Easy FM Quizes

Series and Progressions

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[h]

Series and Progressions #1
[q] Sum of the first 5 natural numbers?
[a] 15
\frac 5 2 (1+5) = \frac n 2 (t_1 +t_n)
[q] Sum of the first 7 natural numbers?
[a]28
\frac 7 2 (1+7) = \frac n 2 (t_1 +t_n)
[q] Sum of the first 12 natural numbers?
[a] 78
\frac {12} {2} (1+12) = \frac n 2 (t_1 +t_n)
[q] Sum of the first 100 natural numbers?
[a] 5050
\frac {100} {2} (1+100) = \frac n 2 (t_1 +t_n)
[q] Sum of the first n natural numbers?
[a] \frac n 2 (t_1 +t_n)

[q]Arithmetic progression.
Term 1 = 10. Difference = 7.
Term 7?
[a]52
10 +6(7)
t_n = t_1+(n-1)d

[q]Arithmetic progression.
Term 1 = 2. Difference = 7.
Term 3?
[a]16
2 +2(7)
t_n = t_1+(n-1)d

[q]Arithmetic progression.
Term 1 = 5. Difference = 4.
Term 8?
[a]33
5 +7(4)
t_n = t_1+(n-1)d

[q]Arithmetic progression.
Term 1 = 8. Difference = 5.
Term 4?
[a]23
8 +3(5)
t_n = t_1+(n-1)d

[q]Formula for the nth term of an arithmetic progression, given the first term, the number of terms, and the difference?
[a] t_n = t_1+(n-1)d

[q]Sum of the first 20 even numbers?
[a]420
\frac{20}{2} (2 + 2 + (19)2)
S_n = \frac{n}{2} (t_1 + t_n)= \frac{n}{2} (t_1 + t_1 + (n-1)d)

[q]Sum of the first 50 even numbers?
[a] 2550
\frac{50}{2} (2 + 2 + (49)(2)
S_n = \frac{n}{2} (t_1 + t_n)= \frac{n}{2} (t_1 + t_1 + (n-1)d)

[q]Sum of the first 10 multiples of 3?
[a]165
\frac{10}{2} (3 + 3 + (9)3)
S_n = \frac{n}{2} (t_1 + t_n)= \frac{n}{2} (t_1 + t_1 + (n-1)d)

[q]Sum of the first 7 multiples of 5?
[a]140
\frac{7}{2} (5 + 5 + (6)5)
S_n = \frac{n}{2} (t_1 + t_n)= \frac{n}{2} (t_1 + t_1 + (n-1)d)

[q]Sum of squares of the numbers from 1 to 7?
[a] 140
\frac {(7)(8)(15)}{6} = \frac{(n)(n+1)(2n+1)}{6}

[q]Sum of squares from n=1 to 6?
[a]91
\frac{(6)(7)(13)}{6}= \frac{(n)(n+1)(2n+1)}{6}
[q]Sum of squares from n=1 to 24?
[a]4900
\frac{(24)(25)(49)}{6}=\frac{(n)(n+1)(2n+1)}{6}
[q]Sum of squares from n=1 to 12?
[a]650
\frac{(12)(13)(25)}{6}=\frac{(n)(n+1)(2n+1)}{6}
[q]Sum of squares from n=1 to 10?
[a]385
\frac{(10)(11)(21)}{6}=\frac{(n)(n+1)(2n+1)}{6}

[q] Sum of the first 5 natural numbers?
[a] 15
\frac {5} {2} (1+5) = \frac n 2 (t_1 +t_n)

[q]Arithmetic progression.
Term 1 = 3. Difference = 4.
Term 100?
[a]399
3 +99(4)
t_n = t_1+(n-1)d

[q] Sum of the first 50 natural numbers?
[a] 1275
\frac {50} {2} (1+50) = \frac n 2 (t_1 +t_n)

[q]Sum of the first 35 even numbers?
[a]1260
\frac{35}{2} (2 + 2 + (34)2)
S_n = \frac{n}{2} (t_1 + t_n)= \frac{n}{2} (t_1 + t_1 + (n-1)d)

[q]Arithmetic progression.
Term 1 = 10. Difference = 13.
Term 200?
[a]2597
10 +199(13)
t_n = t_1+(n-1)d

