Applied Mathematics · Class 11 Commerce
Ch 11Basics of Financial Mathematics — Class 11 Applied Mathematics, concept-first.
This concept map shows how the chapter fits together. Financial mathematics at this level covers interest (simple, compound and the effective rate), the time value of money through present and future value (including net present value), annuities (valuing a regular annuity and its applications), the calculation of tax,…
Key concepts
Hover a concept to preview it and jump to its most relevant Q&A.
Introduction
You've been solving problems your whole life. When you see a new type of question, you first figure out what it's asking, then decide which tools to use, then carry out the steps.
Most relevant Q&A
In previous exams
How often this chapter’s concepts have been examined — real appearance data, never estimated.
Chapter contents
The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.
Concept Map
This concept map shows how the chapter fits together. Financial mathematics at this level covers interest (simple, compound and the effective rate), the time value of money through present and future…
Introduction
Money is not just a medium of exchange — it is a tool that grows, shrinks, and changes value over time.
Interest & Interest Rates
Interest is the price you pay for using someone else’s money — or the reward you earn for letting them use yours.
Accumulation with Simple and Compound Interest
When money grows, the pattern of that growth matters enormously. Simple interest adds a fixed amount each period, so the total grows in a straight line — useful for short-term loans or quick calculati…
+−Worked Examplesi5 questions
- Example 1A loan of ₹10,000 has been issued for 6 years. Compute the amount to be repaid by the borrower to the lender if simple interest is charged @…Free
- Example 2The Bank has issued a loan of ₹1,000 to a sole proprietor for a period of 5 years. The Interest Rate for this loan is 5% and the Interest is…Free
- Example 3Divide ₹43,500 into two parts so that the simple interest on the first part when deposited for one year at 9% per annum and that on the seco…Preview
- Example 4At what rate percent per annum will a sum of money triple itself in 16 years (under simple interest)?Preview
- Example 5A sum of money lent out at simple interest amounts to ₹2,200 in one year and ₹2,800 in 4 years. Find the sum of money and the rate of intere…Preview
Simple and Compound Interest Rates with Equivalency
Interest is the price of using someone else’s money, but not all interest is the same. In this section, you will see the critical difference between simple interest, where the base amount never change…
+−Worked Examplesi2 questions
- Example 6Find the amount of ₹20,000 after 10 years at 8% converted quarterly for the first 4 years and at 6% compounded monthly thereafter.Free
- Example 7The difference between the Compound Interest (CI) and Simple Interest (SI) on a certain sum of money at 40% per annum for 2 years is ₹500. F…Preview
Effective Rate of Interest
When you borrow or invest money, the stated annual rate — the nominal rate — is rarely the whole story.
Present Value, Net Present Value and Future Value
Money today is not the same as money tomorrow — a rupee received now can be invested to earn more, so its value is greater than a rupee received later.
+−Worked Examplesi4 questions
- Example 9Assume that you would like to put money in an account today to make sure you have enough money in 10 years to buy a car. If you would like t…Free
- Example 10X Ltd. wants to expand its business and is willing to invest ₹10,00,000. The investment will bring an inflow of ₹1,00,000 in the first year,…Free
- Example 11₹1,000 is invested for 5 years in a savings account earning 10% simple interest paid annually. Find the future value (FV) of this investment…Preview
- Example 12₹1,000 is invested for 5 years at a 10% compounding interest rate. Find the future value (FV) of this investment at the end of 5 years.Preview
Annuities, Calculating Value of Regular Annuity
Annuities are the financial engine behind everything from monthly pension payments to home loan EMIs — a stream of equal cash flows spaced at regular intervals.
+−Worked Examplesi5 questions
- Example 13A man deposits in a bank ₹16,000 at the end of each year, for 8 years. If the rate of interest is 10% per annum compounded annually, what wo…Free
- Example 14Find the least number of years for which an ordinary annuity of ₹1,500 per annum must run in order that its amount just exceeds ₹30,000 at 9…Free
- Example 15A firm anticipates a capital expenditure of ₹1,00,000 for a new equipment in 5 years. How much should be deposited quarterly in a sinking fu…Preview
- Example 16Nidhi buys an LCD set worth ₹48,000 on an instalment plan under which ₹8,000 is to be paid immediately and the balance in 15 equal annual in…Preview
- Example 17For a child's education, a family decides to invest ₹3,000 at the end of each 6-month period in a fund paying 8% per year compounded semi-an…Preview
Simple Applications of Regular Annuities (Upto 3 Periods)
You have already learned how an annuity builds value when payments are made regularly. Now we turn that knowledge into a practical tool.
Tax, Calculation of Tax and Simple Application of Tax Calculation in Goods and Service Tax, Income Tax
6 QTax is not a penalty — it is the price of living in a society that builds roads, pays teachers, and keeps the lights on.
+−Worked Examplesi4 questions
- Example 19Income from Salaries is ₹4,00,000 for the financial year 2019-20. Calculate the Income Tax liability if the deductions under LIC are ₹50,000…Free
- Example 20Income from salaries is ₹2,00,000. Income earned from House property rentals is ₹1,00,000. Income under the head Business and Profession com…Free
- Example 21Raman's monthly salary is ₹1,93,800. HRA is 24% of Basic Salary and Transportation Allowance is ₹8,424 per month. He deposits ₹40,000 on GPF…Preview
- Example 22A product is sold for ₹2,000 and the GST applicable to the product is 12%. Find the net price of the product after adding GST.Preview
+−Exercise 11.1i2 questions
Bills, Tariff Rates, Fixed Charge, Surcharge, Service Charge
When you receive an electricity or utility bill, the total amount is rarely just the cost of the units you consumed.
Calculation and Interpretation of Electricity Bill, Water Supply and Other Supply Bills
We rarely think about the numbers on a utility bill until we have to pay them, but each figure tells a story of consumption, rate, and fixed charges.