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SSC CGL Preparation – Day 11
Quantitative Aptitude: Simple Interest and Compound Interest
1. Introduction
Simple Interest (SI) and Compound Interest (CI) are basic concepts in the Quantitative Aptitude section, commonly asked in banking and SSC exams. You’ll often be required to find the interest, principal, rate, or time.
2. Important Terminologies
- Principal (P): The amount of money invested or borrowed.
- Rate (R): The rate of interest per annum (%).
- Time (T): Time in years.
- Amount (A): Total sum after interest = P + Interest
3. Simple Interest (SI)
Formula: $$\text{SI} = \frac{P \times R \times T}{100}$$
- Linear increase – same interest every year.
- Total Amount after T years:
$$A = P + SI = P\left(1 + \frac{R \times T}{100}\right)$$
4. Compound Interest (CI)
Compound interest is calculated on the principal + previously accrued interest.
Formula when compounded annually: $$A = P\left(1 + \frac{R}{100}\right)^T$$
$$CI=A−P$$
Formula when compounded half-yearly: $$A = P\left(1 + \frac{R}{2 \times 100}\right)^{2T}$$
Formula when compounded quarterly: $$A = P\left(1 + \frac{R}{4 \times 100}\right)^{4T}$$
5. Difference between CI and SI
$$\text{CI – SI (for 2 years)} = P \left(\frac{R}{100}\right)^2$$
This shortcut is useful for comparing both interests over 2 years.
6. Shortcut Tricks
- Double CI in 2 years? $$P = A / \left(1 + \frac{R}{100}\right)^2$$
- CI for 2 years: $$\text{CI} = SI + \frac{SI \times R}{100}$$
7. Examples
Example 1 (SI):
Find the SI on ₹2000 at 5% per annum for 3 years. $$SI = \frac{2000 \times 5 \times 3}{100} = ₹300$$
Example 2 (CI):
Find the CI on ₹1000 at 10% per annum for 2 years. $$A = 1000 \left(1 + \frac{10}{100}\right)^2 = 1000 × 1.21 = ₹1210 $$ $$CI = 1210 − 1000 = ₹210$$
Example 3 (Difference between SI and CI):
Find the difference between SI and CI on ₹1200 at 10% for 2 years. $$\text{Difference} = \frac{P \times R^2}{100^2} = \frac{1200 \times 10^2}{100^2} = ₹12$$
Example 4 (Half-yearly):
Find the CI on ₹1600 at 10% per annum compounded half-yearly for 1 year. $$A = 1600 \left(1 + \frac{10}{2 \times 100}\right)^{2} = 1600 × \left(1.05\right)^2 = ₹1764$$ $$CI = 1764 − 1600 = ₹164$$
8. Practice MCQs
Q1. Find the simple interest on ₹3000 at 6% for 2 years.
A) ₹360
B) ₹300
C) ₹390
D) ₹280
✅ Answer: ₹360
Q2. What will be the compound interest on ₹5000 at 10% p.a. for 2 years?
A) ₹1000
B) ₹1050
C) ₹1100
D) ₹1025
✅ Answer: ₹1050
Q3. In how many years will ₹1000 amount to ₹1200 at 10% SI?
A) 1 year
B) 2 years
C) 3 years
D) 4 years
✅ Answer: 2 years
Q4. Find the difference between CI and SI on ₹4000 at 5% for 2 years.
A) ₹10
B) ₹20
C) ₹15
D) ₹25
✅ Answer: ₹10
Q5. The CI on a certain amount for 2 years at 8% is ₹520. What is the principal?
A) ₹3000
B) ₹3200
C) ₹2500
D) ₹2800
✅ Answer: ₹2500
9. Tips for SSC CGL
Expect direct formula-based questions or CI-SI difference problems.
Memorize all basic formulas.
CI is always more than SI (except when time = 1 year).
Focus on speed using shortcuts.
