Interest That Earns Interest Beats Interest That Does Not
Learn to calculate percentage increase and decrease, work out profit, loss and discount, add tax to a price, and find the amount and compound interest on a principal.
Why does compound interest beat simple interest on the same money?
Because the interest earned is added to the principal, so the next year's interest is calculated on a larger sum. On ₹10000 at for two years, simple interest gives ₹2000 while compound interest gives ₹2100.
The extra ₹100 is the interest on the first year's interest. This page covers everything in the CBSE Class 8 Mathematics chapter's second part: percentage increase and decrease, profit and loss, discount, tax, and compound interest.
The extra ₹100 is the interest on the first year's interest. This page covers everything in the CBSE Class 8 Mathematics chapter's second part: percentage increase and decrease, profit and loss, discount, tax, and compound interest.
How do you calculate percentage increase and decrease?
Both are worked out as a percentage of the original value:
Increase. A price rises from ₹250 to ₹300. The change is ₹50, so
Decrease. A quantity falls from to . The change is , so
Another increase. A salary rises from ₹18000 to ₹19800:
Applying a change. A ₹1500 item increased by becomes
and decreased by becomes .
The base must be the original value, never the new one, and that is what makes equal-looking changes unequal. Rising from 250 to 300 is a increase, but falling back from 300 to 250 is
The same ₹50, two different percentages — because the base changed.
Increase. A price rises from ₹250 to ₹300. The change is ₹50, so
Decrease. A quantity falls from to . The change is , so
Another increase. A salary rises from ₹18000 to ₹19800:
Applying a change. A ₹1500 item increased by becomes
and decreased by becomes .
The base must be the original value, never the new one, and that is what makes equal-looking changes unequal. Rising from 250 to 300 is a increase, but falling back from 300 to 250 is
The same ₹50, two different percentages — because the base changed.
How do you calculate profit, loss and discount?
Profit and loss percentages are always taken on the cost price; discount is always taken on the marked price.
Worked example, profit. An article bought for ₹800 is sold for ₹920:
Worked example, loss. Bought for ₹500 and sold for ₹450:
Finding the selling price. An article costing ₹600 sold at profit:
Finding the cost price. Sold for ₹960 at profit:
Discount. The marked price is the printed price; discount is a reduction on it:
A shirt marked ₹1200 with a discount:
If the shopkeeper's cost price was ₹850, the profit is , which is of ₹850.
The two percentages use different bases, and that is how a discounted sale stays profitable. Here the discount was on ₹1200 and the profit on ₹850 — so the figures are not comparable, and a sale can offer a genuine reduction while still earning.
Worked example, profit. An article bought for ₹800 is sold for ₹920:
Worked example, loss. Bought for ₹500 and sold for ₹450:
Finding the selling price. An article costing ₹600 sold at profit:
Finding the cost price. Sold for ₹960 at profit:
Discount. The marked price is the printed price; discount is a reduction on it:
A shirt marked ₹1200 with a discount:
If the shopkeeper's cost price was ₹850, the profit is , which is of ₹850.
The two percentages use different bases, and that is how a discounted sale stays profitable. Here the discount was on ₹1200 and the profit on ₹850 — so the figures are not comparable, and a sale can offer a genuine reduction while still earning.
How do you calculate the tax on a price?
Tax is a percentage added on top of the price, so the customer pays more than the marked amount.
or in one step:
Worked example. An article priced ₹2000 with tax at :
In one step: .
Worked example. A meal costing ₹800 with tax at :
Worked example. Stationery priced ₹450 with tax at :
Working backwards from the final amount. A customer pays ₹2360 including tax. The price before tax was
Tax after a discount. An item marked ₹1000 gets a discount, then tax. The discounted price is ₹900, and the tax is of ₹900, not of ₹1000:
That order matters, and it is the detail examiners test. Tax is charged on the discounted price, because that is what the customer is actually paying — applying the tax to the marked price first would overcharge them.
or in one step:
Worked example. An article priced ₹2000 with tax at :
In one step: .
Worked example. A meal costing ₹800 with tax at :
Worked example. Stationery priced ₹450 with tax at :
Working backwards from the final amount. A customer pays ₹2360 including tax. The price before tax was
Tax after a discount. An item marked ₹1000 gets a discount, then tax. The discounted price is ₹900, and the tax is of ₹900, not of ₹1000:
That order matters, and it is the detail examiners test. Tax is charged on the discounted price, because that is what the customer is actually paying — applying the tax to the marked price first would overcharge them.
Formula
How do you calculate compound interest?
