Simple Interest
When you borrow money from a bank or lend money to someone, extra money is charged or earned for using that money. This extra money is called interest. The simplest way to calculate this interest is called Simple Interest (SI).
In Simple Interest, the interest is calculated only on the original amount (the money you borrowed or deposited). The interest amount remains the same every year.
In Class 7 Mathematics (NCERT), Simple Interest is studied in the chapter Comparing Quantities. You will learn the formula for SI, how to find the principal, rate, time, and amount, and how to solve word problems involving money, loans, and savings.
What is Simple Interest?
Definition: Simple Interest (SI) is the interest calculated on the original principal for a given rate and time period.
Key terms:
- Principal (P): The original amount of money borrowed or deposited. This is the starting amount on which interest is calculated.
- Rate of Interest (R): The percentage of the principal charged or earned per year. Written as R% per annum (p.a.).
- Time (T): The duration for which the money is borrowed or deposited. Usually measured in years.
- Simple Interest (SI): The extra amount earned or paid, calculated using the formula.
- Amount (A): The total money at the end = Principal + Simple Interest.
Important:
- In simple interest, the interest earned each year is the same.
- Interest is always calculated on the original principal, not on the accumulated amount.
- "Per annum" or "p.a." means "per year."
Simple Interest Formula
Simple Interest Formula:
SI = (P × R × T) / 100
Where:
- SI = Simple Interest
- P = Principal (original amount)
- R = Rate of interest per annum (%)
- T = Time in years
Amount Formula:
Amount (A) = P + SI = P + (P × R × T)/100
To find other quantities:
- Principal: P = (SI × 100) / (R × T)
- Rate: R = (SI × 100) / (P × T)
- Time: T = (SI × 100) / (P × R)
Time conversion:
- If time is in months, convert to years: T = months / 12
- If time is in days, convert to years: T = days / 365
- 6 months = 1/2 year = 0.5 years
- 3 months = 1/4 year = 0.25 years
Derivation and Proof
Understanding the formula:
Why SI = PRT/100:
- If you deposit Rs 100 at 5% per annum, the interest for 1 year = 5% of 100 = Rs 5.
- For Rs 100 at R% per annum for 1 year: Interest = R% of 100 = R.
- For Rs P at R% per annum for 1 year: Interest = R% of P = P × R/100.
- For Rs P at R% per annum for T years: Interest = P × R/100 × T = PRT/100.
Why the interest is the same every year:
- Year 1: Interest on P = P × R/100
- Year 2: Interest is still on original P (not on P + interest) = P × R/100
- Year 3: Same again = P × R/100
- After T years: Total SI = T × (P × R/100) = PRT/100
Example to see the pattern:
- P = Rs 1000, R = 10%, T = 3 years
- Year 1 interest = 1000 × 10/100 = Rs 100
- Year 2 interest = Rs 100 (same, calculated on original Rs 1000)
- Year 3 interest = Rs 100
- Total SI = Rs 300 = 1000 × 10 × 3 / 100 ✓
Types and Properties
Types of Simple Interest problems:
1. Finding SI and Amount:
- Given P, R, T — find SI and then Amount.
- Most basic type of problem.
2. Finding Principal:
- Given SI (or Amount), R, T — find the original principal.
- Use P = (SI × 100)/(R × T).
3. Finding Rate of Interest:
- Given P, SI, T — find the rate.
- Use R = (SI × 100)/(P × T).
4. Finding Time:
- Given P, SI, R — find how long the money was kept.
- Use T = (SI × 100)/(P × R).
5. Time in months or days:
- Convert months to years (divide by 12) before using the formula.
6. Finding Amount when principal doubles/triples:
- If amount = 2P, then SI = P. Use this to find T or R.
Solved Examples
Example 1: Example 1: Finding SI and Amount
Problem: Find the Simple Interest and Amount on Rs 5,000 at 8% per annum for 3 years.
Solution:
Given:
- P = Rs 5,000
- R = 8% per annum
- T = 3 years
Using the formula:
- SI = (P × R × T)/100
- SI = (5000 × 8 × 3)/100
- SI = 120000/100
- SI = Rs 1,200
Amount:
- A = P + SI = 5000 + 1200 = Rs 6,200
Answer: SI = Rs 1,200. Amount = Rs 6,200.
Example 2: Example 2: Finding Principal
Problem: The Simple Interest on a certain sum for 4 years at 5% per annum is Rs 600. Find the principal.
