Compound Interest Notes for SSC Exams

Compound Interest is a scoring chapter in SSC Quantitative Aptitude. One or two questions come from it in almost every Tier 1 paper, and the same formula is used for population growth and depreciation questions. These compound interest notes for SSC explain the formula, the half-yearly and quarterly cases and the CI-SI difference shortcuts with solved examples.

What Is Compound Interest?

In compound interest, the interest of each period is added to the principal, and the next interest is calculated on this new amount. In other words, you earn interest on interest. Because of this, compound interest is always more than simple interest for more than one year.

• Amount (A) = P x (1 + R/100)^n
• Compound Interest (CI) = A - P
• For the first year, CI and SI are equal.
• The difference between CI and SI starts from the second year.

Compound Interest Formulas

Useful Powers to Remember

These values are used again and again. Learn them once and the calculations become quick.

Half-Yearly and Quarterly Compounding

When interest is compounded half-yearly, the rate is halved and the number of periods is doubled. When it is compounded quarterly, the rate becomes one-fourth and the number of periods becomes four times. For 10% per annum compounded half-yearly for 1 year, we take 5% for 2 periods, so A = P x 1.05 x 1.05 = P x 1.1025.

Solved Examples

Example 1: Find the compound interest on Rs 10,000 at 10% per annum for 2 years.
Solution: A = 10000 x (1.1)^2 = 10000 x 1.21 = 12,100. CI = 12,100 - 10,000 = Rs 2,100.

Example 2: Find the difference between compound interest and simple interest on Rs 5,000 at 10% per annum for 2 years.
Solution: Difference = P (R/100)^2 = 5000 x (0.1)^2 = 5000 x 0.01 = Rs 50.

Example 3: Find the compound interest on Rs 8,000 for 1 year at 10% per annum compounded half-yearly.
Solution: Rate per period = 5%, periods = 2. A = 8000 x 1.05 x 1.05 = 8,820. CI = Rs 820.

Example 4: A sum of Rs 5,000 earns interest at 10% in the first year and 20% in the second year. Find the amount.
Solution: A = 5000 x 1.1 x 1.2 = Rs 6,600.

Example 5: In how many years will Rs 1,000 become Rs 1,331 at 10% per annum compound interest?
Solution: (1.1)^n = 1.331 = (1.1)^3, so n = 3 years.

Example 6: The population of a town is 50,000 and it increases by 4% every year. Find the population after 2 years.
Solution: Population = 50000 x (1.04)^2 = 50000 x 1.0816 = 54,080.

Quick Tips to Solve Faster

• For 2 years, use the shortcut CI = P x (2R + R squared / 100) / 100, or simply calculate 1.0x squared.
• Use the CI - SI difference formula to skip finding both interests.
• Memorise the powers of 1.05, 1.1, 1.2 and 1.25 given in the table.
• Always check the compounding period. Half-yearly doubles the periods and halves the rate.
• If the same sum becomes double in n years at CI, it becomes 4 times in 2n years and 8 times in 3n years.

Common Mistakes to Avoid

• Using the simple interest formula for compound interest questions.
• Forgetting to subtract the principal when the question asks for compound interest and not the amount.
• Not halving the rate and not doubling the time in half-yearly compounding.
• Using the wrong formula for CI - SI over 3 years.
• Rounding the powers of 1.1 or 1.2 too early.

Quick Revision Points

• A = P (1 + R/100)^n and CI = A - P.
• Half-yearly: rate R/2, time 2n. Quarterly: rate R/4, time 4n.
• CI - SI (2 years) = P (R/100)^2.
• Growth uses (1 + R/100)^n and depreciation uses (1 - R/100)^n.
• CI is greater than SI for periods of more than 1 year.

Practice Questions With Answers

1. Find the compound interest on Rs 4,000 at 5% per annum for 2 years.
   Answer: Rs 410 (4000 x 0.1025).
2. Find the amount of Rs 2,500 at 20% per annum compound interest for 2 years.
   Answer: Rs 3,600 (2500 x 1.44).
3. Find the difference between CI and SI on Rs 8,000 at 5% per annum for 2 years.
   Answer: Rs 20 (8000 x 0.05 x 0.05).
4. Find the compound interest on Rs 1,000 at 10% per annum compounded half-yearly for 1 year.
   Answer: Rs 102.50 (1000 x 1.1025 - 1000).
5. Find the amount of Rs 2,000 at 10% per annum for 3 years at compound interest.
   Answer: Rs 2,662 (2000 x 1.331).
6. At what rate per annum will a sum become 1.44 times in 2 years at compound interest?
   Answer: 20% ((1.2)^2 = 1.44).
7. A machine costing Rs 20,000 depreciates by 10% per year. Find its value after 2 years.
   Answer: Rs 16,200 (20000 x 0.9 x 0.9).
8. Find the difference between CI and SI on Rs 1,000 at 10% per annum for 3 years.
   Answer: Rs 31 (1000 x 0.01 x 3.1).
9. Rs 10,000 amounts to Rs 12,100 in 2 years at compound interest. Find the rate.
   Answer: 10% (1.21 = (1.1)^2).
10. A sum doubles in 4 years at compound interest. In how many years will it become 16 times?
    Answer: 16 years (2 -> 4 -> 8 -> 16 takes 4 doubling periods).

How to Practise This Chapter

1. Learn the formulas in the table until you can write them without looking.
2. Solve the solved examples again on your own, without reading the solution.
3. Attempt the practice questions above with a timer of 10 minutes.
4. Solve the matching practice papers to test yourself in exam style.
5. Check the previous year papers to see how SSC frames this topic.

Related Notes and Practice Papers

• Simple Interest Notes
• Percentage Notes
• Profit and Loss Notes
• Ratio and Proportion Notes
• SSC Percentage Practice Paper

Explore More SSC Subjects

SSC exams test many subjects, so connect this topic with the related subjects below:

• Reasoning Notes
• Statistics Notes
• Indian Economy Notes
• English Notes
• General Awareness Notes
• All SSC subjects and notes

Frequently Asked Questions

What is compound interest?

Compound interest is the interest calculated on the principal and on the interest already earned. It is also called interest on interest.

What is the compound interest formula?

Amount = P x (1 + R/100)^n and CI = Amount - P.

How many questions come from compound interest in SSC exams?

One or two questions usually come from compound interest in SSC CGL and CHSL Tier 1.

What is the shortcut for CI - SI for 2 years?

The difference is P x (R/100)^2.

How do I solve half-yearly compound interest?

Halve the rate and double the number of years. Then apply the normal formula.

Is compound interest always more than simple interest?

Yes, for periods longer than one year at the same rate. For the first year both are equal.

How is population growth related to compound interest?

Population growth follows the same formula, P x (1 + R/100)^n, so the same shortcuts can be used.

What is depreciation?

Depreciation is the fall in the value of a machine or vehicle every year. It uses the formula P x (1 - R/100)^n.

How can I calculate compound interest quickly?

Memorise the powers given in the table, use multipliers such as 1.1 and 1.2, and use the CI - SI difference formula whenever it is given.