FM Flashcards
1
Q
Prospective Method
A
forward-looking based on future cash flow
time-t outstanding loan balance
=
PV(remaining loan payments with i)
2
Q
Liquidity Preferance Theory / Opportunity Cost Theory
A
To persuade lenders to lend for a longer time, borrowers will have to pay higher interest rate as an incentive.
3
Q
weighted average of individual asset’s duration
A
Duration of Portfolio
4
Q
Annuity-Immediate Present Value
A
A angle n, with i. ( 1 - v^(n) ) / i
5
Q
Accumulation function for Constant Force of Interest
A
a(t) = e ^(delta * time)
6
Q
Duration of Portfolio
A
weighted average of individual asset’s duration
7
Q
Payer
A
party who agrees to pay the fixed rate and receive the variable rates
8
Q
a(t) = e ^(delta * time)
A
Accumulation function for Constant Force of Interest
9
Q
Terminology Bond Amortization:
Write-down (Premium Bonds)
Write-Up (Discount Bonds)
A
Loan Amortization: Principal Repaid
10
Q
Expectation theory
A
Interest rate for a long term investment provides future expectation for interest on short term investments
for example; consider 2 year loan with higher interest rate then a 1 year loan. Then one year from now the interest rate on the 1 year loan is expected to be higher than the current interest of the 1 year loan.
11
Q
Settlement dates
A
specified dates during the swap tenor when the interest payments are exchanged
12
Q
A(t) = A(0) * ( 1 - (d/m) )^(-mt)
A
Amount Function Nominal Discount Rate
13
Q
Loan Amoritization:
Pt = R * ( vn-t+1 )
A
Principal Repaid when R is level
14
Q
A
15
Q
A(t)
=
A(0)*(1 + i)t
A
Amount Function Effective Interest Rate
16
Q
S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i
A
Annuity-Immediate Accumulated Value
17
Q
Loan Amortization
A
repaying a loan with payments at regular intervals
18
Q
Coupons
A
Periodic interest payments which form an annuity
19
Q
Loan consist of what two components
A
1.) Interest Due
2.) Principal Repaid
20
Q
Write-Up for bond
A
Absolute value of write-down
Pt = | (Fr - C*(i)) * (vn-t+1) |
Discount Bonds
21
Q
First Order Modified Approx.
A
P(in)
=
P(io)*[1 - (in - io)(ModD)]
22
Q
S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d
A
Annuity-Due Accumulated Value
23
Q
A(t) = A(0)*(1 + i(t))
A
Amount Function Simple Interest
24
Q
Accumulation Function For Variable Force of Interest
A
a(t) = e^( integration from 0 to t) of delta
25
To find R (*swap rate*)
PV(Variable) = PV(Fixed)
26
a(t) = e^( integration from 0 to t) of delta
Accumulation Function For Variable Force of Interest
27
Annuity-Immediate PV to AV relation
(A angle n) =
(S angle n) \* ( v**n **)
28
Annuity-Due AV to PV relation
(S double-dot angle n) =
**(A double-dot angle n) \* ( ( 1 + i )n )**
29
delta = force of interest constant
ln (1 + i)
30
Discount Bond Formula
(Redemption - Price)
or
( C\*(i) - Fr ) \* (a angle n)
31
**Loan: *Outstanding Balance at time t***
***is equal to***
**Present value** at time t of it's remaining **cash flow** using the **loan's interest rate**
32
Notional amount
is the amount used to determine interest payments and swap payments;
to obtain interest payment or swap payment multiply the notional amount by the respective interest rate
**USUALLY THE LOAN AMOUNT**
33
(A(t) - A(t-1)) / A(t-1)
Effective Interest Rate
34
unit decreasing annuity
**(Da) angle n**
**=**
**[n - (a angle n)]**
**/**
**i**
35
Market Segmentation Theory
Borrowers and Lenders have different preferances on how long they want to borrow or lend for, thus causing different interest rates for different terms
36
A angle n, with i. ( 1 - v^(n) ) / i
Annuity-Immediate Present Value
37
Discounting Factor with (d)
( 1 - d )
38
( 1 - d )
Discounting Factor with (d)
39
Yield to Maturity
Level annual effective rate of interest which equates cash inflows to cash outflows
40
Amount Function Nominal Discount Rate
A(t) = A(0) \* ( 1 - (d/m) )^(-mt)
41
Annuity-Due Present Value
A double dot angle n, with i. ( 1 - v^(n) ) / d
42
Internal Rate of Return (IRR)
**also called yield rate**
**it's the rate that**
**produces a NPV of 0**
**also known as breakeven**
43
floating rate
also known as the variable rate
44
**[1 - ( (1 + k) / ( 1 +i ) )n]**
**/**
**( i - k)**
i = interest
k = number of payments in progression/percentage
n = number of total payments
Annuity-Immediate **geometric** progression
45
Implied Forward Rate
**(1 + sn)n**
**=**
**(1 + sn-1)n-1 \* (1 + f[n-1, n])**
46
(A(t) - A(t-1)) / A(t)
Effective Discount Rate
47
**Terminology Bonds Amortization:** Book value
**Loan Amortization:** Outstanding balance
48
(1 + i)^(-1) discount factor
(1 - d)
49
Effective Discount Rate defined as
(A(t) - A(t-1)) / A(t)
50
What is opportunity cost of capital?