[q]Sum of squares from n=1 to 100?
[a]338350
\frac{(100)(101)(201)}{6}= \frac{(n)(n+1)(2n+1)}{6}

[q]Sum of the first 10 multiples of 3?
[a]165
\frac{10}{2} (3 + 3 + (9)3)
S_n = \frac{n}{2} (t_1 + t_n)= \frac{n}{2} (t_1 + t_1 + (n-1)d)

[q]Arithmetic progression.
Term 1 = 2. Difference = 5.
Term 10?
[a]47
2 +9(5)
t_n = t_1+(n-1)d

[q] Sum of the first 1000 natural numbers?
[a] 500500
\frac {1000} {2} (1001) = \frac n 2 (t_1 +t_n)

[q]Sum of squares from n=1 to 9?
[a]285
\frac{(9)(10)(19)}{6}= \frac{(n)(n+1)(2n+1)}{6}

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[h]

Series and Progressions #2

[q]Geometric Progression
First term = 5000. Common ratio = 1.07
30 term?
[a] t_n = t_1 r^{n-1} = 5000 (1.07^{29}) = 35571

[q]Geometric Progression
First term = 1000. Common ratio = 1.03
20th term?
[a] t_n = t_1 r^{n-1} = 1000 (1.03^{19}) = 1753.51

[q]Geometric Progression
First term = t_1 Common ratio = r
n^{th} term?
[a] t_n = t_1 r^{n-1}

[q]Arithmetic progression.
Term 1 = 5. Difference = 4.
Term 8?
[a]33
5 +7(4)
t_n = t_1+(n-1)d

[q]Arithmetic progression.
Term 1 = 8. Difference = 5.
Term 4?
[a]23
8 +3(5)
t_n = t_1+(n-1)d

[q]Geometric Progression
First term = 1. Common ratio = 1.0525
15th term?
[a] t_n = t_1 r^{n-1} = 1 (1.0525^{14}) = 2.046

[q]Geometric progression with first term = 20, common ratio 1.01
Sum of first 40 terms?
[a] 977.73
S_{40} = 20* \frac{1.01^{40} -1}{1.01-1}
S_n = t_1 \frac{r^n -1}{r-1}

[q] Sum of first n terms of geometric progression.
S_n = t_1 \frac{r^n -1}{r-1} \text{ or } t_1 \frac{???}{1-r}
[a] 1-r^n
[q] Sum of the first 5 natural numbers?
[a] 15
\frac 5 2 (1+5) = \frac n 2 (t_1 +t_n)
[q] Sum of the first 12 natural numbers?
[a] 78
\frac {12} {2} (1+12) = \frac n 2 (t_1 +t_n)
[q]Geometric progression with first term = 100, common ratio 1.06
Sum of first 60 terms?
[a] 53312.82
S_{60} = 100* \frac{1.06^{60} -1}{1.06-1}
S_n = t_1 \frac{r^n -1}{r-1}

[q]Sum of first n terms of geometric progression.
S_n = ??? \frac{r^n -1}{r-1} \text{ or } t_1 \frac{1-r^n}{1-r}
[a] t_1

[q]Geometric Progression
First term = 10. Common ratio = 1.001
100 term?
[a] t_n = t_1 r^{n-1} = 10 (1.001^{100}) = 11.05

[q]Geometric progression with first term = 10, common ratio 1.001
Sum of first 100 terms?
[a] 10511.57
S_{100} = 100* \frac{1.001^{100} -1}{1.001-1}
S_n = t_1 \frac{r^n -1}{r-1}

[q]Sum of first n terms of geometric progression.
S_n = t_1 \frac{r^n -1}{r-1} \text{ or } t_1 \frac{1-r^n}{???}
[a] 1-r
[q] Sum of the first 7 natural numbers?
[a]28
\frac 7 2 (1+7) = \frac n 2 (t_1 +t_n)
[q]Sum of first n terms of geometric progression with first term = t_1
S_n = t_1 \frac{r^n -1}{???} \text{ or } t_1 \frac{1-r^n}{1-r}
[a] r-1

[q]Geometric Progression
First term = 1. Common ratio = 1.0525
15th term?
[a] t_n = t_1 r^{n-1} = 1 (1.0525^{14}) = 2.046

[q]Geometric Progression, first term t1, common ratio r
Sum of first n terms?
[a] t_1 \frac{r^n -1}{r-1} \text{ or } t_1 \frac{1-r^n}{1-r}