Solution:
Given:
- SI = Rs 600
- R = 5%
- T = 4 years
Using the formula:
- P = (SI × 100)/(R × T)
- P = (600 × 100)/(5 × 4)
- P = 60000/20
- P = Rs 3,000
Verify: SI = (3000 × 5 × 4)/100 = 60000/100 = 600 ✓
Answer: The principal is Rs 3,000.
Example 3: Example 3: Finding Rate of Interest
Problem: Rs 8,000 amounts to Rs 10,400 in 3 years. Find the rate of interest.
Solution:
Given:
- P = Rs 8,000
- A = Rs 10,400
- T = 3 years
Step 1: Find SI:
- SI = A − P = 10400 − 8000 = Rs 2,400
Step 2: Find Rate:
- R = (SI × 100)/(P × T)
- R = (2400 × 100)/(8000 × 3)
- R = 240000/24000
- R = 10%
Answer: The rate of interest is 10% per annum.
Example 4: Example 4: Finding Time
Problem: At what time will Rs 4,000 earn Rs 960 as Simple Interest at 6% per annum?
Solution:
Given:
- P = Rs 4,000
- SI = Rs 960
- R = 6%
Using the formula:
- T = (SI × 100)/(P × R)
- T = (960 × 100)/(4000 × 6)
- T = 96000/24000
- T = 4 years
Answer: The time is 4 years.
Example 5: Example 5: Time in months
Problem: Find the SI on Rs 12,000 at 10% per annum for 9 months.
Solution:
Given:
- P = Rs 12,000
- R = 10%
- T = 9 months = 9/12 = 3/4 years
Using the formula:
- SI = (P × R × T)/100
- SI = (12000 × 10 × 3/4)/100
- SI = (12000 × 10 × 3)/(4 × 100)
- SI = 360000/400
- SI = Rs 900
Answer: The Simple Interest is Rs 900.
Example 6: Example 6: When amount doubles
Problem: In how many years will Rs 2,500 double itself at 10% per annum Simple Interest?
Solution:
Given:
- P = Rs 2,500
- A = 2P = Rs 5,000 (doubles)
- R = 10%
Step 1: Find SI:
- SI = A − P = 5000 − 2500 = Rs 2,500
Step 2: Find Time:
- T = (SI × 100)/(P × R)
- T = (2500 × 100)/(2500 × 10)
- T = 250000/25000
- T = 10 years
Answer: The sum will double in 10 years.
Example 7: Example 7: Comparing two investments
Problem: Ramesh deposits Rs 6,000 at 8% p.a. and Suresh deposits Rs 8,000 at 5% p.a., both for 2 years. Who earns more interest?
Solution:
Ramesh's SI:
- SI = (6000 × 8 × 2)/100 = 96000/100 = Rs 960
Suresh's SI:
- SI = (8000 × 5 × 2)/100 = 80000/100 = Rs 800
Compare:
- Rs 960 > Rs 800
Answer: Ramesh earns more interest (Rs 960 vs Rs 800), even though Suresh deposited more money. The higher rate made the difference.
Example 8: Example 8: SI on a loan
Problem: Meena borrows Rs 15,000 from a bank at 12% per annum for 2 years. How much does she have to pay back?
Solution:
Given:
- P = Rs 15,000
- R = 12%
- T = 2 years
Step 1: Find SI:
- SI = (15000 × 12 × 2)/100 = 360000/100 = Rs 3,600
Step 2: Find Amount to pay back:
- A = P + SI = 15000 + 3600 = Rs 18,600
Answer: Meena has to pay back Rs 18,600.
Example 9: Example 9: Mixed time period (years and months)
Problem: Find the SI on Rs 20,000 at 9% per annum for 2 years and 4 months.
Solution:
Given:
- P = Rs 20,000
- R = 9%
- T = 2 years 4 months = 2 + 4/12 = 2 + 1/3 = 7/3 years
Using the formula:
- SI = (P × R × T)/100
- SI = (20000 × 9 × 7/3)/100
- SI = (20000 × 9 × 7)/(3 × 100)
- SI = 1260000/300
- SI = Rs 4,200
Answer: The Simple Interest is Rs 4,200.
Example 10: Example 10: Finding the sum when amount and SI are related
Problem: A sum of money triples itself in 20 years at Simple Interest. Find the rate of interest.
