FM Flashcards
Prospective Method
forward-looking based on future cash flow
time-t outstanding loan balance
=
PV(remaining loan payments with i)
Liquidity Preferance Theory / Opportunity Cost Theory
To persuade lenders to lend for a longer time, borrowers will have to pay higher interest rate as an incentive.
weighted average of individual asset’s duration
Duration of Portfolio
Annuity-Immediate Present Value
A angle n, with i. ( 1 - v^(n) ) / i
Accumulation function for Constant Force of Interest
a(t) = e ^(delta * time)
Duration of Portfolio
weighted average of individual asset’s duration
Payer
party who agrees to pay the fixed rate and receive the variable rates
a(t) = e ^(delta * time)
Accumulation function for Constant Force of Interest
Terminology Bond Amortization:
Write-down (Premium Bonds)
Write-Up (Discount Bonds)
Loan Amortization: Principal Repaid
Expectation theory
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.
Settlement dates
specified dates during the swap tenor when the interest payments are exchanged
A(t) = A(0) * ( 1 - (d/m) )^(-mt)
Amount Function Nominal Discount Rate
Loan Amoritization:
Pt = R * ( vn-t+1 )
Principal Repaid when R is level
A(t)
=
A(0)*(1 + i)t
Amount Function Effective Interest Rate
S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i
Annuity-Immediate Accumulated Value
Loan Amortization
repaying a loan with payments at regular intervals
Coupons
Periodic interest payments which form an annuity
Loan consist of what two components
1.) Interest Due
2.) Principal Repaid
Write-Up for bond
Absolute value of write-down
Pt = | (Fr - C*(i)) * (vn-t+1) |
Discount Bonds
First Order Modified Approx.
P(in)
=
P(io)*[1 - (in - io)(ModD)]
S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d
Annuity-Due Accumulated Value
A(t) = A(0)*(1 + i(t))
Amount Function Simple Interest
Accumulation Function For Variable Force of Interest
a(t) = e^( integration from 0 to t) of delta
To find R (swap rate)
PV(Variable) = PV(Fixed)
a(t) = e^( integration from 0 to t) of delta
Accumulation Function For Variable Force of Interest
Annuity-Immediate PV to AV relation
(A angle n) =
(S angle n) * ( vn )
Annuity-Due AV to PV relation
(S double-dot angle n) =
(A double-dot angle n) * ( ( 1 + i )n )
delta = force of interest constant
ln (1 + i)
Discount Bond Formula
(Redemption - Price)
or
( C*(i) - Fr ) * (a angle n)
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
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
(A(t) - A(t-1)) / A(t-1)
Effective Interest Rate
unit decreasing annuity
(Da) angle n
=
[n - (a angle n)]
/
i
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
A angle n, with i. ( 1 - v^(n) ) / i
Annuity-Immediate Present Value
Discounting Factor with (d)
( 1 - d )
( 1 - d )
Discounting Factor with (d)
Yield to Maturity
Level annual effective rate of interest which equates cash inflows to cash outflows
Amount Function Nominal Discount Rate
A(t) = A(0) * ( 1 - (d/m) )^(-mt)
Annuity-Due Present Value
A double dot angle n, with i. ( 1 - v^(n) ) / d
Internal Rate of Return (IRR)
also called yield rate
it’s the rate that
produces a NPV of 0
also known as breakeven
floating rate
also known as the variable rate
[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
Implied Forward Rate
(1 + sn)n
=
(1 + sn-1)n-1 * (1 + f[n-1, n])
(A(t) - A(t-1)) / A(t)
Effective Discount Rate
Terminology Bonds Amortization: Book value
Loan Amortization: Outstanding balance
(1 + i)^(-1) discount factor
(1 - d)
Effective Discount Rate defined as
(A(t) - A(t-1)) / A(t)
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.
