Simple & Compound Interest – Study Notes
(Puducherry Patwari / Lekhpal – Quantitative Aptitude)
1. Introduction
Interest is the cost of borrowing money or the return on an investment.
In quantitative aptitude, we deal mainly with Simple Interest (SI) and Compound Interest (CI).
Both are calculated on a principal amount but differ in the period on which the interest is applied.
2. Simple Interest (SI)
2.1 Definition
Interest calculated only on the original principal for the whole period.
2.2 Formula
[ \text{SI} = \frac{P \times R \times T}{100} ]
| Symbol | Meaning | Units |
|---|---|---|
| (P) | Principal (initial amount) | ₹ / $ |
| (R) | Rate of interest per annum | % |
| (T) | Time (in years) | years |
2.3 Total Amount
[ A = P + \text{SI} = P \left(1 + \frac{R T}{100}\right) ]
3. Compound Interest (CI)
3.1 Definition
Interest calculated on the principal plus all previously earned interest.
3.2 Formula
[ A = P \left(1 + \frac{R}{n \times 100}\right)^{nT} ]
where
- (n) = number of compounding periods per year
- (T) = time in years
Alternatively, the compound interest earned:
[ \text{CI} = A - P = P \left[\left(1 + \frac{R}{n \times 100}\right)^{nT} - 1\right] ]
3.3 Common Compounding Frequencies
| (n) | Frequency |
|---|---|
| 1 | Annually |
| 2 | Semi‑annually |
| 4 | Quarterly |
| 12 | Monthly |
| 365 | Daily |
4. Key Points & Tips
| # | Point | Why It Matters |
|---|---|---|
| 1 | SI is linear – same interest each year. | Easier to compute; no compounding effect. |
| 2 | CI grows exponentially – interest on interest. | Small differences in rate or compounding frequency can lead to large differences. |
| 3 | Time must be in years (unless formula adjusted). | Avoids unit mismatch. |
| 4 | Convert rate to decimal before using in CI formula (e.g., 8 % → 0.08). | Prevents calculation errors. |
| 5 | Use parentheses carefully in CI formula. | Ensures correct order of operations. |
| 6 | Check compounding frequency – most problems state it (annual, semi‑annual, etc.). | Determines (n). |
| 7 | Round only at the end (unless the problem specifies otherwise). | Keeps intermediate values accurate. |
5. Worked Examples
5.1 Simple Interest Example
Problem
A person deposits ₹ 12,000 in a bank at an annual simple interest rate of 6 % for 3 years.
What is the total amount at the end of 3 years?
Solution
-
Identify variables:
- (P = 12{,}000)
- (R = 6%)
- (T = 3) years
-
Plug into SI formula:
[ \text{SI} = \frac{12{,}000 \times 6 \times 3}{100} = \frac{216{,}000}{100} = 2{,}160 ]
- Calculate total amount:
[ A = P + \text{SI} = 12{,}000 + 2{,}160 = 14{,}160 ]
Answer: ₹ 14,160
5.2 Compound Interest Example
Problem
₹ 8,000 is invested at an annual interest rate of 5 % compounded quarterly.
Find the amount after 4 years.
Solution
-
Convert rate to decimal and determine (n):
- (R = 5% = 0.05)
- (n = 4) (quarterly)
-
Time: (T = 4) years
-
Apply CI formula:
[ A = 8{,}000 \left(1 + \frac{0.05}{4}\right)^{4 \times 4} = 8{,}000 \left(1 + 0.0125\right)^{16} = 8{,}000 \times (1.0125)^{16} ]
- Compute ((1.0125)^{16}) (use calculator):
[ (1.0125)^{16} \approx 1.215 ]
- Multiply by principal:
[ A \approx 8{,}000 \times 1.215 = 9{,}720 ]
Answer: ≈ ₹ 9,720
(If exact CI is required: (\text{CI} = 9{,}720 - 8{,}000 = 1{,}720)).
6. Common Pitfalls
| Pitfall | Fix |
|---|---|
| Using years for (T) when compounding is monthly/daily | Convert time to years or use (T) in the same units as (n). |
| Forgetting to divide the rate by 100 in SI | Always convert percentage to decimal. |
| Not using parentheses in CI formula | (A = P\ |