Solution:
Given:
- A = 3P (triples)
- T = 20 years
Step 1: Find SI:
- SI = A − P = 3P − P = 2P
Step 2: Use the formula:
- SI = (P × R × T)/100
- 2P = (P × R × 20)/100
- 2 = 20R/100
- 2 = R/5
- R = 2 × 5 = 10%
Answer: The rate of interest is 10% per annum.
Real-World Applications
Real-world uses of Simple Interest:
- Bank deposits: When you deposit money in a savings account, the bank pays you interest. For short-term deposits, simple interest is often used.
- Loans: When you borrow money from a bank or friend, you pay back the principal plus interest. Many personal loans use simple interest calculation.
- Car and vehicle loans: Some vehicle loans calculate interest using the simple interest method.
- Government bonds: Some government savings bonds pay simple interest at a fixed rate.
- Instalment plans: When you buy something on instalments, the shopkeeper may charge simple interest on the remaining amount.
- Agriculture loans: Farmers often take short-term loans for seeds and fertilisers, calculated using simple interest.
- Everyday lending: When you lend money to a friend for a few months, simple interest is the easiest way to calculate the return.
Key Points to Remember
- Simple Interest formula: SI = (P × R × T)/100.
- Amount = Principal + Simple Interest.
- SI is calculated on the original principal only — it does not change each year.
- The interest earned is the same every year in Simple Interest.
- P = Principal, R = Rate (% per annum), T = Time (in years).
- Always convert time to years before using the formula (months ÷ 12, days ÷ 365).
- To find P: P = (SI × 100)/(R × T).
- To find R: R = (SI × 100)/(P × T).
- To find T: T = (SI × 100)/(P × R).
- If a sum doubles, then SI = P. If it triples, then SI = 2P.
Practice Problems
- Find the SI on Rs 7,500 at 6% per annum for 5 years.
- What amount will Rs 10,000 become in 3 years at 12% per annum SI?
- The SI on a certain sum for 2 years at 8% is Rs 1,280. Find the principal.
- At what rate will Rs 6,000 earn Rs 1,080 as SI in 3 years?
- In how many years will Rs 5,000 amount to Rs 6,500 at 10% per annum SI?
- Find the SI on Rs 18,000 for 1 year and 6 months at 10% per annum.
- A sum of money doubles in 8 years at SI. Find the rate of interest.
- Priya borrows Rs 25,000 at 9% per annum SI. How much does she pay back after 4 years?
Frequently Asked Questions
Q1. What is Simple Interest?
Simple Interest is the interest calculated on the original principal amount for a given time at a given rate. The formula is SI = (P × R × T)/100. The interest remains the same every year.
Q2. What is the difference between Simple Interest and Compound Interest?
In Simple Interest, interest is calculated only on the original principal. In Compound Interest, interest is calculated on the principal plus the interest already earned. So Compound Interest grows faster. SI is the same each year; CI increases each year.
Q3. What does 'per annum' mean?
'Per annum' (p.a.) means 'per year.' When we say 8% per annum, it means 8% interest is charged or earned for every year.
Q4. How do you convert months to years for the SI formula?
Divide the number of months by 12. For example, 6 months = 6/12 = 0.5 years. 9 months = 9/12 = 0.75 years. 18 months = 18/12 = 1.5 years.
Q5. What is the difference between Amount and Simple Interest?
Simple Interest is only the extra money earned or charged. Amount is the total = Principal + SI. If you deposit Rs 1000 and earn Rs 200 as SI, the Amount is Rs 1200.
Q6. Can the rate of interest be more than 100%?
Technically yes, but in practice, rates above 100% are very rare and usually indicate exploitative lending. Normal rates range from 4% to 20% per annum.
Q7. In how many years does a sum double at R% Simple Interest?
If a sum doubles, SI = P. Using SI = PRT/100: P = P × R × T/100, so T = 100/R. At 10%, T = 100/10 = 10 years. At 5%, T = 100/5 = 20 years.
Q8. Does the order of P, R, T matter in the formula?
No. Since multiplication can be done in any order, P × R × T = R × T × P = T × P × R. The result is the same regardless of the order.
Related Topics
- Compound Interest
- Profit and Loss
- Introduction to Percentage
- Discount Calculation
- Percentage Increase and Decrease
- Applications of Compound Interest
- Sales Tax and VAT
- Growth and Decay
- Finding Percentage of a Number
- Converting Between %, Fraction and Decimal
- Word Problems on Comparing Quantities
- Word Problems on Profit and Loss
- Converting Percentage to Fraction
- Compound Interest (Half-Yearly & Quarterly)
