Class 10 · Mathematics and money
Simple and compound interest, and an EMI
A shop offers a ₹20,000 phone for "only ₹2,000 a month". How much would you really pay?
What you will learn: Calculate simple and compound interest and read an EMI offer critically.
Small test at the end: scroll down to the end of this page for five short questions that check what you have learnt. Tap an answer, then press Check answer. Go to the questions ↓
Jump to: Check yourself · For grown-ups · For teachers
Safety first
Made-up offers only.
Keep it safe:
- Use made-up offers. Do not sign up for, or share details with, any real loan or EMI offer.
You will need
- Paper and pencil
- A calculatorOptional.
Time: About 45 minutes.
The story
A shop sign says, "New phone! Only ₹2,000 a month!" Tanmay is already choosing a colour. Dadi asks, "For how many months? And what does it cost if you pay today?" In small letters the sign says ₹20,000. How much would he really pay?
The idea
Simple interest is worked out on the starting amount (principal) only: interest = P × r × t, where r is the yearly rate written as a decimal (10% is 0.10) and t the number of years. ₹10,000 × 0.10 × 2 = ₹2,000.
Compound interest adds each year's interest to the amount, so next year's interest is worked out on a bigger amount: A = P(1 + r)^t, with the interest added once a year.
So compound interest grows faster: interest is earned on earlier interest too. ₹10,000 at 10% for 2 years: simple ₹2,000; compound ₹2,100.
For an EMI (equal monthly instalment), multiply the instalment by the number of months to get the total paid. Compare it with the price.
Worked example
Checking the phone offer (made up)
- Price today: ₹20,000.
- Offer: ₹2,000 a month for 12 months.
- Total paid: 2,000 × 12 = ₹24,000.
- Extra cost: 24,000 − 20,000 = ₹4,000, a fifth of the price. This assumes no down payment, fees or final payment; any of these changes the total.
"Only ₹2,000 a month" means ₹24,000 in all: ₹4,000 more than paying today. That ₹4,000 is the extra cash you pay, not a yearly interest rate.
Try it
Simple interest.
Work out P × r × t for ₹10,000 at 10% for 1, 2 and 3 years.
Compound interest.
Each year, add 10% of the current amount.
Compare in a table.
Year by year, simple and compound side by side.
Check an EMI.
Instalment × months = total. Subtract the price to find the extra.
Write a verdict.
Is the offer worth it? What else would you ask the shop?
What you make (paper or offline)
Your interest comparison
A year-by-year table of simple and compound interest.
An EMI check with total cost and extra cost.
A verdict with one question to ask the seller.
Make it on paper. Keep it with you. Nothing to upload.
Check yourself
Five questions about what this page teaches. Choose an answer and press Check answer, or open "See the answer and why". Nothing is saved or sent: your choices stay on this screen and disappear when you leave or reload the page.
How do you want to answer? You choose, and you can change at any time.
See the answer and why
- A. ₹2,100 Not this one. That is compound interest for 2 years.
- B. ₹2,000 Correct. 10,000 × 0.10 × 2 = 2,000.
- C. ₹1,000 Not this one. That is one year only.
- D. ₹200 Not this one. That uses 1% instead of 10%.
See the answer and why
- A. ₹11,000 Not this one. That is after one year.
- B. ₹2,100 Not this one. That is the interest only, not the whole amount.
- C. ₹12,000 Not this one. That is the simple-interest amount.
- D. ₹12,100 Correct. 11,000 after one year, then 11,000 + 1,100 = 12,100.
See the answer and why
- A. Interest is added to the amount, so interest is earned on interest Correct. Each year starts from a bigger amount.
- B. The rate goes up every year Not this one. The rate stays the same: 10%.
- C. Banks add a bonus each year Not this one. There is no bonus. It is the adding of interest that does it.
- D. Simple interest is charged only in the first year Not this one. Simple interest is charged every year, on the starting amount.
See the answer and why
- A. ₹22,000 Not this one. Multiply 2,000 by 12.
- B. ₹20,000 Not this one. That is the price today, not the total of the instalments.
- C. ₹2,000 Not this one. That is one month.
- D. ₹24,000 Correct. 2,000 × 12 = 24,000.
See the answer and why
- A. ₹20,000 Not this one. That is the price, not the extra.
- B. Nothing, because each payment is small Not this one. Small payments still add up to more.
- C. ₹4,000 Correct. 24,000 − 20,000 = 4,000.
- D. ₹12,000 Not this one. 12 is the number of months.
Think back
Were you surprised by the extra cost?
When could borrowing be worth paying extra for?
Investigate further
- Work out compound interest for 5 years. How far ahead of simple interest is it?
- Look at a newspaper EMI advert. What information is missing?
For grown-upsTap a heading to open it. The safety notes are at the top of the page.
Before you start
- Talk about a real purchase decision, without sharing private figures if you prefer.
Questions that help
- "How much is that in total?"
- "Is it worth paying more to have it now?"
What's really going on
Understanding total cost protects young people from expensive borrowing.
Compound interest works for savers too: money left to grow earns interest on interest.
Other ways to do it
- Use savings in a piggy bank with a made-up 10% "family interest".
For teachersLearning aims, classroom ideas and what to look for.
Learning aims
- Calculate simple and compound interest.
- Evaluate an instalment offer by total cost.
Subject links
- Mathematics: percentages and growth.
- Social science: financial literacy.
These links are general. They have not been checked against a specific board syllabus.
In the classroom
- Groups compare made-up offers and present which is the best deal and why.
What to look for
- Compound interest built on the new amount each year.
- Total cost found from instalments.