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Simple and Compound Interest

Practice MCQs

None

Quantitative Aptitude Simple and Compound Interest Competitive Exams

Simple and Compound Interest is an important quantitative aptitude topic based on principal, rate of interest, time, amount, simple interest, compound interest, annual compounding, half-yearly compounding, and difference between SI and CI. These questions are commonly asked in banking exams, SSC, railway exams, entrance tests, and aptitude tests.

What are Simple and Compound Interest?

Interest is the extra money paid or earned for using money for a certain period. The original amount borrowed or invested is called the principal.

Simple Interest is calculated only on the original principal. Compound Interest is calculated on the principal plus accumulated interest. That is why compound interest grows faster than simple interest.

Quick idea: Simple Interest remains the same every year, while Compound Interest increases because interest is added back to the principal.
Term Meaning Example
Principal Original amount borrowed or invested ₹10,000
Rate Interest charged per year 10% per annum
Time Duration for which money is used 2 years
Amount Principal plus interest ₹12,000
Interest Extra money earned or paid ₹2,000

“In interest questions, first identify principal, rate, time, and whether the interest is simple or compound.”

Aptitude Tip
Key points
  • Principal is the original amount.
  • Simple Interest is calculated on principal only.
  • Compound Interest is calculated on growing amount.
  • Amount = Principal + Interest.
  • Rate is usually given per annum.
  • CI is greater than SI for the same principal, rate, and time.
principal rate time amount interest

Visual Understanding

These diagrams show how simple interest and compound interest grow differently over time.

Simple Interest Growth
Year 1 Year 2 Year 3 Year 4 Fixed increase every year
\[ SI=\frac{P \times R \times T}{100} \]

In Simple Interest, the interest for each year remains fixed.

Compound Interest Growth
Year 1 Year 2 Year 3 Year 4 Growth becomes faster
\[ A=P\left(1+\frac{R}{100}\right)^T \]

In Compound Interest, interest is added to principal and then earns more interest.

Principal, Interest and Amount
Principal P + Interest I Amount
\[ A=P+I \]

Amount is the final value after adding interest to the principal.

Simple Interest vs Compound Interest
SI CI Compound Interest grows faster than Simple Interest
\[ CI = A-P \]

For the same principal, rate, and time, compound interest is usually more than simple interest.

Important Formulas and Rules

Simple Interest
\[ SI=\frac{P \times R \times T}{100} \]

\(P\) is principal, \(R\) is rate, \(T\) is time.

Amount in SI
\[ A=P+SI \]

Final amount under simple interest.

Compound Amount
\[ A=P\left(1+\frac{R}{100}\right)^T \]

Used for annual compound interest.

Compound Interest
\[ CI=A-P \]

Compound interest is amount minus principal.

Find Principal
\[ P=\frac{SI \times 100}{R \times T} \]

Used when SI, rate, and time are known.

Find Rate
\[ R=\frac{SI \times 100}{P \times T} \]

Used when SI, principal, and time are known.

Find Time
\[ T=\frac{SI \times 100}{P \times R} \]

Used when SI, principal, and rate are known.

CI for 2 Years
\[ CI=P\left[\left(1+\frac{R}{100}\right)^2-1\right] \]

Useful for common two-year CI questions.

Half-Yearly Compounding
\[ A=P\left(1+\frac{R}{200}\right)^{2T} \]

Rate is halved and time is doubled.

Quarterly Compounding
\[ A=P\left(1+\frac{R}{400}\right)^{4T} \]

Rate is divided by 4 and time is multiplied by 4.

Difference for 2 Years
\[ CI-SI=P\left(\frac{R}{100}\right)^2 \]

Shortcut for two years only.

Amount Relation
\[ A=P+I \]

Works for both SI and CI.

Rule: In Simple Interest, interest is calculated on the original principal. In Compound Interest, interest is calculated on the updated amount after each period.

Common Types of Questions

Simple Interest

Find SI, principal, rate, time, or amount.

  • Find SI
  • Find principal
  • Find rate
  • Find time
Compound Interest

Find amount or CI using compounding formula.

  • Annual CI
  • Half-yearly CI
  • Quarterly CI
  • CI amount
Difference Between SI and CI

Compare interest values for the same principal, rate, and time.

  • Two-year difference
  • Three-year difference
  • Find rate
  • Find principal
Amount-Based Questions

Use final amount to find interest or principal.