[q]Geometric Progression
First term = 1. Common ratio = 1.0025
100 term?
[a] t_n = t_1 r^{n-1} = 1 (1.0025^{100}) = 1.28

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Interest Theory

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[h]

Interest Theory #1
[q]v is the ??? of 1+i
[a]reciprocal
v = \frac{1}{1+i}= (1+i)^{-1}
[q] 1+i = 1.003
What is v?
[a] 0.997
[q]??? is the reciprocal of 1+i
[a]v
[q]v is the reciprocal of ???
[a]1+i
[q] What is d in terms of v?
[a] d is the ones compliment of v
d=1-v
[q] What is v in terms of d?
[a] v is the ones compliment of d
v=1-d
[q]v=0.99 \quad d=???
[a]0.01
[q]i = 0.12. v = ?
[a]0.8929
[q]v=0.99\quad d=???
[a]0.01
[q]i = 0.02. v = ?
[a]0.9804
[q]i = 0.06. d = ?
[a]0.05660
d = \frac{i}{(1+i)}
[q] The force of interest = 0.001. What is i?
[a] i=e^{\delta}-1 = 0.001
[q]i = 0.01. v = ?
[a]0.9901
v = \frac{1}{1+i}= (1+i)^{-1}
[q]d = 0.04. i = ?
[a] 0.0417
i = \frac{d}{(1-d)}
[q]d = 0.02 i = ?
[a] 0.0204
i = \frac{d}{(1-d)}
[q]v=0.98\quad d=???
[a]0.02
[q]i = 0.02. v = ?
[a]0.9804
[q] i=.01
What is the force of interest (\delta )?
[a] \delta = \ln(1.01)
[q]v=0.92\quad d=???
[a]0.08
[q]i = 0.01. d = ?
[a]0.00990
[q]d = 0.10. i = ?
[a] 0.1111
i = \frac{d}{(1-d)}
[q]d = 0.08. i = ?
[a] 0.0870
i = \frac{d}{(1-d)}
[q]d = 0.06. i = ?
[a] 0.0638
i = \frac{d}{(1-d)}
Or solve for v, then solve for i.
[q]v=0.85\quad d=???
[a]0.15
[q]i = 0.09. v = ?
[a]0.9174
v = \frac{1}{1+i}
[q]i = 0.08. v = ?
[a]0.9259
v = \frac{1}{1+i}
[q]i = 0.0525. v = ?
[a]0.9501
v = \frac{1}{1+i}=(1+i)^{-1}
[q]i = 0.05. d = ?
[a]d = \frac{i}{(1+i)}
Easier to just solve for v, then solve for d.
v = (1+i)^{-1} = 0.9524
d = 1-v = 0.0476
[q]i = 0.04. d = ?
[a]0.03846
d = \frac{i}{(1+i)}
[q]i = 0.03. d = ?
[a]0.02913
d = \frac{i}{(1+i)}
[q]i = 0.02. d = ?
[a]0.01961
d = \frac{i}{(1+i)}
[q]effective rate of interest, in functional terms
[a] i_t=\frac{a(t)-a(t-1)}{a(t-1)}
[q]effective rate of discount, in functional terms
[a] i_t=\frac{a(t)-a(t-1)}{a(t)}
[q] d=???v
[a]i
[q] d= i???
[a]v
[q]a(1)=???
[a]1+1
[q]a(0)=???
[a]1
[q] \delta = \ln(???)
[a] 1+i
[q] What is i in terms of v?
[a] i=\frac {1}{v} -1
[q] What is v in terms of i?
[a] \frac {1}{1+i}
[q] What is d in terms of i?
[a] \frac{i}{1+i}
[q] What is v in terms of \delta ?
[a] e^{-\delta}
[q] What is i in terms of \delta ?
[a] e^{\delta}-1
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Options

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[h]

