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Unit 3 Flashcards

1
Q

Calculating the value of a given capital in a future

moment is called …

A

compounding

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2
Q

Calculating the value of a given capital in an earlier moment in time is called …

A

discounting

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3
Q

Annuities are defined as …

A

the calculated value of a set of capitals due in different moments in time.

sets of capitals due in different moments in time.

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4
Q

Annuities are …

A

a sequence of periodic payments made at equal intervals of time.

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5
Q

The elements of an annuity are …

A
  1. Payment interval
  2. Term of the annuity
  3. Actual payment of the annuity
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6
Q

The payment interval is …

A

the time that elapses between two consecutive capitals or terms.

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7
Q

Constant period annuities are …

A

annuities where the period is the same for the entire duration of the annuity.

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8
Q

“n” is …

A

the number of terms of the annuity.

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9
Q

Annuities can be grouped …

A
  1. According to the relation between the capitals
  2. According to the duration of the rent
  3. According to the moment in which the capitals are received
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10
Q

There are _____ types of annuities that are grouped according to the relation between the capitals, and they are:

A

2

  1. Constant annuity
  2. Variable annuity
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11
Q

Constant annuity is where ….

A

all capitals are equal

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12
Q

Variable annuity is where …

A

capitals are different from each other

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13
Q

Two of annuities that are grouped according to the duration of the rent are:

A
  1. Temporary annuity

2. Perpetual annuity

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14
Q

A temporary annuity is when …

A

when n is a natural number.

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15
Q

A perpetual annuity is when …

A

when n is infinite.

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16
Q

Types of annuities that are grouped according to the moment in which the capitals are received are:

A
  1. Advance or prepaid annuities

2. Overdue or postpaid annuities

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17
Q

Advance or prepaid annuities are when the …

A

capital is received at the beginning of the period.

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18
Q

Overdue or postpaid annuities are those where

A

capitals are collected at the end of the period.

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19
Q

Advance annuities are also called

A

prepaid annuity

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20
Q

An overdue annuity is also called

A

postpaid annuity

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21
Q

The value of an annuity is the value of a capital dated at some specific moment which is equivalent to all the payments of the annuity.

A

True

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22
Q

Discounted value of the annuity (DV) is defined as

A

the value of the annuity dated at the beginning of the term (t0).

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23
Q

Compounded value of the annuity (CV) is defined as

A

the value dated at the end of the term (tn).

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24
Q

Present value of the annuity (PV)

A

is the value of that annuity at the present moment.

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25
Q

The discounted value and the present value coincide if

A

the beginning of the annuity is today (immediate annuity)

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26
Q

The beginning of an annuity can be later than today (deferred annuity)

A

True

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27
Q

A deferred annuity is when

A

the beginning of the annuity is later than today

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28
Q

An immediate annuity is when

A

the beginning of the annuity is today

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29
Q

In an IMMEDIATE ANNUITY, DV=PV and CV=DV(1+i)^n

A

True

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30
Q

DV means

A

discounted value or beginning of the annuity

31
Q

PV means

A

Present value or Today

32
Q

In a DEFERRED ANNUITY, DV=PV(1+i)^-k and CV=DV(1+I)^N

33
Q

CV means end of term

34
Q

In an ANTICIPATED ANNUITY, PV=DV(1+i)^k and CV=DV(1+I)^N

35
Q

A deferred annuity and anticipated annuity have the same compounded value (CV) formula

36
Q

For most of the operations that involve an annuity, the payments are due at the end of each period.

37
Q

Annuities paid at the end of each period are called

A

an ordinary annuity/immediate annuity/ post-payable annuity.

38
Q

Some examples of ordinary annuities are

A
  1. Wages paid to the workers
  2. Mortgage payments
  3. Coupons of a bond
39
Q

an ordinary annuity is also called

A

an immediate annuity or a post-payable annuity.

40
Q

An annuity due/ pre-payable annuity is one where

A

the payments are due at the beginning of each period.

41
Q

Some examples of annuities due are

A

house rents or leasing payments

42
Q

We can verify that an annuity due is the same as an immediate annuity anticipated in one period.

43
Q

The relation between an annuity due and an immediate annuity is

DV Annuity due = DV immediate annuity*(1+i)

44
Q

When all the payments of the annuity are equal, we are dealing with a __________

A

constant annuity

45
Q

The initial value of a constant annuity would be the result of discounting all the capitals to t=0.

46
Q

The discounted value (DV) of a constant annuity is equal to the sum of the elements of a geometric progression.

