Skip to content
← Business Mathematics and Statistics

Business Mathematics and Statistics · Class 11 Commerce

Ch 7Financial Mathematics (Annuities; Stocks, Shares, Debentures and Brokerage) — Class 11 Business Mathematics and Statistics, concept-first.

A single deposit growing under compound interest, studied earlier in this course, answers 'what does one lump sum become after years?' Many real financial commitments — a monthly salary saved into a recurring deposit, a home-loan EMI, a pension paid every year after retirement — instead involve a series of equal paymen…

30

Q&A

6

Concepts

Not available

Exam weightage

Start learning — read this chapter →

Key concepts

Hover a concept to preview it and jump to its most relevant Q&A.

Future Value of an Annuity

The future value of an ordinary annuity, , is the total accumulated value of all instalments plus compound interest, valued at the time of the last instalment; the annuity-due version multiplies this by a further .

Most relevant Q&A

Start with this concept →

Chapter contents

The NCERT structure, section by section. Open a section to see its questions, then read the concept-first solution.

1

Annuity — Meaning and Types

A single deposit growing under compound interest, studied earlier in this course, answers 'what does one lump sum become after years?' Many real financial commitments — a monthly salary saved into a r…

2

Future Value of an Annuity

The future value (or amount) of an annuity is the total accumulated value of all its instalments, together with the compound interest each has earned, at the moment the very last instalment is paid.

3

Present Value of an Annuity

The present value of an annuity is the single lump sum, invested today at the same rate of interest, that would be exactly enough to fund every future instalment of the annuity — the value 'discounted…

4

Stocks and Shares — Basic Terms

The second half of this chapter shifts from savings/loan mathematics to the mathematics of investing in a company's securities.

5

Debentures and Brokerage

A debenture is a certificate of loan issued by a company to raise borrowed (not owned) capital — a debenture-holder is a creditor of the company, not a part-owner as a shareholder is, and is entitled…

6

Rate of Return on Investment

The final, and most practically important, question an investor asks is not 'what is the dividend rate' but 'what return am I actually earning on the money I put in' — and these two numbers can differ…

Exercises

+Show 6 questions6 questions
  1. Q6Find the future value of an annuity due of ₹4,000 paid at the beginning of every year for 3 years, at 10% per annum compound interest. [Give…Free
  2. Q7A person invests in 300 shares of face value ₹10 each at a market price of ₹15 per share, with the company declaring a dividend of 20%. Find…Free
  3. Q8Which is the better investment: 8% shares of face value ₹100 available at ₹80, or 10% shares of face value ₹100 available at ₹120? Compare u…Preview
  4. Q9A person sells 150 shares of face value ₹10 each at a market price of ₹18, paying a brokerage of ₹0.50 per share. Find the net amount receiv…Preview
  5. Q10Find the present value of an ordinary annuity of ₹6,000 paid at the end of every year for 3 years at 9% per annum compound interest. [Given…Preview
  6. Q11Classify each of the following as an annuity immediate (ordinary annuity) or an annuity due, giving a reason: (i) Equal monthly instalments…Preview

Sample & Board Papers

Sample papers and previous-year board questions for this subject.

+Show 19 questions19 questions
  1. Q1Purchasing price of one share of face value 100 available at a discount of $9\frac{1}{2}\%$ with brokerage $\frac{1}{2}\%$ is : (a) ₹ 95 (b)…Preview
  2. Q2Dividend is expressed as : (a) No. of shares (b) Investment (c) Percentage (d) None of thesePreview
  3. Q3Find the amount of an ordinary annuity of ₹ 3,200 per annum for 12 years at the rate of interest of 10% per year. $[(1.1)^{12} = 3.1384]$Preview
  4. Q4(a) A photographer purchases a camera on instalments. He has to pay 7 annual instalments each of ₹ 36,000 right from the date of purchase. I…Preview
  5. Q5Purchasing price of one share of face value ₹ 100 available at a discount of $9\dfrac{1}{2}\%$ with brokerage $\dfrac{1}{2}\%$ is : (a) ₹ 91…Preview
  6. Q6Find the market value of 62 shares available at ₹ 132 having the par value of ₹ 100.Preview
  7. Q7A person bought 12% stock for ₹ 54,000 at a discount of 17%. If he paid 1% brokerage, find the percentage of his income.Preview
  8. Q8The calculation of dividend is based on : (a) Market value (b) Capital (c) Face value (d) None of thesePreview
  9. Q9Example of Contigent annuity is : (a) An endowment fund to give scholarship to the students. (b) Personal loan from a Bank. (c) Instalment o…Preview
  10. Q10Find the Market value of 325 shares of Face value ₹ 100 at a premium of ₹ 18.Preview
  11. Q11Which is better investment, 20% stock at ₹ 140 or 10% stock at ₹ 70 ?Preview
  12. Q12(a) If the payment of ₹ 2,000 is made at the end of every quarter for 10 years at the rate of 8% per year, then find the amount of annuity.…Preview
  13. Q13If '$a$' is the annual payment '$n$' is the number of periods and '$i$' is compound interest for $\text{\rupee}\,1$ then future amount of th…Preview
  14. Q14The dividend received on 200 shares of Face Value $\text{\rupee}\,100$ at 8% stock is : (a) $\text{\rupee}\,1500$ (b) $\text{\rupee}\,1600$…Preview
  15. Q15Which is better investment? 20% stock at $\text{\rupee}\,140$ (or) 10% stock at $\text{\rupee}\,70$.Preview
  16. Q16If the payment of $\text{\rupee}\,2{,}000$ is made at the end of every quarter for 10 years at the rate of 8% per year, then find the amount…Preview
  17. Q17What is the amount realised on selling 8% Stock of 200 shares of Face Value ₹ 100 at ₹ 50 ? (a) ₹ 7,000 (b) ₹ 16,000 (c) ₹ 9,000 (d) ₹ 10,00…Preview
  18. Q18Example of contingent annuity is : (a) An endowment fund to give scholarships to students (b) Personal loan from a bank (c) Installments of…Preview
  19. Q19What is the present value of an annuity due of ₹ 1,500 for 16 years at 8% per annum ? $[(1.08)^{-16}=0.2919]$Preview

More questions

+Show 5 questions5 questions
  1. Example 1Find the future value of an ordinary annuity of ₹5,000 paid at the end of every year for 4 years, at 10% per annum compound interest. [Given…Free
  2. Example 2A person wants to receive ₹8,000 at the end of every year for 3 years. Find the amount they must invest today at 8% per annum compound inter…Free
  3. Example 3Find the amount of each equal annual instalment needed to repay a loan of ₹1,00,000 in 5 equal yearly instalments at 10% per annum compound…Preview
  4. Example 4A person holds 200 shares of face value ₹10 each in a company that declares a dividend of 15% for the year. Find the total dividend income r…Preview
  5. Example 5A person buys 50 debentures of face value ₹100 each, at a market price of ₹96 per debenture, paying a brokerage of ₹1 per debenture. The deb…Preview