  • Amount after years
  • Principal from amount
  • Growth comparison
  • Installment-style problems
Exam approach: Read carefully whether the question asks for interest or amount. Many mistakes happen because students calculate amount but mark interest, or vice versa.
Method Bank
Find Simple Interest

Use \(P\), \(R\), and \(T\).

\[ SI=\frac{P \times R \times T}{100} \]
Find Amount

Add interest to principal.

\[ A=P+I \]
Find Compound Amount

Use annual compounding formula.

\[ A=P\left(1+\frac{R}{100}\right)^T \]
Find CI from Amount

Subtract principal from compound amount.

\[ CI=A-P \]

Tip: For half-yearly compounding, use half the rate and twice the time.

Interest Solving Flow
Identify P,R,T SI or CI? Use Formula Find Answer Principal → Rate → Time → SI/CI formula
First identify the given values, then decide whether the question is based on SI or CI.
\[ A=P+I \]
\[ CI=A-P \]

Step-by-Step Solving Method

Step Simple Interest Compound Interest
Step 1 Identify principal, rate, and time. Identify principal, rate, time, and compounding period.
Step 2 Use \(SI=\frac{P\times R\times T}{100}\). Use \(A=P\left(1+\frac{R}{100}\right)^T\).
Step 3 Calculate simple interest. Calculate compound amount.
Step 4 Add SI to principal if amount is needed. Subtract principal from amount if CI is needed.
Step 5 Check whether answer should be interest or amount. Check annual, half-yearly, or quarterly compounding.
Important: In CI questions, always check whether compounding is yearly, half-yearly, or quarterly before applying the formula.

Solved Examples

Question Method Answer
Find the simple interest on ₹5,000 at 10% per annum for 2 years. Here \(P=5000\), \(R=10\), \(T=2\).
\[ SI=\frac{P \times R \times T}{100} \]
\[ SI=\frac{5000\times10\times2}{100}=1000 \]
₹1,000
Find the amount on ₹8,000 at 5% simple interest for 3 years. Simple Interest:
\[ SI=\frac{8000\times5\times3}{100}=1200 \]
Amount:
\[ A=8000+1200=9200 \]
₹9,200
Find the principal if SI is ₹1,200 at 8% per annum for 3 years.
\[ P=\frac{SI\times100}{R\times T} \]
\[ P=\frac{1200\times100}{8\times3}=5000 \]
₹5,000
Find the compound amount on ₹10,000 at 10% per annum for 2 years.
\[ A=P\left(1+\frac{R}{100}\right)^T \]
\[ A=10000\left(1+\frac{10}{100}\right)^2 \]
\[ A=10000(1.1)^2=12100 \]
₹12,100
Find the compound interest on ₹10,000 at 10% per annum for 2 years. Amount:
\[ A=12100 \]
Compound Interest:
\[ CI=A-P=12100-10000=2100 \]
₹2,100
Find the difference between CI and SI on ₹10,000 at 10% for 2 years. Shortcut:
\[ CI-SI=P\left(\frac{R}{100}\right)^2 \]
\[ CI-SI=10000\left(\frac{10}{100}\right)^2=100 \]
₹100
Find the amount on ₹4,000 at 10% per annum compounded half-yearly for 1 year. Half-yearly: rate \(=5\%\), periods \(=2\).
\[ A=4000\left(1+\frac{5}{100}\right)^2 \]
\[ A=4000(1.05)^2=4410 \]
₹4,410
At what rate will ₹6,000 give ₹900 SI in 3 years?
\[ R=\frac{SI\times100}{P\times T} \]
\[ R=\frac{900\times100}{6000\times3}=5 \]
5% per annum

Note: If the question asks for amount, include principal. If it asks for interest, do not include principal.

Common Traps and Shortcuts

Common Traps
  • Confusing interest with amount.
  • Using CI formula when the question asks for SI.
  • Forgetting to subtract principal from amount to get CI.
  • Ignoring half-yearly or quarterly compounding.
  • Using rate as a decimal incorrectly.
  • Taking time in months without converting to years.
Useful Shortcuts
  • For SI, interest is same every year.
  • For CI, amount grows after each period.
  • For 2 years, \(CI-SI=P(R/100)^2\).
  • Half-yearly: halve rate and double time.
  • Quarterly: divide rate by 4 and multiply time by 4.
  • Always check whether final answer is amount or interest.
Exam approach: Write \(P\), \(R\), and \(T\) separately before calculation. This reduces mistakes in substitution.

