- The document discusses compound interest and how its calculation changes based on how frequently interest is compounded - whether annually, monthly, daily, etc.
- As the frequency of compounding increases, approaching continuous compounding, the growth rate converges to a limit of approximately 2.718 or e.
- This demonstrates the concept of limits, a foundational idea in calculus, and shows that even with continuous compounding, the bank cannot offer an interest rate higher than approximately 171.8%.
Students often wonder how to do my statistics homework in time? It is a critical issue but in Statisticshelpdesk we care for your concern and zeal to be a topper. All our tutors are expert and will offer you best study help. Contact us today.
Students often wonder how to do my statistics homework in time? It is a critical issue but in Statisticshelpdesk we care for your concern and zeal to be a topper. All our tutors are expert and will offer you best study help. Contact us today.
The power point explains the concept of simple interest and compound interest.It also explains the development of the formula.It is made for VIIIth standard S.S.C text book.
This presentation explains the Capital Budgeting Techniques including Payback Period, NPV, IRR, Modified IRR, Profitability Index. It further explains the capital budgeting process and the types of projects
The power point explains the concept of simple interest and compound interest.It also explains the development of the formula.It is made for VIIIth standard S.S.C text book.
This presentation explains the Capital Budgeting Techniques including Payback Period, NPV, IRR, Modified IRR, Profitability Index. It further explains the capital budgeting process and the types of projects
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An introductory talk on scientific computing in Python. Statistics, probability and linear algebra, are important aspects of computing/computer modeling and the same is covered here.
In this talk, we will discuss the concept of data structures and some of the common properties. We will also look at a few sample programs in Python, which we will run during the session and analyse.
The motivation of this talk would be to help us understand the need for data structures and what is responsible for the fast web-search
provided by the google search engine.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
The Art Pastor's Guide to Sabbath | Steve ThomasonSteve Thomason
What is the purpose of the Sabbath Law in the Torah. It is interesting to compare how the context of the law shifts from Exodus to Deuteronomy. Who gets to rest, and why?
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
This is a presentation by Dada Robert in a Your Skill Boost masterclass organised by the Excellence Foundation for South Sudan (EFSS) on Saturday, the 25th and Sunday, the 26th of May 2024.
He discussed the concept of quality improvement, emphasizing its applicability to various aspects of life, including personal, project, and program improvements. He defined quality as doing the right thing at the right time in the right way to achieve the best possible results and discussed the concept of the "gap" between what we know and what we do, and how this gap represents the areas we need to improve. He explained the scientific approach to quality improvement, which involves systematic performance analysis, testing and learning, and implementing change ideas. He also highlighted the importance of client focus and a team approach to quality improvement.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Cambridge International AS A Level Biology Coursebook - EBook (MaryFosbery J...
A basic idea
1. A basic idea
- Ashok
Govindarajan
20-12-2017 Technology sharing series 1
2. Contents
20-12-2017 Technology sharing series 2
• 2 basic formulae
• Simple Interest
• Compound Interest
• Compound interest computation
• The fundamental idea
• Acknowledgements and References
3. 2 basic formulae
20-12-2017
Technology sharing series 3
1 +
1
𝑛
𝑛
n =1 : result is 1
n=2 : result is 9/4
n=3 : result is 64/27
.
.
.
.
n = 100 : result is (1.01)^100
= 2.7048; small number in-spite
of n= 100
1 + 𝑛 𝑛
n =1 : result is 1
n=2 : result is 9
n=3 : result is 64
.
.
.
.
n = 100 : result is (101)^100
= large number
4. Simple Interest – example and calculation
20-12-2017
Technology sharing series 4
Jan 1st /2015 Jan 1st /2016 Jan 1st /2017
Amount in
account is A =
P+ I, where P is
the principal
and I is the
interest
Re.1;
Principal is
Re.1, amount
is Re.1;
Interest yet to
start
accumulating,
hence 0.
Re.2;
Principal is
Re.1, Amount
is Re.2; Total
Interest is Re.1
Re.3;
Principal is
Re.1, Amount
is Re.3; Total
Interest is Re.2
Consider the case of simple interest offered by a Bank. The bank is a very
generous and offers 100% interest . So, the below table depicts the amount of
money present in the account over 3 years
Takeaway : The principal never changes in simple interest, at the start of the second or
the third year. It is always Re. 1! Interest is always added at the start of the new year.
Time series is : 1,2,3,4,5,6……
5. Compound Interest – example and
calculation
20-12-2017
Technology sharing series 5
Jan 1st /2015 Jan 1st /2016 Jan 1st /2017
Amount in
account
Re.1;
Principal is
Re.1, amount
is Re.1;
Interest yet to
start
accumulating,
hence 0.
Re.2;
Principal is
Re.2, Amount
is Re.2; Total
Interest is Re.1
Re.4;
Principal is
Re.4, Amount
is Re.4; Total
Interest is Re.3
Consider the case of compound interest offered by the same bank. The bank is a
very generous and offers 100% interest. So, the below table depicts the amount
of money present in the account over 3 years
Takeaway : The principal is updated in compound interest, at the start of the second and
the third year. Principal becomes the amount at the start of every new year.
The interest is added once a year as in the case of simple interest. Time series is
1,2,4,8,16, 32…..
6. Compound Interest – example and
calculation, continued
20-12-2017
Technology sharing series 6
The bank is compounding interest annually……Can it compound once every six
months?
Once every 3 months?
Once every month?
Once every day?
Once every hour?
Once every second, milli second, micro second and so on…..
Let us look at an example :
In the time series for the compound interest, let us magnify on the portion
between 1 and 2, that is the first year.
7. Compound Interest – example and calculation,
continued
20-12-2017 Technology sharing series 7
• Formula to compute compound interest is : A = P*(1+ {r/100}) ^ n
• r = 100 % for n = 1; so r = 50% for n = 2 and so on. r = 100/n
• n = 1 is 1 year, n = 2 is 6 months, n = 12 is 1 month
• So, in this context the above formula reduces to 1*(1+{1/n}) ^ n
• Once every year [n = 1 in the above formula]
• 1 --> 2.0000000000000000000000000000000
• Once every month [n = 12 in the above formula]
• 12 --> 2.6130352902246781602995330443549
• Once every hour [n = 365*24 in the above formula]
• 365*24 --> 2.7181266916204521189161380653965
• Once every second [n = 365*24*60 in the above formula]
• 365*24*60*60 -->2.7182817853609708212635582662979
• Once every millisecond, micro, nano
WHERE ARE WE HEADING? ANY IDEAS/GUESSES?
WILL WE GET INFINITE AMOUNT OF MONEY OR FINITE AMOUNT OF MONEY?
Shall we take a look at slide 3, again?
8. The fundamental idea
20-12-2017
Technology sharing series 8
The two formulae in slide 3 represents 2 cases : As “n” increases, the value of the formula
decreases and in the other case the value increases.
Compound interest computation refers to the case where it decreases with
increase in “n “
This idea is one of the basis for introducing limits in class 12 state board syllabus. An example
formula for limits, which is relevant here is:
Coming back to our case, the value will converge to “e” which is approx. equal to
2.71828, based on the above formula
So, even if compouded “continously” in time, the bank cannot offer more than 171.828 %
interest. There is a “LIMIT”
Understanding LIMITS could facilitate the better understanding of Calculus. It is one of the
building blocks
lim
𝑛→∞
1 +
1
𝑛
𝑛
= 𝑒
Limits
As n -> infinity, 1/n -> 0