Výsledek obrázku pro euler number

https://www.youtube.com/watch?v=AuA2EAgAegE

Pre-listening tasks.

1.      What is a mathematical constant? …………………………………………..

2.      Complete the missing information.

-         Archimedes’constant …..

-         ………………………. e

-         Pythagora’s constant …..

-         ……………………….. i

-         The Feigenbaum constants …

-         Apéry’s constant  ………..

-         The golden ratio   ………

-         The Euler-Mascheroni constant …

-         …………………………………..

-         ………………………………….

3.      How is the constant e different from π or √2? ………………………………………………..
 4.  What is the constant e related
to?.................................................................
 5. What is compound interest? …………………………………………………

6)     Imagine that your bank is extremely generous. You have 1 pound on your account and they
offer you a 100% interest. How much money will you get if this interest is paid annually ?…………………..

7)     If you interest is 50% in every six months, is it better or worse? Why? ………………

8)     What happens if you do that more often? What about every month, week or day? How much will
you earn? …………………………………………………………………………………….

9)     How would you define continuous interest?……………………………………..

10) What interest can you get nowadays on savings accounts and how is it calculated?
……………………………………………………………………………………….

Listening. Now listen to the talk and note other important information about constant e.  (when,
why, how, where, what)

A Visual Guide to Simple, Compound and Continuous Interest Rates

https://betterexplained.com/articles/a-visual-guide-to-simple-compound-and-continuous-interest-rate
s/

1.      Study the first part and try to explain the underlined words – you can use a synonym.

2.      Complete the missing items in a survey.

Interest rates are confusing, despite their ubiquity. This post takes an in-depth look at why
interest rates behave as they do.

Understanding these concepts will help understand finance (mortgages & savings rates), along with
the omnipresent e and natural logarithm. Here’s our table:

Words to complete:   growth    inflation   instant     principal   temperature     yield

                                  fixed        annual

                                               Term

                                              Formula

                                        Description & Usage

Simple

\displaystyle{P \cdot (1 + r \cdot n)}

a)…., non-growing return (bond coupons)

Compound
(b)…….)

\displaystyle{P \cdot (1 + r)^n}

Changes each year (stock market, c)………)

Compound
(n times per year)

\displaystyle{P \cdot (1 + r/n)^{nt}}

Changes each month/week/day (savings account)

Continuous d)……..

\displaystyle{P \cdot e^{rt}}

Changes each e)…… (radioactive decay, f)………)

APR

Annual Percentage Rate (compounding not included)

APY

Annual Percentage g)……….. (all compounding effects included)
  * P = h)……., your initial investment (i.e., $1,000)
  * r = interest rate (i.e., 5% per year)
  * n = number of time periods (i.e., 3 years)

 3. Have a look at graphs which show several kinds of interests. Try to suggest some key words for
each graph and explain what happens. Add signposting language and present those three graphs.
 4. Try to consider and answer three questions. Explain your answers.

-         Is a 4.5 APY better than a 4.4 APR, compounded quarterly? ………………..

-         Should I pay my mortgage at the end of the month, or the beginning?.............

-         Should I use several small payments, or one large payment?.............................


a)

compound interest graph

b)

simple interest

c)

compound interest factory