**Rate of return**
**on an equally-risky asset**
**an investor could have earned**
**if he or she had NOT invested in the project.**
51
Given a price
lowest yield rate calculated is the minimum yield that an investor would earn
52
swap rate
known as the fixed rate
53
Calculating Interest Due
**It *(Interest Due)***
**=**
**(i) \* Bt-1 *(outstanding balance of previous period)***
54
Effective Interest Rate defined as
(A(t) - A(t-1)) / A(t-1)
55
Annuity-Immediate AV to PV relation
(S angle n)=
(A angle n) \* ( ( 1 + i )n )
56
# Bonds
**A bond's *BOOK VALUE* at time t**
**is equal to**
**Present value** at time t of its remaining **cash flows** using the bond's initial **yield rate**
57
Interest Rate Swap
agreement between two parties in which both parties agree to exchange a series of cash flow based on interest rates
58
Accreting Swap
if notional amount increases over time
59
Solving for bonds
Step 1: Identify Cash Flows
Step 2: Calculate the bond price as the PV of future cash flow at time 0
60
Spot Rates
Annual Effective Yield rates on a zero-coupon bond
Measures the yield from the beginning of the investment to the end of the single cash flow
61
Annuity-Immediate **geometric** progression
**[1 - ( (1 + k) / ( 1 +i ) )n]**
**/**
**( i - k)**
i = interest
k = number of payments in progression/percentage
n = number of total payments
62
Given a yield rate
the lowest price calculated is the maximum price that an investor would pay
63
**Terminology Bond Amortization:** Coupon payment
**Loan Amortization:** Loan Payment
64
Retrospective Formula
**Bt**
**=**
**L(1+i)t - R(s angle t)**
65
Write-Down for bond
same as principal repaid for loans
(Coupon Payment - Interest Earned)
**Pt = | (Fr - C\*(i)) \* (vn-t+1) |**
Premium bonds
66
Calculating Outstanding Balance end of period
**Bt *(Outstanding loan balance time t)***
**=**
**Bt-1 *(Outstanding loan balance time t-1)* - Pt *(Principal repaid time t)***
67
Redemption Value
One large payment at the end of the bond term
68
**Bonds:** Basic Formula
**P(*Price of bond*)**
**=**
**Fr(a angle n) [*Pv at time 0 of coupon payments over n periods]***
***+***
**C(vn) [*Pv at 0 of the redemption value*]**
69
Callable Bonds
Can be terminated before the redemption dates labeled as call dates
70
Settlement period
is the time between settlement dates
71
Block Payment Annuity
Method 1: Start with payments furthest from the comparison date
2: Make adjustments when moving towards the comparison date
72
Swap Term / Swap Tenor
specified period of the swap
73
Bond's Yield Rate
Rate of Return from investor's point of view
constant rate discounting future cash flow
74
P and Q formula for annuity increasing Arithmetic Progression
**PV = P\*(a angle n)**
**+**
**[(Q)\*((a angle n) - n( vn )] / i**
P = first term
Q = constant amount of increase for each payment
n = number of payments one period before the first payment date
75
Interest earned on a Bond calculation
(BOOK VALUE of PREVIOUS PERIOD) \* (YIELD RATE)
76
a(t) = (1 + i(t))
Accumulation Function Simple Interest
77
Finding additional payment
(Annuity Immediate AV)
**[** (pmt) \* (annuity-immediate(AV)) **]**
+
**[** (fv) - (PV)(AV factor) **]**
=
0
78
Face amount / par value
not a cash flow
used to determine coupon amount
79
Amount Function Effective Discount Rate
**A(t) = A(0) \* ( 1 - d )-t**
80
Bank Reserve Requirement
A central bank requires every bank to deposit and maintain a specific amount of money with it
81
**e(delta) * (t)**
**=**
**( 1 + i )t**
Relationship between Constant Force Of Interest and Constant effective interest rate
82
(1 - d)^(-1) accumulation factor
(1 + i)
83
What interest rate should be used to discount the cash flow for NPV?