Given a price
lowest yield rate calculated is the minimum yield that an investor would earn
swap rate
known as the fixed rate
Calculating Interest Due
It (Interest Due)
=
(i) * Bt-1 (outstanding balance of previous period)
Effective Interest Rate defined as
(A(t) - A(t-1)) / A(t-1)
Annuity-Immediate AV to PV relation
(S angle n)=
(A angle n) * ( ( 1 + i )n )
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
Interest Rate Swap
agreement between two parties in which both parties agree to exchange a series of cash flow based on interest rates
Accreting Swap
if notional amount increases over time
Solving for bonds
Step 1: Identify Cash Flows
Step 2: Calculate the bond price as the PV of future cash flow at time 0
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
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
Given a yield rate
the lowest price calculated is the maximum price that an investor would pay
Terminology Bond Amortization: Coupon payment
Loan Amortization: Loan Payment
Retrospective Formula
Bt
=
L(1+i)t - R(s angle t)
Write-Down for bond
same as principal repaid for loans
(Coupon Payment - Interest Earned)
Pt = | (Fr - C*(i)) * (vn-t+1) |
Premium bonds
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)
Redemption Value
One large payment at the end of the bond term
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]
Callable Bonds
Can be terminated before the redemption dates labeled as call dates
Settlement period
is the time between settlement dates
Block Payment Annuity
Method 1: Start with payments furthest from the comparison date
2: Make adjustments when moving towards the comparison date
Swap Term / Swap Tenor
specified period of the swap
Bond’s Yield Rate
Rate of Return from investor’s point of view
constant rate discounting future cash flow
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
Interest earned on a Bond calculation
(BOOK VALUE of PREVIOUS PERIOD) * (YIELD RATE)
a(t) = (1 + i(t))
Accumulation Function Simple Interest
Finding additional payment
(Annuity Immediate AV)
[ (pmt) * (annuity-immediate(AV)) ]
+
[ (fv) - (PV)(AV factor) ]
=
0
Face amount / par value
not a cash flow
used to determine coupon amount
Amount Function Effective Discount Rate
A(t) = A(0) * ( 1 - d )-t
Bank Reserve Requirement
A central bank requires every bank to deposit and maintain a specific amount of money with it
e(delta) * (t)
=
( 1 + i )t
Relationship between Constant Force Of Interest and Constant effective interest rate
(1 - d)^(-1) accumulation factor
(1 + i)
What interest rate should be used to discount the cash flow for NPV?
interest rate used =
cost of capital
or
opportunity cost of capital
Premium Bond Formula
(Price - Redemption)
or
(Fr - C*(i)) * (a angle n)
Finding additional payment
(Annuity Immediate PV )
[ (pmt) * ( annuity - immediate( PV ) ) ]
+
[ (fv)(discounted factor) - ( PV ) ]
=
0
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.
Amount Function Simple Interest
A(t) = A(0)*(1 + i(t))
A(t)
=
A(0) * ( 1 + (i/m) )(mt)
Amount Function Nominal Interest Rate
Loan Amortization
It = R * (1−vn−t+1)
Interest Due when R is Level
Bonds: Premium/Discount Formula
P(Price of bond)
=
C(Redemption value)
+
(Fr - C * i)(a angle n)
Prospective Method Formula
Bt
=
R(a angle (n-t))
Bank’s Reserve
The actual amount of deposit with the central bank
Accumulation Function Simple Interest
a(t) = (1 + i(t))
Annuity-Immediate Accumulated Value
S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i
Force Of Interest
a’(t) / a(t)
Amount Function Effective Interest Rate
A(t) = A(0)*(1 + i)^t
Receiver
counter party who receives the fix rate
and
pays the variable rate
Amortizing Swap
if the notional amount decreases over time
Amount Function Nominal Interest Rate
A(t) = A(0) * ( 1 + (i/m) )^(mt)
Final Amortization Value for Bond
The book value at the end of the bond term which is the redemption value C
Calculating Principal Repaid
Pt (Principal Repaid)
=
Rt (loan repayment) - It (interest due)
Continous Varying Annuities PV
PV = [integration from 0 to n]
of
[f(t) * e - (integration from o to t) of ( delta )]
Annuity-Due Accumulated Value
S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d
Loan Amoritization:
Pt+k
/
(1 + i)k
Principal Repaid when R is Level
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
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.
