Class 8 — Mathematics (NCERT)

Comparing Quantities: Discount, Tax and Compound Interest

Class 8

✓By the end of this lesson students will be able to understand and calculate discount and discount percentage.
✓By the end of this lesson students will be able to calculate the final price of an item after applying discount or adding tax (GST).
✓By the end of this lesson students will be able to differentiate between Simple Interest and Compound Interest.
✓By the end of this lesson students will be able to calculate Compound Interest and the amount when interest is compounded annually.
✓By the end of this lesson students will be able to solve real-life problems involving discount, tax, and compound interest.

Key concepts

Discount

Discount is a reduction given on the Marked Price (M.P.) of an article. It is offered to attract customers or to clear old stock. The customer has to pay the Selling Price (S.P.) after the discount. Discount is always calculated on the Marked Price.

Discount = Marked Price - Selling Price\nDiscount % = (Discount / Marked Price) × 100

Sales Tax / Goods and Services Tax (GST)

Sales Tax or Goods and Services Tax (GST) is a tax charged by the government on the sale of an article. It is added to the Selling Price (S.P.) of the article. The customer has to pay the S.P. plus the tax amount. GST is a uniform tax system implemented across India.

Tax Amount = (Tax Rate / 100) × Selling Price\nFinal Price = Selling Price + Tax Amount

Compound Interest (C.I.)

Compound Interest is the interest calculated on the principal amount as well as on the interest accumulated from previous periods. In simple interest, the principal remains the same throughout the loan period, but in compound interest, the principal changes at the end of each interest period. The interest earned in the first period is added to the principal to become the new principal for the second period, and so on.

Amount (A) = P(1 + R/100)^n\nCompound Interest (C.I.) = A - P\nWhere:\nP = Principal\nR = Rate of Interest per annum\nn = Time period in years (when compounded annually)

Key facts to remember

1Discount is always calculated on the Marked Price (M.P.).
2Selling Price (S.P.) = Marked Price - Discount.
3Tax (GST) is always calculated on the Selling Price (S.P.) of the item.
4Final Price = Selling Price + Tax Amount.
5Simple Interest (S.I.) = (P × R × T) / 100.
6Compound Interest (C.I.) involves interest on interest, leading to faster growth of money.
7The formula for Amount (A) under Compound Interest, compounded annually, is A = P(1 + R/100)^n.
8Compound Interest (C.I.) = Amount (A) - Principal (P).

Worked examples

Example 1

The Marked Price of a refrigerator is ₹18,000. A shopkeeper offers a discount of 15% on it. Find the Selling Price of the refrigerator.

IGiven: Marked Price (M.P.) = ₹18,000

IIDiscount % = 15%

IIIFirst, calculate the discount amount:

IVDiscount = 15% of M.P.

VDiscount = (15/100) × 18,000

VIDiscount = 15 × 180

VIIDiscount = ₹2,700

VIIINow, calculate the Selling Price (S.P.):

9S.P. = M.P. - Discount

10S.P. = 18,000 - 2,700

11S.P. = ₹15,300

Answer

The Selling Price of the refrigerator is ₹15,300.

Alternatively, S.P. = M.P. × (100 - Discount %)/100 = 18000 × (100-15)/100 = 18000 × 85/100 = ₹15,300.

Example 2

Rohan bought a pair of shoes for ₹1,200. If the GST charged is 18%, find the amount Rohan had to pay for the shoes.

IGiven: Selling Price (S.P.) of shoes = ₹1,200

IIGST Rate = 18%

IIIFirst, calculate the GST amount:

IVGST Amount = 18% of S.P.

VGST Amount = (18/100) × 1,200

VIGST Amount = 18 × 12

VIIGST Amount = ₹216

VIIINow, calculate the total amount Rohan had to pay:

9Total Amount = S.P. + GST Amount

10Total Amount = 1,200 + 216

11Total Amount = ₹1,416

Answer

Rohan had to pay ₹1,416 for the shoes.

The final price is always the selling price plus the tax amount.

Example 3

Calculate the Amount and Compound Interest on ₹10,000 for 2 years at 10% per annum, compounded annually.

IGiven: Principal (P) = ₹10,000

IIRate (R) = 10% per annum

IIITime (n) = 2 years

IVUsing the formula for Amount (A) compounded annually:

VA = P(1 + R/100)^n

VIA = 10,000(1 + 10/100)^2

VIIA = 10,000(1 + 1/10)^2

VIIIA = 10,000(11/10)^2

9A = 10,000 × (11/10) × (11/10)

10A = 10,000 × 121/100

11A = 100 × 121

12A = ₹12,100

13Now, calculate the Compound Interest (C.I.):

14C.I. = A - P

15C.I. = 12,100 - 10,000

16C.I. = ₹2,100

Answer

The Amount is ₹12,100 and the Compound Interest is ₹2,100.

For Class 8, interest is typically compounded annually. Ensure 'n' represents the number of compounding periods.

Common mistakes

✗Calculating discount on the Selling Price instead of the Marked Price.
✗Calculating tax (GST) on the Marked Price instead of the Selling Price.
✗Confusing Simple Interest with Compound Interest, or using the wrong formula.
✗Incorrectly applying the power 'n' in the Compound Interest formula, especially for time periods.
✗Forgetting to subtract the Principal from the Amount to find the Compound Interest.

Exam tips

★Read the question carefully to identify whether it involves discount, tax, or compound interest, and what is being asked (e.g., S.P., final price, C.I., Amount).
★Always write down the given values (P, R, T/n, M.P., Discount %, S.P., Tax %) and the relevant formula before starting calculations.
★Show all steps clearly and systematically. This helps in avoiding errors and also fetches partial marks in case of a calculation mistake.
★Double-check your calculations, especially for Compound Interest problems which can involve multiple steps and powers. Ensure units are consistent (e.g., rate and time period).

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