**interest rate used =**
**cost of capital**
**or**
**opportunity cost of capital**
84
Premium Bond Formula
(Price - Redemption)
or
(Fr - C\*(i)) \* (a angle n)
85
Finding additional payment
(Annuity Immediate PV )
**[** (pmt) \* ( annuity - immediate( PV ) ) **]**
+
**[** (fv)(discounted factor) - ( PV ) **]**
=
0
86
Default Risk
Is the risk of loan defaulting, the borrower is unable to make a promised payment at the contracted time and for the contracted amount.
87
Amount Function Simple Interest
A(t) = A(0)\*(1 + i(t))
88
**A(t)**
**=**
**A(0) \* ( 1 + (i/m) )(mt)**
Amount Function Nominal Interest Rate
89
Loan Amortization
It = R \* (1−vn−t+1)
Interest Due when R is Level
90
**Bonds:** Premium/Discount Formula
P(*Price of bond*)
=
C(*Redemption value)*
+
(Fr - C \* i)(a angle n)
91
Prospective Method Formula
**Bt**
**=**
**R(a angle (n-t))**
92
Bank's Reserve
The actual amount of deposit with the central bank
93
Accumulation Function Simple Interest
a(t) = (1 + i(t))
94
Annuity-Immediate Accumulated Value
S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i
95
Force Of Interest
a'(t) / a(t)
96
Amount Function Effective Interest Rate
A(t) = A(0)\*(1 + i)^t
97
Receiver
counter party who receives the fix rate
and
pays the variable rate
98
Amortizing Swap
if the notional amount decreases over time
99
Amount Function Nominal Interest Rate
A(t) = A(0) \* ( 1 + (i/m) )^(mt)
100
**Final Amortization Value for Bond**
**The book value at the end of the bond term which is the *redemption value C***
101
Calculating Principal Repaid
**Pt *(Principal Repaid)***
**=**
**Rt *(loan repayment)* - It *(interest due)***
102
Continous Varying Annuities PV
**PV = [integration from 0 to n]**
**of**
**[f(t) \* e - (integration from o to t) of ( delta )]**
103
Annuity-Due Accumulated Value
S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d
104
Loan Amoritization:
Pt+k
/
(1 + i)k
Principal Repaid when R is Level
105
Net Present Value (NPV)
**NPV = Σ CFt \* (vt)**
**summation from (t = 0) to n**
**NPV = sum of the present value of all cash flow over ( n ) years**
106
Preferred Habit Theory
Borrowers and Lenders if given enough incentive will be willing to go out of their boundaries.
For example, a lender who only wants to lend for a certain time may be willing to lend for a longer time if given enough incentives.
