2 June Maths I
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Maths Dr. T.K. Jain. AFTERSCHOOOL M: 9414430763 [email protected] www.afterschool.tk www.afterschoool.tk
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What is the value of 100 Rs. After 3 years, if compound interest rate is 10%? • One rupee will become 1.1 after one year (.1 of interest on 1 rupee) • One rupee will become 1.1*1.1 after two years, and so on • =100*1.1*1.1*1.1 =133.1 Ans
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What will be the value of annuity of 100 Rs. After 3 years, if compound interest rate is 10% p.a. Annuity means, annual deposits. It means we are depositing Rs. 100 every year. 2.6.8: The 100 Rs. Deposited will be worth Rs. 133.1 2.6.9: The 100 Rs. Deposited after one year from today will be worth: 100*1.1*1.1 = 121 • 2.6.10: the worth of the 100 deposited on this day will be 100*1.1 =110 • 2.6.11: (assuming that we deposit Rs. 100 on that day also). the value of all the money deposited so far is : 133.1+121+110+100 = 464.1 ans. • • • •
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What is the worth of Rs. 220 that we will receive after one year? (r=10%) • We will use here a formulae to calculate present worth. • =(100* amt) /(100+(r*t)) • R= rate of interest, t= time. • =(100*220)/(100+(10*1))= 22000/110 • =200 Ans.
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What is the worth of Rs. 399 which we will receive after 3 years. R=10? • Applying present worth formulae: • =(100*399)/(100+(10*3) = • 39900/130 =306.9 Ans.
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If I have two options to receive a payment: (1) Rs. 10000 today (2) Rs. 13345 after 3 years. Which is preferable? (r=12%)
• • • •
We will use present worth formulae. =(100*13345) / (100+(12*3)) =1334500/136 =9812 Naturally, getting Rs. 10000 today is preferable to me.
www.afterschoool.tk
If some money becomes Rs. 100000 after 8 years, and it is 40000 today. What will it be after 4 year. Compound interest is being followed. Interest rate is not given.
• Four years are middle value between today and 8 years hence. Because it is using compound interest, we will use Geometric Mean to find the answer. • =square root of (40000*100000) • =square root of 4000000000 • =63245 Ans.
www.afterschoool.tk
If some money becomes Rs. 100000 after 8 years, and it is 40000 today. What will it be after 4 year. Simple interest is being followed. Interest rate is not given.
• Now this is a question of arithmetic progression. • Difference between 100000 and 40000 = 60000 • Annual interest is : 60000/8=7500 • Money after 4 years: 40000+(7500*4) = 70000 Ans. www.afterschoool.tk
Population of Bikaner is 500000 today. It is growing @10% p.a. What was the population 3 years ago. • It is a question similar to compound interest question. Population of 100 will be 110 after one year, 121 after 2 years and 133.1 after 3 years. 1 will be 1.331 after 3 years. We want to go back 3 years, so let us divide this amount by 1.331. • =500000 / 1.331 = 375657 Ans. • You can also solve it as : 500000/(1.1*1.1*1.1) • You can check it : • 375657*1.1*1.1*1.1 = 500000
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Population of my town increases by 10% and then decreases by 5% and again increases by 10% and again decreases by 5% and so on. What will be the population of my town after 5 years, if it is 100000 today & this year it will increase.
• • • • •
When it increases: multiply by 1.1 When it decreases, multiply by .95 Therefore answer is: 100000*1.1*.95*1.1*.95*1.1 =120122 Ans. www.afterschoool.tk
In the previous question, will the answer be different, if it first decreases by 5% for 2 years and then increases by 10% for 3 years?
• We can verify it by using the same structure: • 100000*.95*.95*1.1*1.1*1.1 = 120122 • Thus there is no difference in answer.
www.afterschoool.tk
Our population is 100000 today. Population growth rate is 20%. When was it half of present population? • Multiplying 100000 by 1/1.2, we get 83333, which was the population one year ago. Multiplying it with 1/1.2, we get 69444, which was two years ago, similarly, population was 57870 three years ago. Similarly, the population was 48000 4 years ago. Thus the population was 50000 about 3 years and 10 months (approx.) back.
www.afterschoool.tk
Mohan will pay me 1404 in two equal half yearly instalments. If I want to get the entire money now, how much should I demand? R =8 • I shall be getting Rs. 702 in two instalments. • First instalment is due 6 months, so its present worth is : • =100*702/(100+(8*1/2) = 70200/104 • =675 • Other instalment is due after one year, its present worth is : • 100*702/(100+(8*1) = 70200/108 =650 • =1325 Ans.
