Read each topic in order. Study the formula cards first, then work through the solved examples on paper with the solution covered. Finally, attempt the exam-style questions before looking at the answers. Currency amounts in this chapter are in Indian Rupees (₹).
Topic 1 – Goods and Services Tax (GST)
A. Learning Objectives
After studying this topic you should be able to:
- Explain what GST is and why it replaced the earlier system of separate taxes such as VAT, service tax and excise duty.
- Distinguish between CGST, SGST and IGST, and know when each applies.
- Compute the GST charged on a taxable value for a given GST rate.
- Find the taxable value (and the tax) when only the GST-inclusive price is given.
- Use input tax credit to find the net GST payable by a dealer.
- Solve word problems on billing, invoices and tax payable by a customer.
B. Basic Concepts and Definitions
GST is a single indirect tax levied on the supply of goods and services across India. It came into effect on 1 July 2017. It replaced a large number of separate taxes (VAT, service tax, central excise, etc.) with one tax, so that a good or service is taxed only once at each stage.
The value on which GST is calculated. It is usually the price of the goods or services before adding GST. It is also called the base price or the selling price (excluding tax).
For a supply within the same state (intra-state), GST is split into two equal halves:
- CGST (Central GST) – goes to the Central Government.
- SGST (State GST) – goes to the State Government.
For a supply between two different states (inter-state), a single tax called IGST (Integrated GST) is charged at the full GST rate.
A dealer pays GST on the goods they purchase (input GST) and collects GST on the goods they sell (output GST). The input GST can be set off against the output GST. The amount actually paid to the government is the net GST = output GST − input GST.
C. Important Formulas
D. Step-by-Step Solved Examples
Level 1 Direct GST on a taxable value
A shop sells an item for a taxable value of ₹2,500. If the GST rate is 18%, find the GST charged and the total amount the customer pays.
Given: Taxable value = ₹2,500, GST rate = 18%.
Required: GST amount and total amount.
Answer: GST = ₹450; total amount = ₹2,950. Tip: check that the total is 1.18 times the taxable value.
Level 2 Intra-state supply and bill
A dealer in Karnataka sells goods worth ₹4,000 (taxable value) to a customer in Karnataka. The GST rate is 12%. Find the CGST, the SGST and the total bill amount.
Given: Taxable value = ₹4,000, GST rate = 12%. The sale is within the same state, so it is split into CGST and SGST.
Answer: CGST = ₹240, SGST = ₹240, total bill = ₹4,480.
Level 3 Input tax credit – net GST payable
A trader in Maharashtra buys goods for ₹20,000 and pays GST at 18%. He sells the same goods for ₹30,000 (before tax), also within Maharashtra, at 18%. Find the input GST, the output GST and the net GST he must pay to the government.
Given: Purchase = ₹20,000, sale = ₹30,000, rate = 18%, both intra-state.
Answer: Input GST = ₹3,600; output GST = ₹5,400; net GST payable = ₹1,800. Check: net GST = 18% of the value added, i.e. 18% of ₹10,000 = ₹1,800.
E. Examination-Oriented Questions
Find the GST on a taxable value of ₹6,400 at 12%.
Show answer
GST = \(\dfrac{12}{100} \times 6400 = \text{₹}768\).
The price of an article including 18% GST is ₹5,900. Find the taxable value.
Show answer
Taxable value = \(\dfrac{5900}{1.18} = \text{₹}5{,}000\). (Then GST = \(5900 - 5000 = \text{₹}900\).)
A dealer in Tamil Nadu sells goods for ₹12,000 within the state. GST is 28%. Find CGST, SGST and the amount payable by the buyer.
Show answer
Total GST = \(0.28 \times 12000 = \text{₹}3{,}360\). CGST = SGST = \(\text{₹}1{,}680\). Amount payable = \(12000 + 3360 = \text{₹}15{,}360\).
A manufacturer sells to a wholesaler in another state for ₹40,000 (taxable value) at 18% GST. Find the IGST charged and the invoice total.
Show answer
Inter-state supply, so IGST = \(0.18 \times 40000 = \text{₹}7{,}200\). Invoice total = \(40000 + 7200 = \text{₹}47{,}200\).
A trader buys goods for ₹25,000 and pays 18% GST. He then sells them for ₹32,000 (before tax) at 18%, within the same state. Find the net CGST and net SGST he pays.
Show answer
Input GST = \(0.18 \times 25000 = \text{₹}4{,}500\) (CGST ₹2,250, SGST ₹2,250). Output GST = \(0.18 \times 32000 = \text{₹}5{,}760\) (CGST ₹2,880, SGST ₹2,880). Net CGST = \(2880 - 2250 = \text{₹}630\); net SGST = ₹630. Total net GST = ₹1,260.