107
Retrospective Method
**backward-looking; based on previous cash flows;**
**time t outstanding loan balance**
**=**
**AV(Orginal loan with i) - AV(loan payments)**
108
Discounting Factor with (i)
v = ( 1 / ( 1 + i )^(n))
109
Call Price
additional cash flow the investor receives if the bond terminates on a call date
110
v = ( 1 / ( 1 + i )^(n))
Discounting Factor with (i)
111
Perpetuity-Immediate increasing
**(Ia) angle infinity**
**=**
**( ( P / i ) + ( Q / ( i2 ) )**
112
A(t) = A(0)\*(1-d)^(-t)
Amount Function Effective Discount Rate
113
114
Relationship between Constant Force Of Interest and Constant effective interest rate
e^(delta) = ( 1 + i )
115
Unit Increasing Annuity
[(Ia) angle n]
P = Q
[(Ia) angle n]
=
**(P) \* [( a double dot angle n ) - n( vn )]**
**/**
**i**
116
Annuity-Due PV to AV relation
(A double-dot angle n) =
(S double-dot angle n) \* ( v**n **)
117
**Σ t \* vt+1 \* CFt**
**/**
**Σ vt \* CFt**
Modified Duration Formula
118
a'(t) / a(t)
Force Of Interest
119
Pt ( *principal repaid for bonds at time t )*
Pt ( *principal repaid for bonds at time t )*
*=*
**|** ( Fr - C(i) )\*( vn-t+1 ) **|**
120
A double dot angle n, with i. ( 1 - v^(n) ) / d
Annuity-Due Present Value
121
Default Risk Premium
compensates investors for the possibility that a borrower will default
122
# Reversed Cards
**forward-looking based on future cash flow**
**time-t outstanding loan balance**
**=**
**PV(remaining loan payments with i)**
Prospective Method
123
# Reversed Cards
To persuade lenders to lend for a longer time, borrowers will have to pay higher interest rate as an incentive.
Liquidity Preferance Theory / Opportunity Cost Theory
124
# Reversed Cards
Duration of Portfolio
weighted average of individual asset's duration
125
# Reversed Cards
A angle n, with i. ( 1 - v^(n) ) / i
Annuity-Immediate Present Value
126
# Reversed Cards
a(t) = e ^(delta \* time)
Accumulation function for Constant Force of Interest
127
# Reversed Cards
weighted average of individual asset's duration
Duration of Portfolio
128
# Reversed Cards
party who agrees to pay the fixed rate and receive the variable rates
Payer
129
# Reversed Cards
Accumulation function for Constant Force of Interest
a(t) = e ^(delta \* time)
130
# Reversed Cards
**Loan Amortization:** Principal Repaid
**Terminology Bond Amortization:**
Write-down (*Premium Bonds*)
Write-Up (*Discount Bonds*)
131
# Reversed Cards
Interest rate for a long term investment provides future expectation for interest on short term investments
for example; consider 2 year loan with higher interest rate then a 1 year loan. Then one year from now the interest rate on the 1 year loan is expected to be higher than the current interest of the 1 year loan.
Expectation theory
132
# Reversed Cards
specified dates during the swap tenor when the interest payments are exchanged
Settlement dates
133
# Reversed Cards
Amount Function Nominal Discount Rate
A(t) = A(0) \* ( 1 - (d/m) )^(-mt)
134
# Reversed Cards
Principal Repaid when R is level
Loan Amoritization:
Pt = R \* ( vn-t+1 )
135
136
# Reversed Cards
Amount Function Effective Interest Rate
**A(t)**
**=**
**A(0)\*(1 + i)t**
137
# Reversed Cards
Annuity-Immediate Accumulated Value
S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i
138
# Reversed Cards
repaying a loan with payments at regular intervals
Loan Amortization
139
# Reversed Cards
Periodic interest payments which form an annuity
Coupons
140
# Reversed Cards
**1.) Interest Due**
**2.) Principal Repaid**
Loan consist of what two components
141
# Reversed Cards
Absolute value of write-down
Pt = **|** (Fr - C\*(i)) \* (vn-t+1) **|**
**Discount Bonds**
Write-Up for bond
142
# Reversed Cards
**P(in)**
**=**
**P(io)\*[1 - (in - io)(ModD)]**
First Order Modified Approx.