Retrospective Method
backward-looking; based on previous cash flows;
time t outstanding loan balance
=
AV(Orginal loan with i) - AV(loan payments)
Discounting Factor with (i)
v = ( 1 / ( 1 + i )^(n))
Call Price
additional cash flow the investor receives if the bond terminates on a call date
v = ( 1 / ( 1 + i )^(n))
Discounting Factor with (i)
Perpetuity-Immediate increasing
(Ia) angle infinity
=
( ( P / i ) + ( Q / ( i2 ) )
A(t) = A(0)*(1-d)^(-t)
Amount Function Effective Discount Rate
Relationship between Constant Force Of Interest and Constant effective interest rate
e^(delta) = ( 1 + i )
Unit Increasing Annuity
[(Ia) angle n]
P = Q
[(Ia) angle n]
=
(P) * [( a double dot angle n ) - n( vn )]
/
i
Annuity-Due PV to AV relation
(A double-dot angle n) =
(S double-dot angle n) * ( vn )
Σ t * vt+1 * CFt
/
Σ vt * CFt
Modified Duration Formula
a’(t) / a(t)
Force Of Interest
Pt ( principal repaid for bonds at time t )
Pt ( principal repaid for bonds at time t )
=
| ( Fr - C(i) )*( vn-t+1 ) |
A double dot angle n, with i. ( 1 - v^(n) ) / d
Annuity-Due Present Value
Default Risk Premium
compensates investors for the possibility that a borrower will default
Reversed Cards
forward-looking based on future cash flow
time-t outstanding loan balance
=
PV(remaining loan payments with i)
Prospective Method
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
Reversed Cards
Duration of Portfolio
weighted average of individual asset’s duration
Reversed Cards
A angle n, with i. ( 1 - v^(n) ) / i
Annuity-Immediate Present Value
Reversed Cards
a(t) = e ^(delta * time)
Accumulation function for Constant Force of Interest
Reversed Cards
weighted average of individual asset’s duration
Duration of Portfolio
Reversed Cards
party who agrees to pay the fixed rate and receive the variable rates
Payer
Reversed Cards
Accumulation function for Constant Force of Interest
a(t) = e ^(delta * time)
Reversed Cards
Loan Amortization: Principal Repaid
Terminology Bond Amortization:
Write-down (Premium Bonds)
Write-Up (Discount Bonds)
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
Reversed Cards
specified dates during the swap tenor when the interest payments are exchanged
Settlement dates
Reversed Cards
Amount Function Nominal Discount Rate
A(t) = A(0) * ( 1 - (d/m) )^(-mt)
Reversed Cards
Principal Repaid when R is level
Loan Amoritization:
Pt = R * ( vn-t+1 )
Reversed Cards
Amount Function Effective Interest Rate
A(t)
=
A(0)*(1 + i)t
Reversed Cards
Annuity-Immediate Accumulated Value
S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i
Reversed Cards
repaying a loan with payments at regular intervals
Loan Amortization
Reversed Cards
Periodic interest payments which form an annuity
Coupons
Reversed Cards
1.) Interest Due
2.) Principal Repaid
Loan consist of what two components
Reversed Cards
Absolute value of write-down
Pt = | (Fr - C*(i)) * (vn-t+1) |
Discount Bonds
Write-Up for bond
Reversed Cards
P(in)
=
P(io)*[1 - (in - io)(ModD)]
First Order Modified Approx.
