Simple & Compound Interest – Quick Study Guide
AFCAT – Quantitative Aptitude
This guide covers the fundamentals, key formulas, common pitfalls, and a worked example for both Simple Interest (SI) and Compound Interest (CI). Keep it handy for quick revision before the exam.
1. Simple Explanation
| Concept | What it means |
|---|---|
| Principal (P) | Initial amount of money invested or borrowed. |
| Rate of Interest (r) | Annual percentage rate. Usually expressed as a whole number (e.g., 8 % → 0.08). |
| Time (t) | Number of years (or fraction of a year). |
| Simple Interest (SI) | Interest earned only on the initial principal. |
| Compound Interest (CI) | Interest earned on the principal and on previously accumulated interest. |
Key takeaway:
Simple interest is a straight‑line calculation, whereas compound interest grows exponentially because each interest addition becomes part of the new principal.
2. Key Points & Formulas
| Term | Formula | Notes |
|---|---|---|
| Simple Interest | (\displaystyle SI = \frac{P \times r \times t}{100}) | r is in percent; SI in same currency as P. |
| Maturity Amount (Simple) | (\displaystyle A_{SI} = P + SI) | The total amount after t years. |
| Compound Interest | (\displaystyle CI = P \left[ \left(1 + \frac{r}{n}\right)^{nt} - 1 \right]) | r in decimal, n = compounding periods per year. |
| Maturity Amount (Compound) | (\displaystyle A_{CI} = P \left(1 + \frac{r}{n}\right)^{nt}) | Same as above multiplied by P. |
| Effective Annual Rate (EAR) | (\displaystyle EAR = \left(1 + \frac{r}{n}\right)^n - 1) | Useful when comparing different compounding frequencies. |
| Finding r, t, or P | Rearrange the appropriate formula accordingly. | Often requires algebraic manipulation or logarithms for CI. |
| Half‑year, quarter‑year, etc. | Convert time to years: (t_{\text{yrs}} = \frac{\text{months}}{12}) or (\frac{\text{quarters}}{4}). | Keeps formulas consistent. |
Common Pitfalls
| Mistake | Fix |
|---|---|
| Using r as a decimal in SI formula (but formula expects percent). | Either use r% in the numerator or divide by 100 consistently. |
| Forgetting to raise the base to the power (nt) in CI. | Double‑check the exponent. |
| Mixing up the compounding frequency (n). | Verify whether interest is annual, semi‑annual, quarterly, monthly, etc. |
| Using the wrong time unit (months vs. years). | Always convert to years before plugging into the formulas. |
3. Worked Example
Problem
A invests ₹10 000 in a savings account that offers 8 % p.a. interest, compounded quarterly.
How much will the account be worth after 3 years?
Step‑by‑Step
-
Identify the variables
- (P = ₹10,000)
- (r = 8% = 0.08) (as decimal)
- (n = 4) (quarterly compounding)
- (t = 3) years
-
Plug into the CI maturity formula
[ A_{CI} = P \left(1 + \frac{r}{n}\right)^{nt} ] [ A_{CI} = 10,000 \times \left(1 + \frac{0.08}{4}\right)^{4 \times 3} ] -
Compute the base
[ 1 + \frac{0.08}{4} = 1 + 0.02 = 1.02 ] -
Compute the exponent
[ nt = 4 \times 3 = 12 ] -
Raise to the power
[ 1.02^{12} \approx 1.26824 ] -
Multiply by the principal
[ A_{CI} \approx 10,000 \times 1.26824 = ₹12,682.40 ]
Answer: After 3 years, the account will hold approximately ₹12 682.40.
4. Quick Revision Summary
-
Simple Interest (SI)
- (SI = \dfrac{P \times r \times t}{100})
- (A_{SI} = P + SI)
- Linear growth; easier algebra.
-
Compound Interest (CI)
- (A_{CI} = P \left(1 + \dfrac{r}{n}\right)^{nt})
- (CI = A_{CI} - P)
- Exponential growth; depends on compounding frequency (n).
-
Common Conversion Tips
- Convert time to years if not already.
- Convert rate to decimal when inserting into formulas.
- Remember: (n) = # of compounding periods per year.
-
When to Use Which Formula?
- If interest is credited only once per period on the original principal, use SI.
- If each period’s interest is added to the principal for subsequent periods, use CI.
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