You keep Rs 10,000 in a bank at 15% a year. How much extra money do you earn in 2 years? The answer is Rs 3,000. That extra money is called simple interest.
This article gives the formula, the shortcuts, and five solved examples. Each example says why the method works.
- Simple interest: I = P × R × T ÷ 100.
- Amount: A = P + I.
- Principal: P = 100 × I ÷ (R × T).
- Rate: R = 100 × I ÷ (P × T).
- Time: T = 100 × I ÷ (P × R).
- Months: change them to years first.
- Becoming n times: T = 100 × (n − 1) ÷ R.
What is simple interest and how do you find it?
What is simple interest?
Interest is the extra money paid for using someone’s money. Banks pay it when you deposit. You pay it when you borrow.
In simple interest, the interest is always counted on the original sum.
Sources: NCERT Class 8 Maths: Comparing Quantities, simple interest worked example.
What do P, R and T stand for?
P is the principal, the sum lent or borrowed. R is the rate, in percent per year. T is the time, in years.
The amount is what you pay back in the end. It equals principal plus interest.
Sources: NCERT Class 8 Maths: Comparing Quantities, interest and amount.
Why do we divide by 100?
A rate of 15% means Rs 15 on every Rs 100 for one year.
So on Rs 10,000, one year gives 15 × 10000 ÷ 100 = Rs 1,500. The 100 comes from the word percent.
Sources: NCERT Class 8 Maths: Comparing Quantities, interest on 100 for one year; Practice question: interest on Rs 2000.
What is the amount after T years?
Add the interest to the principal. So A = P + I.
For Rs 2,000 at 9% for 4 years, I = 720. The amount is 2000 + 720 = Rs 2,720.
Which shortcuts make these problems quick?
How do you find the principal when interest is known?
Turn the formula around. P = 100 × I ÷ (R × T).
If I = 3850, R = 7 and T = 5, then P = 385000 ÷ 35 = Rs 11,000.
Sources: Practice question: finding the sum.
How do you find the rate?
Use R = 100 × I ÷ (P × T).
If P = 24500, I = 5880 and T = 2, then R = 588000 ÷ 49000 = 12%.
Sources: Practice question: finding the rate.
How do you find the time?
Use T = 100 × I ÷ (P × R).
If P = 4500, I = 1575 and R = 7, then T = 157500 ÷ 31500 = 5 years.
Sources: Practice question: finding the time.
How long does money take to become n times itself?
The interest must equal (n − 1) times the principal. So T = 100 × (n − 1) ÷ R.
At 5%, tripling needs 100 × 2 ÷ 5 = 40 years. The principal cancels out, so any sum works.
Sources: Practice question: tripling at 5%.
How do you use two amounts at two different times?
Subtract the two amounts. The gap is the interest for the gap in years.
If Rs 5,200 grows to Rs 6,000 between year 3 and year 5, two years earn Rs 800. So one year earns 400. The principal is 5200 − 3 × 400 = Rs 4,000.
How is simple interest different from compound interest?
In simple interest, the principal stays the same each year. In compound interest, each year’s interest joins the principal.
On Rs 100 at 10% for 3 years, simple interest is 30 and compound interest is 33.10.
Sources: NCERT Class 8 Maths: Comparing Quantities, simple versus compound interest.
Check 1
Simple interest on Rs 10,000 at 15% for 2 years is Rs 3,000.
Check 2
8 months should be written as 8 in the formula.
Check 3
At 10% simple interest, money triples in 20 years.
Check 4
The interest grows each year in simple interest.
How do you solve five typical problems step by step?
Example 1: Find the interest and amount on Rs 10,000 at 15% for 2 years.
Step 1. Interest for one year is 10000 × 15 ÷ 100 = Rs 1,500.
Step 2. For 2 years, I = 1500 × 2 = Rs 3,000.
Step 3. Amount = 10000 + 3000 = Rs 13,000.
Check. 13000 − 10000 = 3000, which matches the interest.
Why this works. Each year earns the same Rs 1,500. So two years earn twice that.
Sources: NCERT Class 8 Maths: Comparing Quantities, borrowing Rs 10,000 at 15%.
Example 2: Find the interest on Rs 7,200 at 5% for 3 years.
Step 1. Multiply: P × R × T = 7200 × 5 × 3 = 108000.
Step 2. Divide by 100: 108000 ÷ 100 = Rs 1,080.
Check. One year gives 360. Three years give 3 × 360 = 1080.
Why this works. 5% of 7200 is 360. That is the interest for one year.
Example 3: Rs 6,000 becomes Rs 7,200 in 4 years. Find the rate.
Step 1. Interest = 7200 − 6000 = Rs 1,200.
Step 2. R = 100 × 1200 ÷ (6000 × 4) = 120000 ÷ 24000.
Step 3. So R = 5% per year.
Check. 6000 × 5 × 4 ÷ 100 = 1200.
Why this works. Rate is interest per Rs 100 per year. We divide the interest by the principal and by the years.
Example 4: In how many years does Rs 3,500 earn Rs 1,120 at 8%?
Step 1. T = 100 × I ÷ (P × R).
Step 2. The top is 100 × 1120 = 112000. The bottom is 3500 × 8 = 28000.
Step 3. So T = 112000 ÷ 28000 = 4 years.
Check. 3500 × 8 × 4 ÷ 100 = 1120.
Why this works. Yearly interest is 3500 × 8 ÷ 100 = 280. We ask how many 280s make 1120.
Example 5: Find the interest on Rs 4,800 at 6% for 8 months.
Step 1. Change 8 months to years. 8 ÷ 12 = 2/3 year.
Step 2. I = 4800 × 6 × (2/3) ÷ 100.
Step 3. 4800 × 6 = 28800. Then 28800 × 2/3 = 19200. Then 19200 ÷ 100 = Rs 192.
Check. One year gives 288. Eight months is 2/3 of that, which is 192.
Why this works. The rate is per year. So the time must be in years too.
How do you avoid careless mistakes?
What habits keep answers right?
Write P, R and T first. Then check the units. Time must be in years.
Test your answer by putting it back in the formula. It should give the same interest.
Check 5
Interest on Rs 2,000 at 9% for 4 years is Rs 2,720.
Check 6
A sum earning Rs 400 a year, at 5%, is Rs 8,000.
Exam traps
Amount trap. Interest and amount are different. Amount is principal plus interest.
Months trap. Never put months in T. Divide by 12 first.
Percent trap. Rate is a percent, so divide by 100 once.
Compound trap. Simple interest does not grow on interest. The yearly sum is fixed.
Subtraction trap. For two amounts, the gap is interest for the gap in years only.
MCQ on Simple Interest
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