Module 1: Time Value of Money Flashcards

1
Q

what is a(0)

A

1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

what is A(t)

A

k*a(t) or k/v(t)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

how to calculate interest earned?

A

A(n)-A(n-1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

exact simple interest method

A

ignores leap years, assume every year has 365 days, t = # of days/365

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

ordinary simple interest method

A

approximates by rounding full months to 30 days each and each year to 12 x 30 = 360 days, t = approximate # of days/360

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

bankers rule

A

counts # of days exactly but uses 360 as # of days in a year, t = number of days/360

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

a(t) for simple interest

A

1 + it

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

v(t) for simple interest

A

1 - it

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

a(t) for compound interest

A

(1+i)^t, t>=0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

v(t) for compound interest

A

(1-i)^t

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

what happens to a(t) between 0

A

a(t) for simple interest > a(t) for compound interest

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

what happens to a(t) at t = 0 and t = 1

A

a(t) for simple interest = a(t) for compound interest

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

Effective interest rate of period (t1, t2)

A

i[t1, t2] = interest earned during period/amount at beginning of period = A(t2) - A(t1)/A(t1) = a(t2)-a(t1)/a(t1)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

what is the accumulation factor

A

(1+i). This is the growth factor

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

effective rate of discount in nth year

A

=discount (interest) earned in nth year / amount at the end of nth year
= A(n) - A(n-1) / A(n)
= a(n) - a(n-1) / a(n)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

EIR

A

(1+i/n)^n - 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

EDR

A

(1-i/n)^-n - 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

a(t) when t < 0

A

a(t) < 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

a(t) when t > 0

A

a(t) > 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

v(t) for simple discount

A

v(t) = 1 - dt, 0 <= t < 1/d

21
Q

are effective rates with simple interest increasing/decreasing with time?

A

decreasing

22
Q

are effective rates with simple discount increasing/decreasing with time?

A

increasing

23
Q

v(t) for compound discount

A

(1-d)^t for t>=0

24
Q

effective rate formula for i

A

(1+(i/m))^m - 1

25
what is i^(m)
annual effective rate compounded m times
26
what is i^(m)/m
"quarterly" effective rate
27
effective rate formula for d
1-(1-d/m)^m
28
going from effective interest rate to discount rate
i = d / (1-d)
29
going from effective discount rate to interest rate
d = i / (1 + i)
30
how does I^m change as m increases
decreases at a decreasing rate
31
how does d^m change as m increases
increases at a decreasing rate
32
how does i^m and d^m change as m changes
they are both approaching the same limit, i^m as m is small and d^m as m is big
33
what is δ
constant force of interest; annual nominal rate of interest with continuous compounding
34
formula for δ
= i^(infinity) = ln(1+i)
35
what is δt
instantaneous relative change in accumulation function
36
what is a(t) for δ
a(t) = e^δt
37
what is a(t) for δt
a(t) = e^(integral from time 1 to time 2 of δt)
38
what is p(t)
price index function
39
what is ã
real accumulation function
40
what is p(0)
1
41
formula for real accumulation function ã
ã = a(t) / p(t)
42
what is p(t) formula
(1+r)^t
43
what is ã(t) formula
(1 + ĭ)^t
44
what is r
annual effective rate of inflation
45
what is ĭ
annual effective rate of "real" interest
46
what is ĭ formula
i - r / 1 + r
47
how to solve for ĭ^(m)
ĭ^(m)/m = i^(m)/m - r^(m)/m / 1 + r^m / m
48
what does payments of $100 at time t mean?
$100 / (1+i)^t
49
what is i^(infinity) = δ formula in general
derivative of a(t) / a(t) = d/dt of ln(a(t))