ssc gd compound interest

• What is Compound Interest? The Basics
• Understanding the Compound Interest Formula (Yearly)
• Simple Interest vs. Compound Interest: The Key Difference

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What is Compound Interest? The Basics

Welcome! We are going to learn about compound interest ssc gd. This is a very important topic for your exam. Think of compound interest as getting “extra money on your extra money.”

Simple Theory of Compound Interest

• When you put money in a bank, the bank gives you a little extra money back. This extra money is called Interest.
• In Simple Interest (SI), you only get extra money on the first amount you put in.
• In Compound Interest (CI), you get extra money on the first amount plus the extra money you earned last time.
• This means your money grows much faster! This is why understanding compound interest ssc gd questio is crucial.
• For SSC GD exams, we usually calculate this extra money once every year (Yearly Compounding).

Key Terms to Remember

4 Solved Examples: Step-by-Step Calculation

These ssc gd compound interest questions show the basic idea without using the main formula yet.

Example 1: Finding CI for 2 Years

P = ₹100, R = 10% per year, T = 2 years. Find the Compound Interest.

Solution:

1. First, let’s find the extra money for Year 1.

   • The starting money (P) is ₹100.
   • Extra money (Interest) = $\text{Math input error}$.
   • Money at the end of Year 1 = $\text{Math input error}$.

2. Now, let’s find the extra money for Year 2.

   • The new starting money for Year 2 is ₹110 (the interest from Year 1 is added!).
   • Extra money (Interest) = $\text{Math input error}$.

3. Calculate the Total Compound Interest (CI).

   • CI = Interest from Year 1 + Interest from Year 2
   • CI = $\text{Math input error}$.

4. So, the answer is ₹21.

Example 2: CI Calculation with a Higher Rate

A person invests ₹200 for 2 years at 5% Compound Interest. What is the total Amount?

Solution:

1. Find the interest for Year 1.

   • P = ₹200. R = 5%.
   • Interest Year 1 = $\text{Math input error}$.
   • New Principal for Year 2 = $\text{Math input error}$.

2. Find the interest for Year 2.

   • Interest Year 2 = $\text{Math input error}$.

3. Calculate the Total Amount (A).

   • Amount (A) = Principal + Total CI
   • Total CI = $\text{Math input error}$.
   • A = $\text{Math input error}$.

4. The total Amount is ₹220.50. These types of ssc gd compound interest questions pdfn are common.

Example 3: Finding CI for 3 Years (Basic)

P = ₹1000, R = 10%, T = 3 years. Find the CI.

Solution:

1. Year 1:

   • Interest = $\text{Math input error}$.
   • New Principal = $\text{Math input error}$.

2. Year 2:

   • Interest = $\text{Math input error}$.
   • New Principal = $\text{Math input error}$.

3. Year 3:

   • Interest = $\text{Math input error}$.

4. Total CI:

   • CI = $\text{Math input error}$.
   • The compound interest ssc gd answer is ₹331.

Example 4: Calculating the Principal after 1 Year

If the CI earned on a sum is ₹50 in the first year at 5%, what was the Principal? (Yearly compounding)

Solution:

1. Understand the rule: In the first year, CI is the same as Simple Interest (because no previous interest has been added yet).
2. Write down what we know: Interest (I) = ₹50. Rate (R) = 5%. Time (T) = 1 year. We need to find P.
3. Use the simple interest formula for Year 1: $I=\frac{P\times R\times T}{100}$.
   • $50=\frac{P\times 5\times 1}{100}$.
4. Solve for P:
   • $50\times 100=P\times 5$.
   • $5000=5P$.
   • $\text{Math input error}$.
5. The Principal was ₹1000. This helps us solve complex compound interest ssc gd questio.

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Understanding the Compound Interest Formula (Yearly)

Calculating CI year-by-year takes too long, especially for 5 or 10 years. We use a special formula for the compound interest ssc gd exam.

The Formula Explained

The main formula helps us find the final Amount (A) directly.

$$A=P{(1+\frac{R}{100})}^T$$

• $A$: The final Amount (Principal + Interest).
• $P$: The starting Principal (Money).
• $R$: The Rate (in percent).
• $T$: The Time (in years).

Once you find A, you find the Compound Interest (CI) using this simple step:

$$CI=A-P$$

4 Solved Examples: Using the Formula

These are standard ssc gd compound interest questions that require the formula.

Example 5: Direct Formula Application

Calculate the Amount for ₹5000 at 4% per annum for 2 years, compounded yearly.

Solution:

1. Identify the values:

   • $P=5000$.
   • $R=4$.
   • $T=2$.

2. Write the formula and substitute the numbers:

   • $A=P{(1+\frac{R}{100})}^T$
   • $A=5000{(1+\frac{4}{100})}^2$

3. Simplify the fraction inside the bracket:

   • $1+\frac{4}{100}=1+0.04=1.04$.
   • $A=5000(1.04{)}^2$.

4. Calculate the power:

   • $(1.04{)}^2=1.04\times 1.04=1.0816$.
   • $A=5000\times 1.0816$.

5. Final Calculation:

   • $\text{Math input error}$.
   • The Amount is ₹5408. This is a typical compound interest ssc gd questio.

Example 6: Finding CI using the Formula

Find the Compound Interest on ₹10,000 for 3 years at 10% per annum.

Solution:

1. Identify the values: $P=10000$, $R=10$, $T=3$.

2. Calculate the Amount (A):

   • $A=10000{(1+\frac{10}{100})}^3$
   • $A=10000(1+0.1{)}^3$
   • $A=10000(1.1{)}^3$

3. Calculate the power:

   • $(1.1{)}^3=1.1\times 1.1\times 1.1=1.331$.
   • $\text{Math input error}$.