The marked price of an article is ₹3,200. A shopkeeper offers a discount of 10% on the marked price, and then charges GST at 18% on the discounted price. Find the amount the customer pays.
Show answer
Discounted (taxable) value = \(3200 - 10\% \text{ of } 3200 = 3200 - 320 = \text{₹}2{,}880\). GST = \(0.18 \times 2880 = \text{₹}518.40\). Amount paid = \(2880 + 518.40 = \text{₹}3{,}398.40\).
F. Common Mistakes
| # | Common mistake | Correct approach |
|---|---|---|
| 1 | Charging CGST and SGST each at the full GST rate. | CGST and SGST are each half the GST rate; together they equal the full rate. |
| 2 | Charging IGST for a sale within the same state. | Use IGST only for inter-state supply; intra-state uses CGST + SGST. |
| 3 | Applying GST to the GST-inclusive price by multiplying by the rate. | First find the taxable value as \(\frac{\text{inclusive price}}{1 + r/100}\), then find GST. |
| 4 | Adding GST to the purchase and sale both and reporting the sum as tax paid. | Use input tax credit: net GST = output GST − input GST. |
| 5 | Forgetting to subtract a discount before computing GST. | Discount is applied to the marked price first; GST is charged on the discounted value. |
| 6 | Rounding the taxable value wrongly when working backwards. | Keep full accuracy until the final rupee value; round money only at the end. |
| 7 | Writing ₹ instead of the correct unit or leaving units out. | State all money answers with the rupee sign and correct rounding to 2 decimals if needed. |
| 8 | Treating CGST and SGST as payable to the same authority. | CGST goes to the Centre and SGST to the State; the amounts are equal but credited separately. |
G. Examination Tips
- Always write down "Given" and "To find" – ICSE awards marks for correct method, not just the final answer.
- If a sale is "within the state", immediately write CGST = SGST = half of the GST rate; this earns method marks early.
- For input tax credit, show output GST and input GST separately, then subtract. Do not just write the final number.
- When a discount is involved, compute the discount first; GST applies to the price after discount.
- Include units (₹) in every step. A correct number without the unit can lose a presentation mark.
H. Quick Revision Sheet – GST
- GST = (Rate/100) × taxable value.
- Intra-state: CGST = SGST = half of GST. Inter-state: full IGST.
- Taxable value from inclusive price = inclusive ÷ (1 + rate/100).
- Net GST = output GST − input GST.
- Discount is applied before GST.
Topic 2 – Banking: Recurring Deposit Accounts
A. Learning Objectives
After studying this topic you should be able to:
- Explain what a Recurring Deposit (RD) account is and how it differs from a fixed deposit.
- Calculate the interest earned on a recurring deposit using the standard ICSE formula.
- Find the maturity value of an RD account.
- Work backwards to find the rate of interest or the number of instalments.
- Solve problems involving monthly deposits, time periods and interest.
B. Basic Concepts and Definitions
A scheme in which a fixed sum of money is deposited every month for a fixed number of months. At the end of the period the depositor receives the total of all deposits plus the interest earned. It encourages regular saving.
The fixed amount deposited each month. If a person deposits ₹500 every month, then the instalment P = ₹500.
The total amount the depositor receives on maturity = total of all monthly deposits + interest earned. It is also called the maturity amount.
Each monthly instalment earns interest for a different length of time. The first instalment stays in the bank for \(n\) months, the second for \(n-1\) months, and so on, down to the last instalment which earns interest for 1 month. Summing these gives the standard formula below.
C. Important Formulas
D. Step-by-Step Solved Examples
Level 1 Interest and maturity value
Mr. Sharma deposits ₹500 every month in a recurring deposit account for 24 months at 6% per annum. Find the interest earned and the maturity value.
Given: \(P = 500\), \(n = 24\), \(r = 6\).
Answer: Interest = ₹750; maturity value = ₹12,750.
Level 2 Larger period and rate
Ms. Rao deposits ₹1,000 per month for 36 months at 8% per annum. Compute the interest and the maturity value.
Given: \(P = 1000\), \(n = 36\), \(r = 8\).
Answer: Interest = ₹4,440; maturity value = ₹40,440.
Level 3 Comparing schemes / finding rate
A person deposits ₹800 per month for 20 months and receives a total interest of ₹1,050. Find the rate of interest per annum.
Given: \(P = 800\), \(n = 20\), \(I = 1050\). Find \(r\).
Answer: The rate of interest is 7.5% per annum. Check: with r = 7.5, I = 800 × 210 × 7.5/1200 = ₹1,050.
E. Examination-Oriented Questions
Find the interest on a recurring deposit of ₹400 per month for 12 months at 6% per annum.
Show answer
\(\frac{n(n+1)}{2} = \frac{12 \times 13}{2} = 78\). \(I = 400 \times 78 \times \frac{6}{1200} = \text{₹}156\).