A

True

C*∑ 1/(1+i)^t, where t begins at 1

47
Q

To calculate the discounted value in excel, the formula is

A

DV = C*PV, where PV = an)i = (1-(1+i)^-n)/i

48
Q

PV = an)i = (1-(1+i)^-n)/i

49
Q

In Excel, PV = (rate;nper;-C) or C*PV(rate;nper;-1)

A

FALSE

DV = (rate;nper;-C) or C*PV(rate;nper;-1)

50
Q

The compounded value (CV) of a temporary constant annuity would be the result of accumulating
the discounted value until the end.

51
Q

In a temporary constant annuity, CV =

A

CV = DV(1+i)^n

52
Q

Perpetual constant annuities are …

A

when the term of the annuity is constant and not known

when we assume that the payments of the annuity will continue forever

When the term of the annuity is infinity (t=∞).

53
Q

Perpetual constant annuities are when the term of the annuity is constant and not known

54
Q

The discounted value of a perpetual annuity is DV = a∞)i or DV = C/i

A

True

DV = a∞)i

55
Q

The value of 𝑎n)i for infinitive terms is 1/i

56
Q

There is no “end of annuity”, it does not make sense to talk about the compounded value/ final value of perpetual annuities.

57
Q

When the annuities are different for each period, we are dealing with a __________

A

varying annuity.

58
Q

If the capitals of a varying annuity do not have any known relationship between them, we can not apply any rule that provides us with the calculation of the value of the annuity.

59
Q

In a varying annuity, because no rule can be applied for capitals without a known relationship, the capital value will have to be calculated by taking all the capitals of the annuity up to the time of the valuation and adding them at that moment.

60
Q

If the capitals of a varying annuity have some kind of mathematical relationship between them, it may be possible to find abbreviated calculation formulas.

61
Q

Two types of relationships between capitals of varying annuities are:

A
  1. Those that evolve following an arithmetic progression

2. Those that evolve following a geometric progression.

62
Q

In annuities with payments varying in arithmetic progression, the difference between two consecutive payments is a constant (d).

A

True

d = Ct+1 - Ct

63
Q

We can compute the value of any payment of an annuity with payments varying in arithmetic progression if we know the value of any other payment and the value of the difference.

A

True because the difference b/w annuities with arithmetic progression is constant.

Ct = C1 + (t-1)*d

64
Q

The discounted value of an annuity whose payments vary in arithmetic progression is equal to (without demonstration): DV = (C1 * n * d + d/i)PV - (nd)/i

A

True

Where 𝐶1 is the first payment of the annuity;
𝑛 is the term of the annuity;
d is the difference between two consecutive payments;
i is the rate of interest, compounding on the payment interval

65
Q

In the case of a perpetuity whose payments vary in arithmetic progression (without demonstration), the discounted value would be: DV = (C1 + d/i) * i/1

66
Q

In annuities with payments that vary in geometric progression, whose payments grow (or decrease) in a constant growth (decreasing) rate g, the ratio between any given payment and the preceding payment will be equal to 1+g.

67
Q

In annuities with payments that vary in geometric progression, whose payments grow (or decrease) in a constant growth (decreasing) rate g, Ct+1 = Ct(1+g)

68
Q

In annuities with payments that vary in geometric progression, whose payments grow (or decrease) in a constant growth (decreasing) rate g, we can calculate the value of any payment if we know the value of the first payment and the value of g.

A

True

Ct = C1*(1+g)^(n-1)

69
Q

A fractional variable annuity would be an annuity …

A
  1. in which its terms are kept constant for a certain number of K periods
  2. after that number of periods, the capital, K + 1, would be obtained by applying a law of progression (arithmetic or geometric) with respect to the previous capital
  3. and that capital, K + 1, would remain constant during other K periods
  4. this pattern would be maintained until the end of the rent.
70
Q

An annuity which the terms are kept constant for a certain number of K periods, after which, the
capital, K + 1, would be obtained by applying a law of progression (arithmetic or geometric) with respect to the previous capital, and that capital, K + 1, would remain constant during other K periods (with this pattern would be maintained until the end of the rent) is called _________________.

A

Fractional varying annuity

71
Q

Typical examples of fractional varying annuities are …

A
  1. salaries: normally, the monthly salary is
    constant during the year; Once it is finished, a revision of it (usually geometric) is produced, which is kept constant again for one year until the next revision.
  2. rents
72
Q

Normally, this is constant during the year, and once the year is finished, a revision of it (usually geometric) is produced, which is kept constant again for another year until the next revision.

73
Q

A salary is an example of …

A

a fractional varying annuity

FM (11 decks)

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