In compound interest the interest earned each period is added to the principal, so the next period earns interest on the larger sum.
where is the principal, the rate percent per period, the number of periods and the amount.
Worked example. ₹10000 at per annum for years.
Checking year by year, which is how the formula is built:
- Year 1 interest of , so the amount becomes ₹11000
- Year 2 interest of ₹11000 , so the amount becomes ₹12100
Total interest . The same answer.
Comparing with simple interest on the same money:
So compound interest earns ₹100 more, and that ₹100 is exactly of the first year's ₹1000 interest.
Worked example. ₹8000 at for years:
The difference between the two kinds of interest grows with time, and that is the idea to carry away. Simple interest adds the same amount every year, while compound interest adds more each year — so over one period they are identical, and the gap widens from the second period onward.
where is the principal, the rate percent per period, the number of periods and the amount.
Worked example. ₹10000 at per annum for years.
Checking year by year, which is how the formula is built:
- Year 1 interest of , so the amount becomes ₹11000
- Year 2 interest of ₹11000 , so the amount becomes ₹12100
Total interest . The same answer.
Comparing with simple interest on the same money:
So compound interest earns ₹100 more, and that ₹100 is exactly of the first year's ₹1000 interest.
Worked example. ₹8000 at for years:
The difference between the two kinds of interest grows with time, and that is the idea to carry away. Simple interest adds the same amount every year, while compound interest adds more each year — so over one period they are identical, and the gap widens from the second period onward.
Exam tip
Exam tip: identifying the base of every percentage
This chapter stacks several percentages, and each has its own base. Label them.
Write it down: profit percent on the cost price, discount percent on the marked price, tax on the discounted price, percentage change on the original value. Mixing these is the biggest source of lost marks.
For percentage change, divide by the original value — so a rise from 250 to 300 is but the fall back is .
To find a cost price from a selling price, **multiply by — never subtract the percentage from the selling price.
For compound interest, write the formula first, then substitute, and remember the question may want CI rather than the amount** — subtract if so.
And verify compound interest year by year for two periods; it takes two lines and confirms the power was applied correctly.
Write it down: profit percent on the cost price, discount percent on the marked price, tax on the discounted price, percentage change on the original value. Mixing these is the biggest source of lost marks.
For percentage change, divide by the original value — so a rise from 250 to 300 is but the fall back is .
To find a cost price from a selling price, **multiply by — never subtract the percentage from the selling price.
For compound interest, write the formula first, then substitute, and remember the question may want CI rather than the amount** — subtract if so.
And verify compound interest year by year for two periods; it takes two lines and confirms the power was applied correctly.
Did you know
Why does compound interest pull ahead only after the first year?
Because in the first period there is no earlier interest for it to work on.
On ₹10000 at , both kinds give exactly ₹1000 in year one — the principal is the same, so the interest is the same. The difference appears in year two, when compound interest charges on ₹11000 rather than on ₹10000, giving ₹1100 instead of ₹1000.
That ₹100 gap is interest on interest, and it grows every year because the base keeps expanding. Over one period the two are identical, which is why the comparison only becomes interesting from the second period onward.
On ₹10000 at , both kinds give exactly ₹1000 in year one — the principal is the same, so the interest is the same. The difference appears in year two, when compound interest charges on ₹11000 rather than on ₹10000, giving ₹1100 instead of ₹1000.
That ₹100 gap is interest on interest, and it grows every year because the base keeps expanding. Over one period the two are identical, which is why the comparison only becomes interesting from the second period onward.
Key takeaways
Percentage applications: quick revision
- — always on the original value, so 250 to 300 is a rise while 300 to 250 is a fall.
- Profit and loss percent are on the cost price: CP ₹800 and SP ₹920 gives profit.
- , and — never subtract the percentage from the SP.
- Discount is on the marked price: ₹1200 less gives ₹1020, which can still be a profit on a CP of ₹850.
- Tax is added on, and charged on the discounted price: ₹2000 plus is ₹2360.
- and — so ₹10000 at for 2 years gives ₹12100 and CI of ₹2100, which is ₹100 more than simple interest.
You will remember all of this far better after answering five questions on it than after reading it twice.
- Profit and loss percent are on the cost price: CP ₹800 and SP ₹920 gives profit.
- , and — never subtract the percentage from the SP.
- Discount is on the marked price: ₹1200 less gives ₹1020, which can still be a profit on a CP of ₹850.
- Tax is added on, and charged on the discounted price: ₹2000 plus is ₹2360.
- and — so ₹10000 at for 2 years gives ₹12100 and CI of ₹2100, which is ₹100 more than simple interest.
You will remember all of this far better after answering five questions on it than after reading it twice.