#### Chapters

Chapter 2: Algebra

Chapter 3: Analytical Geometry

Chapter 4: Trigonometry

Chapter 5: Differential Calculus

Chapter 6: Applications of Differentiation

Chapter 7: Financial Mathematics

Chapter 8: Descriptive Statistics and Probability

Chapter 9: Correlation and Regression Analysis

Chapter 10: Operations Research

## Chapter 7: Financial Mathematics

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 7 Financial MathematicsExercise 7.1 [Pages 166 - 167]

Find 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]

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. [(1.02)^{40} = 2.2080]

Find the amount of an ordinary annuity of 12 monthly payments of ₹ 1,500 that earns interest at 12% per annum compounded monthly. [(1.01)^{12} = 1.1262]

A bank pays 8% per annum interest compounded quarterly. Find the equal deposits to be made at the end of each quarter for 10 years to have ₹ 30,200? [(1.02)^{40} = 2.2080]

A person deposits ₹ 2,000 at the end of every month from his salary towards his contributory pension scheme. The same amount is credited by his employer also. If 8% rate of compound interest is paid, then find the maturity amount at end of 20 years of service. [(1.0067)^{240} = 4.9661]

Find the present value of ₹ 2,000 per annum for 14 years at the rate of interest of 10% per annum. If the payments are made at the end of each payment period. [(1.1)^{–14} = 0.2632]

Find the present value of an annuity of ₹ 900 payable at the end of 6^{th} month for 6 years. The money compounded at 8% per annum. [(1.04)^{–12} = 0.6252]

Find the amount at the end of 12 years of an annuity of ₹ 5,000 payable at the beginning of each year, if the money is compounded at 10% per annum. [(1.1)^{12} = 3.1384]

What is the present value of an annuity due of ₹ 1,500 for 16 years at 8% per annum? What is the present value of an annuity due of ₹ 1,500 for 16 years at 8% per annum? [(1.08)^{16} = 3.172]

What is the amount of perpetual annuity of ₹ 50 at 5% compound interest per year?

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 7 Financial MathematicsExercise 7.2 [Pages 171 - 172]

Find the market value of 62 shares available at ₹ 132 having the par value of ₹ 100.

How much will be required to buy 125 of ₹ 25 shares at a discount of ₹ 7?

If the dividend received from 9% of ₹ 20 shares is ₹ 1,620, then find the number of shares.

Mohan invested ₹ 29,040 in 15% of ₹ 100 shares of a company quoted at a premium of 20%. Calculate

- the number of shares bought by Mohan
- his annual income from shares
- the percentage return on his investment

A man buys 400 of ₹ 10 shares at a premium of ₹ 2.50 on each share. If the rate of dividend is 12%, then find

- his investment
- annual dividend received by him
- rate of interest received by him on his money

Sundar bought ₹ 4,500, 12% of ₹ 10 shares at par. He sold them when the price rose to ₹ 23 and invested the proceeds in ₹ 25 shares paying 10% per annum at ₹ 18. Find the change in his income.

A man invests ₹ 13,500 partly in 6% of ₹ 100 shares at ₹ 140 and the remaining in 5% of ₹ 100 shares at ₹ 125. If his total income is ₹ 560, how much has he invested in each?

Babu sold some ₹ 100 shares at 10% discount and invested his sales proceeds in 15% of ₹ 50 shares at ₹ 33. Had he sold his shares at 10% premium instead of 10% discount, he would have earned ₹ 450 more. Find the number of shares sold by him.

Which is better investment? 7% of ₹ 100 shares at ₹ 120 (or) 8% of ₹ 100 shares at ₹ 135.

Which is better investment? 20% stock at 140 (or) 10% stock at 70.

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 7 Financial MathematicsExercise 7.3 [Pages 172 - 173]

#### Choose the correct answer

The dividend received on 200 shares of face value ₹ 100 at 8% is __________.

₹ 1600

₹ 1000

₹ 1500

₹ 800

What is the amount realised on selling 8% stock of 200 shares of face value ₹ 100 at ₹ 50?

₹ 16,000

₹ 10,000

₹ 7,000

₹ 9,000

A man purchases a stock of ₹ 20,000 of face value ₹ 100 at a premium of 20%, then investment is ___________.

₹ 20,000

₹ 25,000

₹ 24,000

₹ 30,000

If a man received a total dividend of ₹ 25,000 at 10% dividend rate on a stock of face value ₹ 100, then the number of shares purchased.

3500

4500

2500

300

The brokerage paid by a person on the sale of 400 shares of face value ₹ 100 at 1% brokerage __________.

₹ 600

₹ 500

₹ 200

₹ 400

Purchasing price of one share of face value ₹ 100 available at a discount of `9 1/2%` with brokerage `1/2%` is ____________.

₹ 89

₹ 90

₹ 91

₹ 95

A person brought 100 shares of 9% stock of face value ₹ 100 at a discount of 10%, then the stock purchased is ____________.

₹ 9000

₹ 6000

₹ 5000

₹ 4000

The % of income on 7% stock at ₹ 80 is ___________.

9%

8.75%

8%

7%

The annual income on 500 shares of face value ₹ 100 at 15% is ___________.