143
# Reversed Cards
Annuity-Due Accumulated Value
S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d
144
# Reversed Cards
Amount Function Simple Interest
A(t) = A(0)\*(1 + i(t))
145
# Reversed Cards
a(t) = e^( integration from 0 to t) of delta
Accumulation Function For Variable Force of Interest
146
# Reversed Cards
PV(Variable) = PV(Fixed)
To find R (*swap rate*)
147
# Reversed Cards
Accumulation Function For Variable Force of Interest
a(t) = e^( integration from 0 to t) of delta
148
# Reversed Cards
(S angle n) \* ( v**n **)
Annuity-Immediate PV to AV relation
(A angle n) =
149
# Reversed Cards
**(A double-dot angle n) \* ( ( 1 + i )n )**
Annuity-Due AV to PV relation
(S double-dot angle n) =
150
# Reversed Cards
ln (1 + i)
delta = force of interest constant
151
# Reversed Cards
(Redemption - Price)
or
( C\*(i) - Fr ) \* (a angle n)
Discount Bond Formula
152
# Reversed Cards
**Present value** at time t of it's remaining **cash flow** using the **loan's interest rate**
**Loan: *Outstanding Balance at time t***
***is equal to***
153
# Reversed Cards
is the amount used to determine interest payments and swap payments;
to obtain interest payment or swap payment multiply the notional amount by the respective interest rate
**USUALLY THE LOAN AMOUNT**
Notional amount
154
# Reversed Cards
Effective Interest Rate
(A(t) - A(t-1)) / A(t-1)
155
# Reversed Cards
**(Da) angle n**
**=**
**[n - (a angle n)]**
**/**
**i**
unit decreasing annuity
156
# Reversed Cards
Borrowers and Lenders have different preferances on how long they want to borrow or lend for, thus causing different interest rates for different terms
Market Segmentation Theory
157
# Reversed Cards
Annuity-Immediate Present Value
A angle n, with i. ( 1 - v^(n) ) / i
158
# Reversed Cards
( 1 - d )
Discounting Factor with (d)
159
# Reversed Cards
Discounting Factor with (d)
( 1 - d )
160
# Reversed Cards
Level annual effective rate of interest which equates cash inflows to cash outflows
Yield to Maturity
161
# Reversed Cards
A(t) = A(0) \* ( 1 - (d/m) )^(-mt)
Amount Function Nominal Discount Rate
162
# Reversed Cards
A double dot angle n, with i. ( 1 - v^(n) ) / d
Annuity-Due Present Value
163
# Reversed Cards
**also called yield rate**
**it's the rate that**
**produces a NPV of 0**
**also known as breakeven**
Internal Rate of Return (IRR)
164
# Reversed Cards
also known as the variable rate
floating rate
165
# Reversed Cards
Annuity-Immediate **geometric** progression
**[1 - ( (1 + k) / ( 1 +i ) )n]**
**/**
**( i - k)**
i = interest
k = number of payments in progression/percentage
n = number of total payments
166
# Reversed Cards
**(1 + sn)n**
**=**
**(1 + sn-1)n-1 \* (1 + f[n-1, n])**
Implied Forward Rate
167
# Reversed Cards
Effective Discount Rate
(A(t) - A(t-1)) / A(t)
168
# Reversed Cards
**Loan Amortization:** Outstanding balance
**Terminology Bonds Amortization:** Book value
169
# Reversed Cards
(1 - d)
(1 + i)^(-1) discount factor
170
# Reversed Cards
(A(t) - A(t-1)) / A(t)
Effective Discount Rate defined as
171
# Reversed Cards
**Rate of return**
**on an equally-risky asset**
**an investor could have earned**
**if he or she had NOT invested in the project.**
What is opportunity cost of capital?