4. Calculate the Compound Interest (CI):

   • $CI=A-P$
   • $\text{Math input error}$.

5. The Compound Interest is ₹3310. Practice these ssc gd compound interest questions pdfn often.

Example 7: Calculation with a Lower Principal

What is the CI earned on ₹800 at 5% for 2 years?

Solution:

1. Set up the Amount calculation:

   • $A=800{(1+\frac{5}{100})}^2$
   • $A=800(1.05{)}^2$

2. Calculate the power:

   • $(1.05{)}^2=1.1025$.
   • $A=800\times 1.1025$.

3. Find the Amount:

   • $\text{Math input error}$.

4. Find the CI:

   • $CI=A-P$
   • $\text{Math input error}$.
   • The compound interest ssc gd is ₹82.

Example 8: Finding the Time Period

A sum of ₹100 becomes ₹121 at 10% CI per annum. How many years did it take?

Solution:

1. Identify the knowns: $P=100$, $A=121$, $R=10$. We need to find $T$.

2. Put the numbers in the formula:

   • $A=P{(1+\frac{R}{100})}^T$
   • $121=100{(1+\frac{10}{100})}^T$

3. Simplify the bracket and divide by P:

   • $\frac{121}{100}=(1.1{)}^T$
   • $1.21=(1.1{)}^T$

4. Find the power (T): We know that $1.1\times 1.1=1.21$.

   • So, $1.21=(1.1{)}^2$.
   • This means $T=2$.

5. It took 2 years. This is a tricky ssc gd compound interest questions type.

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Simple Interest vs. Compound Interest: The Key Difference

For your ssc gd compound interest questions, you must know the difference between SI and CI.

Theory: Why CI is Better

• Simple Interest (SI): The interest is calculated only on the original Principal (P) every year. It stays the same amount every year.
• Compound Interest (CI): The interest is calculated on the Principal plus the accumulated interest from previous years. It increases every year.
• The Difference: The difference between CI and SI is always zero for the first year. The difference starts growing from the second year onwards.

Shortcut Formula for CI – SI (2 Years)

This shortcut is very useful for compound interest ssc gd exams:

$$\text{Difference (D)}=P{\left(\frac{R}{100}\right)}^2$$

4 Solved Examples: Finding the Difference

Example 9: Finding the Difference (2 Years)

Find the difference between CI and SI on ₹2000 at 5% per annum for 2 years.

Solution:

1. Identify the values: $P=2000$, $R=5$, $T=2$.

2. Use the 2-year difference formula:

   • $D=P{\left(\frac{R}{100}\right)}^2$
   • $D=2000{\left(\frac{5}{100}\right)}^2$

3. Simplify the fraction:

   • $\frac{5}{100}=0.05$.
   • $D=2000(0.05{)}^2$

4. Calculate the square:

   • $(0.05{)}^2=0.0025$.
   • $D=2000\times 0.0025$.

5. Final Calculation:

   • $\text{Math input error}$.
   • The difference between CI and SI is ₹5. This is a common ssc gd compound interest questions pdfn type.

Example 10: Finding the Principal when Difference is Known

The difference between CI and SI for 2 years at 10% is ₹20. Find the Principal (P).

Solution:

1. Identify the knowns: $D=20$, $R=10$, $T=2$. We need $P$.

2. Use the difference formula and substitute:

   • $D=P{\left(\frac{R}{100}\right)}^2$
   • $20=P{\left(\frac{10}{100}\right)}^2$

3. Simplify the bracket:

   • $\frac{10}{100}=\frac{1}{10}$.
   • $20=P{\left(\frac{1}{10}\right)}^2$

4. Calculate the square:

   • $20=P\times \frac{1}{100}$.

5. Solve for P:

   • $\text{Math input error}$.
   • The Principal is ₹2000. This is a tricky compound interest ssc gd questio.

Example 11: Calculating SI and CI Separately to Find Difference

P = ₹1000, R = 5%, T = 2 years. Calculate the difference (D) without using the shortcut formula.

Solution:

1. Calculate Simple Interest (SI):

   • $SI=\frac{P\times R\times T}{100}$
   • $\text{Math input error}$.

2. Calculate Compound Interest (CI):

   • $A=1000{(1+\frac{5}{100})}^2=1000(1.05{)}^2$
   • $\text{Math input error}$.
   • $\text{Math input error}$.

3. Find the Difference (D):

   • $D=CI-SI$
   • $\text{Math input error}$.

4. The difference is ₹2.50. This confirms the logic for compound interest ssc gd.

Example 12: Finding the Rate

If the Principal is ₹4000 and the difference between CI and SI for 2 years is ₹10, what is the Rate (R)?

Solution:

1. Identify the knowns: $P=4000$, $D=10$, $T=2$. We need $R$.

2. Use the difference formula:

   • $D=P{\left(\frac{R}{100}\right)}^2$
   • $10=4000{\left(\frac{R}{100}\right)}^2$

3. Isolate the bracket: Divide 10 by 4000.

   • $\frac{10}{4000}={\left(\frac{R}{100}\right)}^2$
   • $\frac{1}{400}={\left(\frac{R}{100}\right)}^2$

4. Take the square root of both sides:

   • $\sqrt{\frac{1}{400}}=\frac{R}{100}$
   • $\frac{1}{20}=\frac{R}{100}$

5. Solve for R:

   • $R=\frac{100}{20}=5$.
   • The Rate is 5%. These ssc gd compound interest questions require careful algebra.