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Class 12 Applied Maths Chapter 14 Solutions
Returns, Growth, and Depreciation
EXERCISE – 14.1
Q.1 A person invests Rs.10000 in 10% Rs.100 shares of a company available at a premium of Rs.25. Find his rate of return.
Ans. Cost of investment = Rs.10000
Market value of share = 100 + 25 = Rs.125
Therefore,
No. of shares = 10000/125 = 80
Annual dividend earned = 80 x 10/100 x 100 = Rs.800
Therefore,
Rate of return = 800/10000 x 100 = 8%
Q.2 A man invests Rs.22500 in Rs.50 shares available at a 10% discount. If the dividend paid by the company is 12%, calculate his rate of return.
Ans. Cost of investment = Rs.22500
Market value of share = 50 – 5 = Rs.45
Therefore,
No. of shares = 22500/45 = 500
Annual dividend earned = 500 x 12/100 x 50 = Rs.3000
Therefore,
Rate of return = 3000/22500 x 100 = 13.3%
Q.3 A person invested Rs.200000 in a fund for one year. At the end of the year, the investment was worth Rs.216000. Calculate his rate of return.
Ans. Cost of investment = Rs.200000
Investment at the end = Rs.216000
Therefore,
Rate of return = [(216000 – 200000)/200000] x 100
= 16000/200000 x 100
= 8%
Q.4 Salmaan invests a sum of money in Rs.50 shares paying a 10% dividend quoted at a 20% discount. If his annual dividend is Rs.600, calculate his rate of return from the investment.
Ans. Let investment be x
Market value per share = Rs.40
No. of shares = x/40
Annual dividend earned = No. of share x rate of dividend x face value per share
600 = x/40 x 10/100 x 50
24000/50 = x
X = Rs.4800
Therefore,
Rate of return = 600/4800 x 100
= 12.5%
Q.5 A man invests a sum of money in Rs.100 shares paying a 15% dividend quoted at a 20% premium. If his annual dividend is Rs.540, calculate the rate of return on his investment.
Ans. Let investment be x
Market value of per share = 100 + 20 = Rs.120
Therefore,
No. of shares = x/120
Annual dividend earned = No. of share x rate of dividend x face value per share
540 = x/120 x 15/100 x 100
64800/15 = x
X = Rs.4320
Therefore,
Rate of return = 540/4320 x 100
= 12.5%
Q.6 Mr. Satendra holds 1500, Rs.100 shares of a company paying a 15% dividend annually quoted at a 30% premium. Calculate the rate of return on his investment.
Ans. Let, the cost of investment be x
Market value of one share = 100 + 30 = Rs.130
Therefore,
No. of shares = x/130
Annual dividend earned = No. of share x rate of dividend x face value per share
1500 = x/130 x 15/100 x 100
19500/15 = x
X = Rs.13000
Therefore,
Rate of return = 1500/13000 x 100
= 11.5%
Q.7 Rs.100 shares of a company are sold at a discount of Rs.20. If the return on the investment is 15%, find the rate of dividend declared.
Ans. F.V = Rs.100, C.V = 100 – 20 = Rs.80
Return on investment = 15%
= 80 x 15/100
= Rs.12
Therefore,
Dividend = 12/100 x 100
= 12%
Q.8 A company declared a dividend of 14%. Find the market value of ₹50 shares, if the return on the investment was 10%.
Ans. Rate of dividend = 14%
F.V = Rs.50
Dividend = 14% of 50
= 14/100 x 50
= Rs.7
Return on investment = 10%
So,
Rs.10 return on F.V = Rs.100
Rs.1 return on F.V = Rs.100/10
Rs.7 return on F.V = Rs.100/10 x 7
= Rs.70
Therefore,
F.V = Rs.70
Q.9 Mrs. Gupta invested Rs.16500 on Rs.100 shares at a premium of Rs.1. paying 15% dividend. At the end of the year, she sells the shares at a premium of Rs.20. Find her rate of return.
Ans. Cost of investment = Rs.16500
Market value of share = 100 + 10 = Rs.110
Therefore,
No. of shares = 16500/110 = 150
Annual dividend earned = 150 x 15/100 x 100 = Rs.2250
As Mrs. Gupta sells her share at Rs.20
Therefore,
Value of shares = Rs.120
Selling value of 150 share = 150 x 120 = Rs.18000
Here,
D1 = Rs.2250, P1 = Rs.18000, P0 = Rs.16500
Therefore,
Rate of return = [{D1 + (P1 – P0)}/P0] X 100
= [2250 + (18000 – 16500)]/16500 X 100
= 3750/16500 X 100
= 22.7%
Q.10 Mr. Verma invested Rs.18000 on Rs.100 shares at a discount of Rs.25 paying a 12% dividend. At the end of the year, he sells the shares at a discount of Rs.10. Find his rate of return.
Ans. Cost of investment = Rs.18000
Market value of share = 100 – 25 = Rs.75
Therefore,
No. of shares = 18000/75 = 240
Annual dividend earned = 240 x 12/100 x 100 = Rs.2880
As Mrs. Verma sells his share at a discount of Rs.10
Therefore,
Value of shares = Rs.90
Selling value of 240 share = 240 x 90 = Rs.21600
Here,
D1 = Rs.2880, P1 = Rs.21600, P0 = Rs.18000
Therefore,
Rate of return = [{D1 + (P1 – P0)}/P0] X 100
= [2880 + (21600 – 18000)]/18000 X 100
= 6480/18000 X 100
= 36%
FAQ’s related to Class 12 Applied Maths Chapter 14 on Returns, Growth, and Depreciation :
Q.1 What are the main topics covered in Chapter 14 on Returns, Growth, and Depreciation?
Ans. Chapter 14 covers the following key topics:
- Simple Interest
- Compound Interest
- Depreciation
- Growth rates
- Returns on investments
- Applications of these concepts in real-life scenarios such as savings, loans, and investments.
Q.2 What is the difference between simple interest and compound interest?
Ans. Simple Interest: Interest calculated only on the principal amount. The formula is 𝑆𝐼=(𝑃×𝑅×𝑇)/100 where P is the principal, R is the rate of interest, and T is the time period.
Compound Interest: Interest calculated on the principal amount and also on the interest of previous periods. The formula is CI = P (1 + R/100)^T – P.
Q.6 What are some real-life applications of returns, growth, and depreciation?
Ans. Real-life applications include:
- Calculating interest on savings and loans.
- Determining the future value of investments.
- Estimating the depreciation of assets such as vehicles and machinery.
- Understanding growth rates in populations, economies, and businesses.
These are few Frequently Asked Questions relating to Class 12 Applied Maths Chapter 14
In Class 12 Applied Maths chapter 14, you will explore fascinating topics that form the backbone of practical problem-solving techniques. Through clear explanations, illustrative examples, and step-by-step solutions, you’ll grasp complex concepts effortlessly. Whether you’re preparing for exams or simply eager to deepen your mathematical understanding, Class 12 Applied Maths Chapter 14 promises an enriching learning experience that will set you on the path to success. Class 12 Applied Maths Chapter 14, we delve deep into advanced mathematical concepts that are crucial for understanding.