172
# Reversed Cards
lowest yield rate calculated is the minimum yield that an investor would earn
Given a price
173
# Reversed Cards
known as the fixed rate
swap rate
174
# Reversed Cards
**It *(Interest Due)***
**=**
**(i) \* Bt-1 *(outstanding balance of previous period)***
Calculating Interest Due
175
# Reversed Cards
(A(t) - A(t-1)) / A(t-1)
Effective Interest Rate defined as
176
# Reversed Cards
(A angle n) \* ( ( 1 + i )n )
Annuity-Immediate AV to PV relation
(S angle n)=
177
# Reversed Cards
**Present value** at time t of its remaining **cash flows** using the bond's initial **yield rate**
**A bond's *BOOK VALUE* at time t**
**is equal to**
178
# Reversed Cards
agreement between two parties in which both parties agree to exchange a series of cash flow based on interest rates
Interest Rate Swap
179
# Reversed Cards
if notional amount increases over time
Accreting Swap
180
# Reversed Cards
Step 1: Identify Cash Flows
Step 2: Calculate the bond price as the PV of future cash flow at time 0
Solving for bonds
181
# Reversed Cards
Annual Effective Yield rates on a zero-coupon bond
Measures the yield from the beginning of the investment to the end of the single cash flow
Spot Rates
182
# Reversed Cards
**[1 - ( (1 + k) / ( 1 +i ) )n]**
**/**
**( i - k)**
i = interest
k = number of payments in progression/percentage
n = number of total payments
Annuity-Immediate **geometric** progression
183
# Reversed Cards
the lowest price calculated is the maximum price that an investor would pay
Given a yield rate
184
# Reversed Cards
**Loan Amortization:** Loan Payment
**Terminology Bond Amortization:** Coupon payment
185
# Reversed Cards
**Bt**
**=**
**L(1+i)t - R(s angle t)**
Retrospective Formula
186
# Reversed Cards
(Coupon Payment - Interest Earned)
**Pt = | (Fr - C\*(i)) \* (vn-t+1) |**
Premium bonds
Write-Down for bond
same as principal repaid for loans
187
# Reversed Cards
**Bt *(Outstanding loan balance time t)***
**=**
**Bt-1 *(Outstanding loan balance time t-1)* - Pt *(Principal repaid time t)***
Calculating Outstanding Balance end of period
188
# Reversed Cards
One large payment at the end of the bond term
Redemption Value
189
# Reversed Cards
**P(*Price of bond*)**
**=**
**Fr(a angle n) [*Pv at time 0 of coupon payments over n periods]***
***+***
**C(vn) [*Pv at 0 of the redemption value*]**
**Bonds:** Basic Formula
190
# Reversed Cards
Can be terminated before the redemption dates labeled as call dates
Callable Bonds
191
# Reversed Cards
is the time between settlement dates
Settlement period
192
# Reversed Cards
Method 1: Start with payments furthest from the comparison date
2: Make adjustments when moving towards the comparison date
Block Payment Annuity
193
# Reversed Cards
specified period of the swap
Swap Term / Swap Tenor
194
# Reversed Cards
Rate of Return from investor's point of view
constant rate discounting future cash flow
Bond's Yield Rate
195
# Reversed Cards
**PV = P\*(a angle n)**
**+**
**[(Q)\*((a angle n) - n( vn )] / i**
P = first term
Q = constant amount of increase for each payment
n = number of payments one period before the first payment date
P and Q formula for annuity increasing Arithmetic Progression
196
# Reversed Cards
(BOOK VALUE of PREVIOUS PERIOD) \* (YIELD RATE)
Interest earned on a Bond calculation
197
# Reversed Cards
Accumulation Function Simple Interest
a(t) = (1 + i(t))
198
# Reversed Cards
**[** (pmt) \* (annuity-immediate(AV)) **]**
+
**[** (fv) - (PV)(AV factor) **]**
=
0
Finding additional payment
(Annuity Immediate AV)
199
# Reversed Cards
not a cash flow
used to determine coupon amount
Face amount / par value
200
# Reversed Cards
**A(t) = A(0) \* ( 1 - d )-t**
Amount Function Effective Discount Rate
201
# Reversed Cards
A central bank requires every bank to deposit and maintain a specific amount of money with it
Bank Reserve Requirement
202
# Reversed Cards
Relationship between Constant Force Of Interest and Constant effective interest rate
**e(delta) * (t)**
**=**
**( 1 + i )t**
203
# Reversed Cards
(1 + i)
(1 - d)^(-1) accumulation factor
204
# Reversed Cards
**interest rate used =**
**cost of capital**
**or**
**opportunity cost of capital**
What interest rate should be used to discount the cash flow for NPV?
205
# Reversed Cards
(Price - Redemption)
or
(Fr - C\*(i)) \* (a angle n)
Premium Bond Formula
206
# Reversed Cards
**[** (pmt) \* ( annuity - immediate( PV ) ) **]**
+
**[** (fv)(discounted factor) - ( PV ) **]**
=
0
Finding additional payment
(Annuity Immediate PV )
207
# Reversed Cards
Is the risk of loan defaulting, the borrower is unable to make a promised payment at the contracted time and for the contracted amount.
