5. Simple Interest vs Compound Interest

Why This Chapter Matters

Interest questions look formula-heavy, but most of them reduce to one decision: is the base fixed or is it updating? Once that is clear, you can move through SI, CI, installments, and difference-based shortcuts much faster.

Core Ideas

• Simple interest grows linearly: the principal remains the calculation base.
• Compound interest grows on the updated amount each period.
• If compounding is half-yearly, quarterly, or monthly, split both the rate and the time into matching periods before applying the compound formula.
• For two years at rate $r\%$, compound amount is $P{\left(1+\frac{r}{100}\right)}^2$.
• Difference between CI and SI is often a shortcut-based question in bank exams, especially for $2$ or $3$ years.
• Mixed-rate questions and amount-ratio questions can often be solved without first finding the principal.

High-Value Formulas

How To Approach Questions

1. Write the principal, rate, and time clearly.
2. Use SI when the base stays fixed; use CI when the base keeps changing.
3. If the compounding period is not yearly, convert the annual rate and total duration into the same interval count.
4. For yearly compounding, multiply the growth factors instead of adding rupee interest by guesswork.
5. When only the difference between CI and SI is given, use the shortcut before expanding the full amount expression.

Worked Examples

Example 1

Prompt: Find simple interest on $\text{Rs }15000$ at $8\%$ per annum for $3$ years.

Approach: Use $\text{SI}=\frac{PRT}{100}=\frac{15000\times 8\times 3}{100}=3600$.

Example 2

Prompt: Find the compound interest on $\text{Rs }20000$ at $10\%$ per annum for $2$ years.

Approach: Amount $=20000\times 1.1^2=24200$. So CI $=24200-20000=4200$.

Example 3

Prompt: Rs $7500$ is borrowed at $4\%$ per annum compound interest for $1$ year, compounded half-yearly. Find the amount.

Approach: Use $A=P{\left(1+\frac{r}{200}\right)}^{2n}$. So $A=7500{\left(1+\frac{4}{200}\right)}^2=7500\times 1.02^2=7803$.

Example 4

Prompt: The difference between CI and SI for $2$ years at $5\%$ is Rs $1.50$. Find the principal.

Approach: Use $\text{difference}=P{\left(\frac{r}{100}\right)}^2$. Then $1.5=P\times {\left(\frac{5}{100}\right)}^2=P\times \frac{1}{400}$, so $P=600$.

Common Mistakes

• Using SI formula in a CI question just because the time period is short.
• Keeping the annual rate unchanged even when compounding is half-yearly or quarterly.
• Forgetting that rate is a percent and must be divided by 100.
• Computing compound interest when the question asks only for amount.
• Solving long-form when a standard CI-SI shortcut for 2 years would finish the problem directly.

Quick Revision

Interest becomes manageable once the growth base is identified, the compounding interval is aligned, and the 2-year and 3-year shortcuts are remembered.