₹ 7,500

₹ 5,000

₹ 8,000

₹ 8,500

₹ 5000 is paid as perpetual annuity every year and the rate of C.I. 10%. Then present value P of immediate annuity is __________.

₹ 60,000

₹ 50,000

₹ 10,000

₹ 80,000

If ‘a’ is the annual payment, ‘n’ is the number of periods and ‘i’ is compound interest for ₹ 1 then future amount of the ordinary annuity is

A = `"a"/"i" (1 + "i") [(1 + "i")^"n" - 1]`

A = `"a"/"i" [(1 + "i")^"n" - 1]`

P = `"a"/"i"`

P = `"a"/"i" (1 + "i") [1 - (1 + "i")^(-"n")]`

A invested some money in 10% stock at ₹ 96. If B wants to invest in an equally good 12% stock, he must purchase a stock worth of ____________.

₹ 80

₹ 115.20

₹ 120

₹ 125.40

An annuity in which payments are made at the beginning of each payment period is called ___________.

Annuity due

An immediate annuity

perpetual annuity

none of these

The present value of the perpetual annuity of ₹ 2000 paid monthly at 10% compound interest is ___________.

₹ 2,40,000

₹ 6,00,000

₹ 20,40,000

₹ 2,00,400

Example of contingent annuity is ___________.

Installments of payment for a plot of land

An endowment fund to give scholarships to a student

Personal loan from a bank

All the above

### Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide Chapter 7 Financial MathematicsMiscellaneous Problems [Pages 173 - 179]

Find the amount of annuity of ₹ 2000 payable at the end of each year for 4 years of money is worth 10% compounded annually. [(1.1)^{4} = 1.4641]

An equipment is purchased on an installment basis such that ₹ 5000 on the signing of the contract and four-yearly installments of ₹ 3000 each payable at the end of first, second, third and the fourth year. If the interest is charged at 5% p.a find the cash down price. [(1.05)^{–4} = 0.8227]

Find the amount of an ordinary annuity of ₹ 500 payable at the end of each year for 7 years at 7% per year compounded annually. [(1.07)^{7} = 1.6058]

Calculate the amount of an ordinary annuity of ₹ 10,000 payable at the end of each half-year for 5 years at 10% per year compounded half-yearly. [(1.05)^{10} = 1.6289]

Find the amount of an ordinary annuity of ₹ 600 is made at the end of every quarter for 10 years at the rate of 4% per year compounded quarterly. [(1.01)^{40} = 1.4889]

Find the amount of an annuity of ₹ 2000 payable at the end of every month for 5 years if money is worth 6% per annum compounded monthly. [(1.005)^{60} = 1.3489]

Naveen deposits ₹ 250 at the end of each month in an account that pays an interest of 6% per annum compounded monthly, how many months will be required for the deposit to amount to at least ₹ 6390? [log(1.1278) = 0.0523, log(1.005) = 0.0022]

A cash prize of ₹ 1,500 is given to the student standing first in examination of Business Mathematics by a person every year. Find out the sum that the person has to deposit to meet this expense. Rate of interest is 12% p.a.

Machine A costs ₹ 15,000 and machine B costs ₹ 20,000. The annual income from A and B are ₹ 4,000 and ₹ 7,000 respectively. Machine A has a life of 4 years and B has a life of 7 years. Find which machine may be purchased. (Assume discount rate 8% p.a) [(1.08)^{–4} = 0.7350, (1.08)^{–7} = 0.5835]

Vijay wants to invest ₹ 27,000 in buying shares. The shares of the following companies are available to him. ₹ 100 shares of company A at par value; ₹ 100 shares of company B at a premium of ₹ 25; ₹ 100 shares of company C at a discount of ₹ 10; ₹ 50 shares of company D at a premium of 20%. Find how many shares will he get if he buys shares of

- Company A
- Company B
- Company C
- Company D

Gopal invested ₹ 8,000 in 7% of ₹ 100 shares at ₹ 80. After a year he sold these shares at ₹ 75 each and invested the proceeds (including his dividend) in 18% for ₹ 25 shares at ₹ 41. Find

- his dividend for the first year
- his annual income in the second year
- The percentage increase in his return on his original investment

A man sells 2000 ordinary shares (par value ₹ 10) of a tea company which pays a dividend of 25% at ₹ 33 per share. He invests the proceeds in cotton textiles (par value ₹ 25) ordinary shares at ₹ 44 per share which pays a dividend of 15%. Find

- the number of cotton textiles shares purchased and
- change in his dividend income.

The capital of a company is made up of 50,000 preferences shares with a dividend of 16% and 25,000 ordinary shares. The par value of each of preference and ordinary shares is ₹ 10. The company had a total profit of ₹ 1,60,000. If ₹ 20,000 were kept in reserve and ₹ 10,000 in depreciation, what percent of dividend is paid to the ordinary shareholders.

## Chapter 7: Financial Mathematics

## Tamil Nadu Board Samacheer Kalvi solutions for Class 11th Business Mathematics and Statistics Answers Guide chapter 7 - Financial Mathematics

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Concepts covered in Class 11th Business Mathematics and Statistics Answers Guide chapter 7 Financial Mathematics are Annuities, Stocks, Shares, Debentures and Brokerage.

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