Options #1
[q] Draw the payoff/profit diagram for a long forward
[a] Long Forward
[q] Draw the payoff/profit diagram for a short forward.
[a]Short Forward
[q] Draw the payoff/profit diagram for a long call.
[a]Long Call
The risk of a buyer of a long call is limited to the premium paid, but the maximum profit is unlimited.
[q] Draw the payoff/profit diagram for a short(written) call.
[a]Short Call
The seller of a call recieves a profit in the premium recieved; but the potential loss is unlimited event of a rise in the price of the underlying asset.
[q] Draw the payoff/profit diagram for a long put.
[a]Long Put
The buyer of a put has the right to sell the underlying asset at the strike price. Should the price fall, the put buyer can buy the asset on the market for the market price, then sell it at the (higher) strike price.
[q] Draw the payoff/profit diagram for a short put.
[a]Short Put

The seller of a put recieves a premium, but has the obligation to but the underlying asset at the strike price, at the expiration date of the option.
[q]Buyers are often referred to as ??? and sellers are often referred to as writers.
[a]holders
[q]Buyers are often referred to as holders and sellers are often referred to as ???
[a]writers
[q]An ???, is a contract giving the buyer the right but not the obligation to buy or sell an underlying asset at a specific price on or before a certain date.
[a]option
[q]An option is a contract giving the buyer the ??? but not the obligation to buy or sell an underlying asset at a specific price on or before a certain date.
[a]right
[q]An option is a contract giving the buyer the right but not the ??? to buy or sell an underlying asset at a specific price on or before a certain date.
[a]obligation
[q]The first buyer of options was Greek philosopher ???. Predicting that the next years olive crop would be large, he purchased the right to use olive presses for the next year. When the next year came, and olives were abundant, he rented the presses for a profit.
[a]Thales of Miletus
[q]For a ???, the buyer has the long position and the seller has the short position.
[a]call option
[q]For a call option, the ??? has the long position and the seller has the short position.
[a]buyer
[q]For a call option, the buyer has the long position and the ??? has the short position.
[a]seller
[q]For a ??? option, the buyer has the short position and the seller has the long position.
[a]put
[q]For a put option, the buyer has the ??? position and the seller has the long position.
[a]short
[q]For a put option, the buyer has the short position and the seller has the ??? position.
[a]long
[q]Buyers of puts hope that the price of the stock will ??? before the option expires.
[a]fall
[q]Buyers of calls hope that the stock will ??? substantially before the option expires.
[a]increase
[q]A ??? gives the holder the right to sell an asset at a certain price within a specific period of time.
[a]put
[q]A ??? gives the holder the right to buy an asset at a certain price within a specific period of time.
[a]call
[q]A put option is in-the-money when the share price is ??? the strike price.
[a]below
[q]The total cost of an option is called the ???, which is determined by factors including the stock price, strike price and time remaining until expiration.
[a]premium
[q]When an option expires, it ???
[a]no longer exists, and has no value
[q]The price at which an underlying stock can be purchased or sold is called the ???
[a]strike price
[q]Puts are very similar to having a ??? position on a stock.
[a]short
[q]Buying a ??? option is called a floor.
[a]put
[q]Buying a put option is called a ???.
[a]floor
[q]Buying a ??? option is called a cap.
[a]call
[q]Buying a call option is called a ???.
[a]cap
[q]Writing an option when there is a corresponding long position in an asset is called ??? writing, option overwriting, or selling a covered call.
[a]covered
[q]Writing an option when there is a corresponding long position in an asset is called covered writing, option ???, or selling a covered call.
[a]overwriting
[q]Writing an option when there is a corresponding long position in an asset is called covered writing, option overwriting, or selling a ??? call.
[a]covered
[q]When writer does not have a position in an underlying asset, it is known as ??? writing.
[a]naked
[q]As the strike price ??? the call premium decreases and the put premium increases.
[a]increases
(draw this out)
[q]As the strike price increases the call premium ??? and the put premium increases.
[a]decreases
(draw this out)
[q]As the strike price increases, the call premium decreases and the put premium ???.
[a]increases
(draw this out)
[q]Short Positions

  1. ???
  2. Written Call
  3. Purchased Put

[a]Short Forward
[q]Short Positions

  1. Short Forward
  2. ???
  3. Purchased Put

[a]Written Call
[q]Short Positions

  1. Short Forward
  2. Written Call
  3. ???

[a]Purchased Put
[q]Long Positions

  1. ???
  2. Purchased Call
  3. Written Put

[a]Long Forward
[q]Long Positions

  1. Long Forward
  2. ???
  3. Written Put

[a]Purchased Call
[q]Long Positions

  1. Long Forward
  2. Purchased Call
  3. ???

[a]Written Put
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