.25% | 95.3% |
The effective rate for 2 years is R + R²/100 %. For example, at 10%: 10 + 1 = 11 and 10 + 11 = 21%. Check: 1.1 × 1.1 = 1.21.
Solved Examples
Example 1. Find the SI on 5,000 rupees at 8% for 3 years.
1,200 rupees.
Example 2. Find the CI on 8,000 rupees at 10% for 2 years.
21% of 8,000 = 1,680 rupees.
Example 3. Find the difference of CI and SI on 5,000 rupees at 10% for 2 years.
5000 × 1/100 = 50 rupees.
Example 4. Find the CI on 10,000 rupees at 10% for 1 year, compounded half-yearly.
At 5% for 2 half-years: 10.25% of 10,000 = 1,025 rupees.
Example 5. Find the CI on 1,000 rupees at 20% for 3 years.
72.8% of 1,000 = 728 rupees.
Quick Tips
- Use the effective rate table for CI of 2 and 3 years.
- The CI of 2 years at R% is R + R²/100 %.
- Use half the rate and double the time for half-yearly compounding.
- Remember that for 1 year SI and CI are equal.
Quick Revision Points
- SI = PRT/100.
- A = P(1 + R/100)^n.
- CI minus SI for 2 years = P(R/100)².
- At 10% the CI for 2 years is 21% and for 3 years is 33.1%.
- The half-yearly rate is R/2 and the time is 2n.
Practice Questions With Answers
- Find the SI on 2,000 rupees at 5% for 4 years.
Answer: 400 rupees - Find the CI on 1,000 rupees at 10% for 2 years.
Answer: 210 rupees - What is the effective rate of 20% for 2 years?
Answer: 44% - What is the effective rate of 10% for 3 years?
Answer: 33.1% - Find the difference of CI and SI on 10,000 rupees at 5% for 2 years.
Answer: 25 rupees - A sum doubles in 8 years at SI. Find the rate.
Answer: 12.5% - Find the CI on 5,000 rupees at 20% for 2 years.
Answer: 2,200 rupees - Find the CI on 1,000 rupees at 20% for 3 years.
Answer: 728 rupees - What are the rate and the time for half-yearly compounding at 10% for 1 year?
Answer: 5% for 2 half-years - Are the SI and CI equal for the first year?
Answer: Yes
How to Practise This Chapter
Write each formula on a card, with a solved example on the back, and revise the cards every day. Then test yourself with our practice papers and the previous year papers page. See all guides on the Formula Guide page, and also read the Mathematics notes and Quantitative Aptitude notes. The previous guide is Clock and Calendar. The Arithmetic Formula Guide has the other arithmetic formulas.
Frequently Asked Questions
What is the formula for simple interest?
SI = Principal × Rate × Time / 100.
What is the formula for compound interest?
CI = P(1 + R/100)^n − P.
What is the effective rate for 2 years?
R + R²/100 percent.
What is the difference of CI and SI for 2 years?
P(R/100)².
What is the effective rate of 10% for 2 years?
21%.
How do I find CI for half-yearly compounding?
Use half the rate and double the time.
If a sum doubles in 8 years at SI, what is the rate?
12.5% per year.
Is the first year interest the same in SI and CI?
Yes.
Is interest asked in SSC exams?
Yes. SI and CI are asked in SSC CGL, CHSL and MTS maths.
How much time should I take?
About 30 seconds with the effective rate table.
What are the common mistakes?
Using the wrong time unit and forgetting to subtract the principal.
How can I learn the table?
Revise the effective rates of 5%, 10%, 20% and 25% daily.
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Clock and Calendar Formula Guide: Angle, Overlap, Odd Days and Day Finding Formulas for SSC Reasoning
Next chapter
Average, Ages and Partnership Formula Guide: Important Formulas, Tricks and Solved Examples for SSC Maths
Rahul Kumar
SSC Exam Expert & Content Editor
Rahul is a senior SSC exam strategist with 8+ years of experience helping aspirants crack CGL, CHSL and MTS exams. He writes in-depth notification breakdowns, exam pattern guides and preparation strategies.