Reversed Cards
Annuity-Due Accumulated Value
S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d
Reversed Cards
Amount Function Simple Interest
A(t) = A(0)*(1 + i(t))
Reversed Cards
a(t) = e^( integration from 0 to t) of delta
Accumulation Function For Variable Force of Interest
Reversed Cards
PV(Variable) = PV(Fixed)
To find R (swap rate)
Reversed Cards
Accumulation Function For Variable Force of Interest
a(t) = e^( integration from 0 to t) of delta
Reversed Cards
(S angle n) * ( vn )
Annuity-Immediate PV to AV relation
(A angle n) =
Reversed Cards
(A double-dot angle n) * ( ( 1 + i )n )
Annuity-Due AV to PV relation
(S double-dot angle n) =
Reversed Cards
ln (1 + i)
delta = force of interest constant
Reversed Cards
(Redemption - Price)
or
( C*(i) - Fr ) * (a angle n)
Discount Bond Formula
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
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
Reversed Cards
Effective Interest Rate
(A(t) - A(t-1)) / A(t-1)
Reversed Cards
(Da) angle n
=
[n - (a angle n)]
/
i
unit decreasing annuity
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
Reversed Cards
Annuity-Immediate Present Value
A angle n, with i. ( 1 - v^(n) ) / i
Reversed Cards
( 1 - d )
Discounting Factor with (d)
Reversed Cards
Discounting Factor with (d)
( 1 - d )
Reversed Cards
Level annual effective rate of interest which equates cash inflows to cash outflows
Yield to Maturity
Reversed Cards
A(t) = A(0) * ( 1 - (d/m) )^(-mt)
Amount Function Nominal Discount Rate
Reversed Cards
A double dot angle n, with i. ( 1 - v^(n) ) / d
Annuity-Due Present Value
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)
Reversed Cards
also known as the variable rate
floating rate
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
Reversed Cards
(1 + sn)n
=
(1 + sn-1)n-1 * (1 + f[n-1, n])
Implied Forward Rate
Reversed Cards
Effective Discount Rate
(A(t) - A(t-1)) / A(t)
Reversed Cards
Loan Amortization: Outstanding balance
Terminology Bonds Amortization: Book value
Reversed Cards
(1 - d)
(1 + i)^(-1) discount factor
Reversed Cards
(A(t) - A(t-1)) / A(t)
Effective Discount Rate defined as
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?
Reversed Cards
lowest yield rate calculated is the minimum yield that an investor would earn
Given a price
Reversed Cards
known as the fixed rate
swap rate
Reversed Cards
It (Interest Due)
=
(i) * Bt-1 (outstanding balance of previous period)
Calculating Interest Due
Reversed Cards
(A(t) - A(t-1)) / A(t-1)
Effective Interest Rate defined as
Reversed Cards
(A angle n) * ( ( 1 + i )n )
Annuity-Immediate AV to PV relation
(S angle n)=
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
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
Reversed Cards
if notional amount increases over time
Accreting Swap
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
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
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
Reversed Cards
the lowest price calculated is the maximum price that an investor would pay
Given a yield rate
Reversed Cards
Loan Amortization: Loan Payment
Terminology Bond Amortization: Coupon payment
Reversed Cards
Bt
=
L(1+i)t - R(s angle t)
Retrospective Formula
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
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
Reversed Cards
One large payment at the end of the bond term
Redemption Value
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
Reversed Cards
Can be terminated before the redemption dates labeled as call dates
Callable Bonds
Reversed Cards
is the time between settlement dates
Settlement period
Reversed Cards
Method 1: Start with payments furthest from the comparison date
2: Make adjustments when moving towards the comparison date
Block Payment Annuity
Reversed Cards
specified period of the swap
Swap Term / Swap Tenor
Reversed Cards
Rate of Return from investor’s point of view
constant rate discounting future cash flow
Bond’s Yield Rate
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
Reversed Cards
(BOOK VALUE of PREVIOUS PERIOD) * (YIELD RATE)
Interest earned on a Bond calculation
Reversed Cards
Accumulation Function Simple Interest
a(t) = (1 + i(t))
Reversed Cards
[ (pmt) * (annuity-immediate(AV)) ]
+
[ (fv) - (PV)(AV factor) ]
=
0
Finding additional payment
(Annuity Immediate AV)
Reversed Cards
not a cash flow
used to determine coupon amount
Face amount / par value
Reversed Cards
A(t) = A(0) * ( 1 - d )-t
Amount Function Effective Discount Rate
Reversed Cards
A central bank requires every bank to deposit and maintain a specific amount of money with it
Bank Reserve Requirement
Reversed Cards
Relationship between Constant Force Of Interest and Constant effective interest rate
e(delta) * (t)
=
( 1 + i )t
Reversed Cards
(1 + i)
(1 - d)^(-1) accumulation factor
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?