Default Risk
208
# Reversed Cards
A(t) = A(0)\*(1 + i(t))
Amount Function Simple Interest
209
# Reversed Cards
Amount Function Nominal Interest Rate
**A(t)**
**=**
**A(0) \* ( 1 + (i/m) )(mt)**
210
# Reversed Cards
Interest Due when R is Level
Loan Amortization
It = R \* (1−vn−t+1)
211
# Reversed Cards
P(*Price of bond*)
=
C(*Redemption value)*
+
(Fr - C \* i)(a angle n)
**Bonds:** Premium/Discount Formula
212
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**Bt**
**=**
**R(a angle (n-t))**
Prospective Method Formula
213
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The actual amount of deposit with the central bank
Bank's Reserve
214
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a(t) = (1 + i(t))
Accumulation Function Simple Interest
215
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S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i
Annuity-Immediate Accumulated Value
216
# Reversed Cards
a'(t) / a(t)
Force Of Interest
217
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A(t) = A(0)\*(1 + i)^t
Amount Function Effective Interest Rate
218
# Reversed Cards
counter party who receives the fix rate
and
pays the variable rate
Receiver
219
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if the notional amount decreases over time
Amortizing Swap
220
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A(t) = A(0) \* ( 1 + (i/m) )^(mt)
Amount Function Nominal Interest Rate
221
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**The book value at the end of the bond term which is the *redemption value C***
**Final Amortization Value for Bond**
222
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**Pt *(Principal Repaid)***
**=**
**Rt *(loan repayment)* - It *(interest due)***
Calculating Principal Repaid
223
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**PV = [integration from 0 to n]**
**of**
**[f(t) \* e - (integration from o to t) of ( delta )]**
Continous Varying Annuities PV
224
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S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d
Annuity-Due Accumulated Value
225
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Principal Repaid when R is Level
Loan Amoritization:
Pt+k
/
(1 + i)k
226
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**NPV = Σ CFt \* (vt)**
**summation from (t = 0) to n**
**NPV = sum of the present value of all cash flow over ( n ) years**
Net Present Value (NPV)
227
# Reversed Cards
Borrowers and Lenders if given enough incentive will be willing to go out of their boundaries.
For example, a lender who only wants to lend for a certain time may be willing to lend for a longer time if given enough incentives.
Preferred Habit Theory
228
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**backward-looking; based on previous cash flows;**
**time t outstanding loan balance**
**=**
**AV(Orginal loan with i) - AV(loan payments)**
Retrospective Method
229
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v = ( 1 / ( 1 + i )^(n))
Discounting Factor with (i)
230
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additional cash flow the investor receives if the bond terminates on a call date
Call Price
231
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Discounting Factor with (i)
v = ( 1 / ( 1 + i )^(n))
232
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**(Ia) angle infinity**
**=**
**( ( P / i ) + ( Q / ( i2 ) )**
Perpetuity-Immediate increasing
233
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Amount Function Effective Discount Rate
A(t) = A(0)\*(1-d)^(-t)
234
235
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e^(delta) = ( 1 + i )
Relationship between Constant Force Of Interest and Constant effective interest rate
236
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P = Q
[(Ia) angle n]
=
**(P) \* [( a double dot angle n ) - n( vn )]**
**/**
**i**
Unit Increasing Annuity
[(Ia) angle n]
237
# Reversed Cards
(S double-dot angle n) \* ( v**n **)
Annuity-Due PV to AV relation
(A double-dot angle n) =
238
# Reversed Cards
Modified Duration Formula
**Σ t \* vt+1 \* CFt**
**/**
**Σ vt \* CFt**
239
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Force Of Interest
a'(t) / a(t)
240
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Pt ( *principal repaid for bonds at time t )*
*=*
**|** ( Fr - C(i) )\*( vn-t+1 ) **|**
Pt ( *principal repaid for bonds at time t )*
241
# Reversed Cards
Annuity-Due Present Value
A double dot angle n, with i. ( 1 - v^(n) ) / d
242
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compensates investors for the possibility that a borrower will default
Default Risk Premium