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with IAS, CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs • Most flexible, adaptive but rigorous programme • Available in distance learning mode • Case study focused- latest cases • Industry oriented practical curriculum • Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn www.afterschoool.tk
Workshops from AFTERSCHOOOL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
Specialisations: • • • • • • • • •
Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who wants to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approach • Strong intellectual and business capabilities • World class approach • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time
www.afterschoool.tk
Components Meditation, spiritualisation, and self development Business plan Essential softwares for business Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs • Editing of journals / newsletters • Consultancy / research projects • Assignments, communication skill workshops • • • • • • • •
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
www.afterschoool.tk
What is the value of 100 Rs. After 3 years, if compound interest rate is 10%? • One rupee will become 1.1 after one year (.1 of interest on 1 rupee) • One rupee will become 1.1*1.1 after two years, and so on • =100*1.1*1.1*1.1 =133.1 Ans
www.afterschoool.tk
What will be the value of annuity of 100 Rs. After 3 years, if compound interest rate is 10% p.a. Annuity means, annual deposits. It means we are depositing Rs. 100 every year. 2.6.8: The 100 Rs. Deposited will be worth Rs. 133.1 2.6.9: The 100 Rs. Deposited after one year from today will be worth: 100*1.1*1.1 = 121 • 2.6.10: the worth of the 100 deposited on this day will be 100*1.1 =110 • 2.6.11: (assuming that we deposit Rs. 100 on that day also). the value of all the money deposited so far is : 133.1+121+110+100 = 464.1 ans. • • • •
www.afterschoool.tk
What is the worth of Rs. 220 that we will receive after one year? (r=10%) • We will use here a formulae to calculate present worth. • =(100* amt) /(100+(r*t)) • R= rate of interest, t= time. • =(100*220)/(100+(10*1))= 22000/110 • =200 Ans.
www.afterschoool.tk
What is the worth of Rs. 399 which we will receive after 3 years. R=10? • Applying present worth formulae: • =(100*399)/(100+(10*3) = • 39900/130 =306.9 Ans.
www.afterschoool.tk
If I have two options to receive a payment: (1) Rs. 10000 today (2) Rs. 13345 after 3 years. Which is preferable? (r=12%)
• • • •
We will use present worth formulae. =(100*13345) / (100+(12*3)) =1334500/136 =9812 Naturally, getting Rs. 10000 today is preferable to me.
www.afterschoool.tk
If some money becomes Rs. 100000 after 8 years, and it is 40000 today. What will it be after 4 year. Compound interest is being followed. Interest rate is not given.
• Four years are middle value between today and 8 years hence. Because it is using compound interest, we will use Geometric Mean to find the answer. • =square root of (40000*100000) • =square root of 4000000000 • =63245 Ans.
www.afterschoool.tk
If some money becomes Rs. 100000 after 8 years, and it is 40000 today. What will it be after 4 year. Simple interest is being followed. Interest rate is not given.
• Now this is a question of arithmetic progression. • Difference between 100000 and 40000 = 60000 • Annual interest is : 60000/8=7500 • Money after 4 years: 40000+(7500*4) = 70000 Ans. www.afterschoool.tk
Population of Bikaner is 500000 today. It is growing @10% p.a. What was the population 3 years ago. • It is a question similar to compound interest question. Population of 100 will be 110 after one year, 121 after 2 years and 133.1 after 3 years. 1 will be 1.331 after 3 years. We want to go back 3 years, so let us divide this amount by 1.331. • =500000 / 1.331 = 375657 Ans. • You can also solve it as : 500000/(1.1*1.1*1.1) • You can check it : • 375657*1.1*1.1*1.1 = 500000
www.afterschoool.tk
Population of my town increases by 10% and then decreases by 5% and again increases by 10% and again decreases by 5% and so on. What will be the population of my town after 5 years, if it is 100000 today & this year it will increase.
