Simple Interest Word Problems
Simple Interest (SI) is the interest calculated on the original principal only. Word problems on simple interest involve loans, deposits, and investments where you need to find SI, the principal, rate, time, or the total amount.
The formula is straightforward, but word problems require careful reading to identify which values are given and which need to be found.
What is Simple Interest Word Problems - Grade 7 Maths (Comparing Quantities)?
SI = (P × R × T) / 100
where:
- P = Principal (original amount)
- R = Rate of interest per year (%)
- T = Time in years
- Amount (A) = P + SI
Simple Interest Word Problems Formula
Rearranged formulas:
- P = (SI × 100) / (R × T)
- R = (SI × 100) / (P × T)
- T = (SI × 100) / (P × R)
Types and Properties
Common problem types:
- Find SI when P, R, T are given.
- Find the total amount (A = P + SI).
- Find P when SI, R, T are given.
- Find R or T from given information.
- Compare two investment options.
Solved Examples
Example 1: Finding SI and Amount
Problem: Find the SI and amount on ₹5,000 at 8% per annum for 3 years.
Solution:
- SI = (5000 × 8 × 3)/100 = ₹1,200
- Amount = 5000 + 1200 = ₹6,200
Answer: SI = ₹1,200, Amount = ₹6,200.
Example 2: Finding Principal
Problem: SI on a sum for 2 years at 10% per annum is ₹600. Find the principal.
Solution:
- P = (SI × 100)/(R × T) = (600 × 100)/(10 × 2) = 60000/20 = ₹3,000
Answer: P = ₹3,000.
Example 3: Finding Rate
Problem: ₹4,000 becomes ₹5,200 in 4 years. Find the rate.
Solution:
- SI = 5200 − 4000 = ₹1,200
- R = (1200 × 100)/(4000 × 4) = 120000/16000 = 7.5%
Answer: Rate = 7.5% per annum.
Example 4: Finding Time
Problem: In how many years will ₹2,500 earn ₹750 at 6% per annum?
Solution:
- T = (SI × 100)/(P × R) = (750 × 100)/(2500 × 6) = 75000/15000 = 5 years
Answer: 5 years.
Real-World Applications
Real-world uses:
- Bank deposits: Calculating interest earned on fixed deposits.
- Loans: Calculating interest on education, car, or personal loans.
- Investments: Comparing returns from different schemes.
Key Points to Remember
- SI = (P × R × T) / 100.
- Amount = Principal + SI.
- SI is always calculated on the original principal, not on accumulated amount.
- Time must be in years. Convert months to years if needed (6 months = 0.5 year).
- If time is in months: T = months/12.
Practice Problems
- Find SI on ₹8,000 at 12% for 2 years.
- Find the amount when P = ₹12,000, R = 9%, T = 3 years.
- SI = ₹1,500, R = 10%, T = 5 years. Find P.
- In how many years will ₹6,000 double at 10% per annum simple interest?
Frequently Asked Questions
Q1. What is simple interest?
Simple interest is interest calculated only on the original principal amount. SI = (P × R × T)/100.
Q2. What is the difference between SI and compound interest?
SI is calculated on the original principal only. Compound interest is calculated on the principal plus accumulated interest. SI is always less than or equal to CI for the same P, R, T (when T > 1).
Q3. How do you convert months to years for the formula?
Divide months by 12. For example, 9 months = 9/12 = 3/4 year = 0.75 year.
Related Topics
- Simple Interest
- Compound Interest
- Introduction to Percentage
- Profit and Loss
- Percentage Increase and Decrease
- Discount Calculation
- 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