Reversed Cards
(Price - Redemption)
or
(Fr - C*(i)) * (a angle n)
Premium Bond Formula
Reversed Cards
[ (pmt) * ( annuity - immediate( PV ) ) ]
+
[ (fv)(discounted factor) - ( PV ) ]
=
0
Finding additional payment
(Annuity Immediate PV )
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
Reversed Cards
A(t) = A(0)*(1 + i(t))
Amount Function Simple Interest
Reversed Cards
Amount Function Nominal Interest Rate
A(t)
=
A(0) * ( 1 + (i/m) )(mt)
Reversed Cards
Interest Due when R is Level
Loan Amortization
It = R * (1−vn−t+1)
Reversed Cards
P(Price of bond)
=
C(Redemption value)
+
(Fr - C * i)(a angle n)
Bonds: Premium/Discount Formula
Reversed Cards
Bt
=
R(a angle (n-t))
Prospective Method Formula
Reversed Cards
The actual amount of deposit with the central bank
Bank’s Reserve
Reversed Cards
a(t) = (1 + i(t))
Accumulation Function Simple Interest
Reversed Cards
S angle n, with i. ( ( 1 + i )^(n) - 1 ) / i
Annuity-Immediate Accumulated Value
Reversed Cards
a’(t) / a(t)
Force Of Interest
Reversed Cards
A(t) = A(0)*(1 + i)^t
Amount Function Effective Interest Rate
Reversed Cards
counter party who receives the fix rate
and
pays the variable rate
Receiver
Reversed Cards
if the notional amount decreases over time
Amortizing Swap
Reversed Cards
A(t) = A(0) * ( 1 + (i/m) )^(mt)
Amount Function Nominal Interest Rate
Reversed Cards
The book value at the end of the bond term which is the redemption value C
Final Amortization Value for Bond
Reversed Cards
Pt (Principal Repaid)
=
Rt (loan repayment) - It (interest due)
Calculating Principal Repaid
Reversed Cards
PV = [integration from 0 to n]
of
[f(t) * e - (integration from o to t) of ( delta )]
Continous Varying Annuities PV
Reversed Cards
S double dot angle n, with i. ( ( 1 + i )^(n) - 1 ) / d
Annuity-Due Accumulated Value
Reversed Cards
Principal Repaid when R is Level
Loan Amoritization:
Pt+k
/
(1 + i)k
Reversed Cards
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)
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
Reversed Cards
backward-looking; based on previous cash flows;
time t outstanding loan balance
=
AV(Orginal loan with i) - AV(loan payments)
Retrospective Method
Reversed Cards
v = ( 1 / ( 1 + i )^(n))
Discounting Factor with (i)
Reversed Cards
additional cash flow the investor receives if the bond terminates on a call date
Call Price
Reversed Cards
Discounting Factor with (i)
v = ( 1 / ( 1 + i )^(n))
Reversed Cards
(Ia) angle infinity
=
( ( P / i ) + ( Q / ( i2 ) )
Perpetuity-Immediate increasing
Reversed Cards
Amount Function Effective Discount Rate
A(t) = A(0)*(1-d)^(-t)
Reversed Cards
e^(delta) = ( 1 + i )
Relationship between Constant Force Of Interest and Constant effective interest rate
Reversed Cards
P = Q
[(Ia) angle n]
=
(P) * [( a double dot angle n ) - n( vn )]
/
i
Unit Increasing Annuity
[(Ia) angle n]
Reversed Cards
(S double-dot angle n) * ( vn )
Annuity-Due PV to AV relation
(A double-dot angle n) =
Reversed Cards
Modified Duration Formula
Σ t * vt+1 * CFt
/
Σ vt * CFt
Reversed Cards
Force Of Interest
a’(t) / a(t)
Reversed Cards
Pt ( principal repaid for bonds at time t )
=
| ( Fr - C(i) )*( vn-t+1 ) |
Pt ( principal repaid for bonds at time t )
Reversed Cards
Annuity-Due Present Value
A double dot angle n, with i. ( 1 - v^(n) ) / d
Reversed Cards
compensates investors for the possibility that a borrower will default
Default Risk Premium