• • • • •
When it increases: multiply by 1.1 When it decreases, multiply by .95 Therefore answer is: 100000*1.1*.95*1.1*.95*1.1 =120122 Ans. www.afterschoool.tk
In the previous question, will the answer be different, if it first decreases by 5% for 2 years and then increases by 10% for 3 years?
• We can verify it by using the same structure: • 100000*.95*.95*1.1*1.1*1.1 = 120122 • Thus there is no difference in answer.
www.afterschoool.tk
Our population is 100000 today. Population growth rate is 20%. When was it half of present population? • Multiplying 100000 by 1/1.2, we get 83333, which was the population one year ago. Multiplying it with 1/1.2, we get 69444, which was two years ago, similarly, population was 57870 three years ago. Similarly, the population was 48000 4 years ago. Thus the population was 50000 about 3 years and 10 months (approx.) back.
www.afterschoool.tk
Mohan will pay me 1404 in two equal half yearly instalments. If I want to get the entire money now, how much should I demand? R =8 • I shall be getting Rs. 702 in two instalments. • First instalment is due 6 months, so its present worth is : • =100*702/(100+(8*1/2) = 70200/104 • =675 • Other instalment is due after one year, its present worth is : • 100*702/(100+(8*1) = 70200/108 =650 • =1325 Ans.
www.afterschoool.tk
Thanks Afterschoool conducts three year integrated PGPSE (after class 12 along with IAS, CA & CS) and 18 month PGPSE (Post Graduate Programme in Social Entrepreneurship) along with preparation for CS / CFP / CFA /CMA / FRM. This course is also available online also. It also conducts workshops on social entrepreneurship in schools and colleges all over India – start social entrepreneurship club in your institution today with the help from afterschoool and help us in developing society.
www.afterschoool.tk
About AFTERSCHOOOL PGPSE – the best programme for developing great entrepreneurs • Most flexible, adaptive but rigorous programme • Available in distance learning mode • Case study focused- latest cases • Industry oriented practical curriculum • Designed to make you entrepreneurs – not just an employee • Option to take up part time job – so earn while you learn www.afterschoool.tk
Workshops from AFTERSCHOOOL • • • • • • • • •
IIF, Delhi CIPS, Jaipur ICSI Hyderabad Branch Gyan Vihar, Jaipur Apex Institute of Management, Jaipur Aravali Institute of Management, Jodhpur Xavier Institute of Management, Bhubaneshwar Pacific Institute, Udaipur Engineering College, Hyderabad
www.afterschoool.tk
Specialisations: • • • • • • • • •
Spiritualising business and society Rural development and transformation HRD and Education, Social Development NGO and voluntary work Investment analysis,microfinance and inclusion Retail sector Hospital management and Health care Hospitality sector and culture and heritage Other sectors of high growth, high technology and social relevance
www.afterschoool.tk
Salient features: • The only programme of its kind (in the whole world) • No publicity and low profile course • For those who wants to achieve success in life – not just a degree • Indepth knowledge and expertise • Professional approach • Strong intellectual and business capabilities • World class approach • Scholarships for those from poor economic background • Latest and constantly changing curriculum – keeping pace with the time
www.afterschoool.tk
Components Meditation, spiritualisation, and self development Business plan Essential softwares for business Research projects Participation in conferences / seminars Workshops on leadership, team building etc. Written submissions of research projects/articles / papers Interview of entrepreneurs, writing biographies of entrepreneurs • Editing of journals / newsletters • Consultancy / research projects • Assignments, communication skill workshops • • • • • • • •
www.afterschoool.tk
Pedagogy
• Case analysis • Quiz, seminars, workshops, games, • Visits to entrepreneurs and industrial visits • Presentations • Group discussions and group projects • Periodic self assessment • Mentoring and counselling
www.afterschoool.tk
www.afterschoool.tk social entrepreneurship for better society
www.afterschoool.tk
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