Simple & Compound Interest – Study Notes
Program: LIC ADO | Subject: Quantitative Aptitude | Topic: Simple & Compound Interest
1. Simple Explanation
| Concept | What it Means | When It Is Used |
|---|---|---|
| Simple Interest (SI) | Interest calculated only on the original principal. | Short‑term loans, simple savings accounts, quick calculations. |
| Compound Interest (CI) | Interest is calculated on the principal + accumulated interest. | Long‑term investments, bank deposits, loans with compounding. |
Key Insight:
- SI grows linearly (adds a fixed amount each period).
- CI grows exponentially (interest on interest).
2. Key Points
| Item | Detail | Quick Tip |
|---|---|---|
| Formula for SI | ( I = P \times r \times t ) ( M = P + I = P(1 + rt) ) |
r is annual rate in decimal, t in years. |
| Formula for CI | ( A = P \left(1 + \frac{r}{n}\right)^{nt} ) | n = compounding periods per year (e.g., 4 = quarterly). |
| Annual Effective Rate | ( (1 + \frac{r}{n})^n - 1 ) | Use to compare different compounding frequencies. |
| Continuous Compounding | ( A = P e^{rt} ) | Use when compounding is “infinitely frequent”. |
| Difference (Δ) | ( CI - SI = P \left[(1+\frac{r}{n})^{nt} - (1+rt)\right] ) | Shows the “interest‑on‑interest” benefit. |
| Principal (P) | Initial amount invested or borrowed. | Keep track of units (₹, $, etc.). |
| Rate (r) | Annual interest rate (decimal). | 8 % → 0.08. |
| Time (t) | Number of years. | Convert months: ( t = \frac{m}{12} ). |
| Compounding Frequency (n) | How often interest is added per year. | n = 1 (annually), 2 (semi‑annually), 4 (quarterly), 12 (monthly). |
| Maturity Value (A) | Total amount at the end of the investment period. | For loans, this is the total amount to be repaid. |
| Interest Earned (I) | ( A - P ) for CI; ( P r t ) for SI. | Always double‑check units. |
| Common Pitfalls | 1. Forgetting to convert percentages to decimals. 2. Mixing up compounding periods. 3. Using SI formula for compounding scenario. |
Always label each variable. |
3. Worked Example
Example 1 – Simple Interest
Problem:
Invest ₹12,000 at an annual simple interest rate of 7 % for 3 years.
What is the maturity value?
Solution:
- Convert rate: ( r = 7% = 0.07 )
- Compute interest:
[ I = P \times r \times t = 12{,}000 \times 0.07 \times 3 = 2{,}520 ] - Maturity value:
[ M = P + I = 12{,}000 + 2{,}520 = 14{,}520 ]
Answer: ₹14,520
Example 2 – Compound Interest
Problem:
Deposit ₹15,000 in a bank account that pays 6 % annual interest compounded quarterly for 4 years.
What will be the balance at the end of the period?
Solution:
- Convert rate: ( r = 6% = 0.06 )
- Compounding frequency: ( n = 4 )
- Time: ( t = 4 ) years
- Apply CI formula:
[ A = P \left(1 + \frac{r}{n}\right)^{nt} = 15{,}000 \left(1 + \frac{0.06}{4}\right)^{4 \times 4} ]
[ A = 15{,}000 \left(1 + 0.015\right)^{16} = 15{,}000 \