Practice

A) Multiple Choice Questions
  1. Find SI on ₹4,000 at 10% per annum for 2 years.
    ₹600 ₹700 ₹800 ₹900
  2. If principal is ₹5,000 and SI is ₹1,000, find amount.
    ₹4,000 ₹5,000 ₹6,000 ₹7,000
  3. Find compound amount on ₹1,000 at 10% per annum for 2 years.
    ₹1,100 ₹1,200 ₹1,210 ₹1,220
  4. Difference between CI and SI for 2 years on ₹10,000 at 10% is:
    ₹50 ₹100 ₹150 ₹200
  5. In half-yearly compounding, rate is:
    Doubled Halved Tripled Unchanged
B) Solve the Higher-Order Problems
  1. Find SI on ₹12,000 at 8% per annum for 3 years. (Hint: Use \(SI=\frac{PRT}{100}\).)
  2. Find the amount on ₹15,000 at 6% simple interest for 2 years. (Hint: Amount = Principal + SI.)
  3. Find CI on ₹8,000 at 10% per annum for 2 years. (Hint: First find amount, then subtract principal.)
  4. Find the difference between CI and SI on ₹20,000 at 5% for 2 years. (Hint: Use \(P(R/100)^2\).)
  5. Find the amount on ₹10,000 at 8% per annum compounded half-yearly for 1 year. (Hint: Use 4% for 2 half-years.)
C) Match the Concept with the Correct Meaning
Concept Correct Meaning
Principal Original amount invested or borrowed
Rate Interest percentage per year
Simple Interest Interest calculated only on principal
Compound Interest Interest calculated on principal plus previous interest
Amount Principal plus interest
Half-Yearly Compounding Interest is compounded twice in a year
Aptitude Reminder

Simple Interest is calculated on the original principal only. Compound Interest is calculated on the growing amount. Always check whether the question asks for interest or amount.

Task: Create five questions using SI, amount, CI, difference between CI and SI, and half-yearly compounding.

Show Suggested Answers
Multiple Choice
  1. ₹800
    \[ SI=\frac{4000\times10\times2}{100}=800 \]
  2. ₹6,000
    \[ A=P+SI=5000+1000=6000 \]
  3. ₹1,210
    \[ A=1000\left(1+\frac{10}{100}\right)^2=1210 \]
  4. ₹100
    \[ CI-SI=10000\left(\frac{10}{100}\right)^2=100 \]
  5. Halved
    In half-yearly compounding, the rate is halved and the number of periods is doubled.
Higher-Order Problems
  1. \(P=12000\), \(R=8\), \(T=3\).
    \[ SI=\frac{12000\times8\times3}{100}=2880 \]
    Answer = ₹2,880.
  2. \(P=15000\), \(R=6\), \(T=2\).
    \[ SI=\frac{15000\times6\times2}{100}=1800 \]
    \[ A=15000+1800=16800 \]
    Answer = ₹16,800.
  3. \(P=8000\), \(R=10\), \(T=2\).
    \[ A=8000\left(1+\frac{10}{100}\right)^2 \]
    \[ A=8000(1.21)=9680 \]
    \[ CI=9680-8000=1680 \]
    Answer = ₹1,680.
  4. Difference for 2 years:
    \[ CI-SI=P\left(\frac{R}{100}\right)^2 \]
    \[ CI-SI=20000\left(\frac{5}{100}\right)^2=50 \]
    Answer = ₹50.
  5. Half-yearly compounding: rate \(=4\%\), periods \(=2\).
    \[ A=10000\left(1+\frac{4}{100}\right)^2 \]
    \[ A=10000(1.04)^2=10816 \]
    Answer = ₹10,816.
Concept Matching
  1. Principal → Original amount invested or borrowed
  2. Rate → Interest percentage per year
  3. Simple Interest → Interest calculated only on principal
  4. Compound Interest → Interest calculated on principal plus previous interest
  5. Amount → Principal plus interest
  6. Half-Yearly Compounding → Interest is compounded twice in a year
Clue Explanation

SI grows linearly because it is calculated only on principal. CI grows faster because interest becomes part of the amount and earns further interest.

Exam tips
  • Always write \(P\), \(R\), and \(T\) first.
  • Check whether the question asks for SI, CI, or amount.
  • For CI, calculate amount first and then subtract principal.
  • For half-yearly compounding, rate is halved and time is doubled.
  • For quarterly compounding, rate is divided by 4 and time is multiplied by 4.
  • Use \(CI-SI=P(R/100)^2\) only for 2 years.
Practice MCQs