Mr. Iyer deposits ₹600 each month for 10 months at 9% per annum. Find the maturity value.
Show answer
\(\frac{10 \times 11}{2} = 55\). \(I = 600 \times 55 \times \frac{9}{1200} = \text{₹}247.50\). Total deposits = ₹6,000. MV = \(6000 + 247.50 = \text{₹}6{,}247.50\).
A lady deposits ₹1,200 per month for 30 months at 8% per annum. Find the interest earned and the maturity value.
Show answer
\(\frac{30 \times 31}{2} = 465\). \(I = 1200 \times 465 \times \frac{8}{1200} = 1200 \times 465 \times \frac{1}{150} = \text{₹}3{,}720\). Total deposits = ₹36,000. MV = \(36000 + 3720 = \text{₹}39{,}720\).
Find the number of months for which ₹500 per month must be deposited at 10% per annum to earn an interest of ₹1,250.
Show answer
\(1250 = 500 \times \frac{n(n+1)}{2} \times \frac{10}{1200}\). So \(\frac{n(n+1)}{2} = \frac{1250 \times 1200}{500 \times 10} = 300\). Then \(n(n+1) = 600 = 24 \times 25\), so \(n = 24\) months.
Ravi opens an RD account and deposits ₹1,500 per month for 2 years at 7% per annum. Find the total interest and the maturity value. How much more interest would he have earned at 8% per annum?
Show answer
\(n = 24\), \(\frac{24 \times 25}{2} = 300\). At 7%: \(I = 1500 \times 300 \times \frac{7}{1200} = \text{₹}2{,}625\). MV = \(36000 + 2625 = \text{₹}38{,}625\). At 8%: \(I = 1500 \times 300 \times \frac{8}{1200} = \text{₹}3{,}000\). Extra interest = \(3000 - 2625 = \text{₹}375\).
A recurring deposit account pays an interest of ₹6,090 on a monthly deposit of ₹2,000 at 9% per annum. Find the number of months and the maturity value.
Show answer
Use \(I = P \cdot \frac{n(n+1)}{2} \cdot \frac{r}{1200}\): \(6090 = 2000 \times \frac{n(n+1)}{2} \times \frac{9}{1200}\). So \(\frac{n(n+1)}{2} = \frac{6090 \times 1200}{2000 \times 9} = 406\). Then \(n(n+1) = 812 = 28 \times 29\), so \(n = 28\) months. Total deposits = \(2000 \times 28 = \text{₹}56{,}000\). Maturity value = \(56000 + 6090 = \text{₹}62{,}090\).
F. Common Mistakes
| # | Common mistake | Correct approach |
|---|---|---|
| 1 | Using the simple interest formula \(I = \frac{PRT}{100}\) with \(T = n\) months directly. | Use the recurring deposit formula \(I = P \cdot \frac{n(n+1)}{2} \cdot \frac{r}{1200}\), which accounts for each instalment's own time. |
| 2 | Forgetting the factor \(\frac{1}{12}\) to convert the annual rate to a monthly basis. | The rate is per annum, so divide by 12 (equivalently use 1200 in the denominator). |
| 3 | Using \(n(n+1)\) instead of \(\frac{n(n+1)}{2}\). | The sum of the first \(n\) natural numbers is \(\frac{n(n+1)}{2}\). |
| 4 | Reporting the total deposits as the maturity value. | Maturity value = total deposits + interest. |
| 5 | Taking the number of months as years. | Convert years to months first (2 years = 24 months). |
| 6 | Expecting the last instalment to earn interest for \(n\) months. | The last instalment stays only 1 month; that is why the sum is \(\frac{n(n+1)}{2}\) and not \(n^2\). |
| 7 | Rounding the interest to the nearest rupee too early. | Keep the exact value through the working and round only at the final answer. |
| 8 | Accepting a non-integer number of months as an answer. | The number of instalments must be a whole number; check your result. |
G. Examination Tips
- Write the formula first, then substitute. This secures method marks even if a calculation slips.
- Compute \(\frac{n(n+1)}{2}\) as a separate step – it is easy to mark and prevents errors.
- If the question asks for maturity value, always find interest first, then add total deposits.
- Convert all times to months before substituting.
- State the final answer clearly with the rupee sign and units (months, % per annum).
H. Quick Revision Sheet – Banking
- \(I = P \times \frac{n(n+1)}{2} \times \frac{r}{1200}\) (with \(r\) in % per annum).
- Maturity value = \(P\,n + I\).
- Sum of months \(= \frac{n(n+1)}{2}\).
- Convert years to months before using the formula.
- \(n\) must always be a whole number of months.
Now that you have revised all three topics, attempt the topic quiz for instant feedback, then the practice paper and finally the timed chapter test.