Unit 4 Flashcards
When repaying a loan and you get extra money, what are your two options?
Reduce the duration and maintain the initial installment
Reduce the installment and maintain the duration
Partial amortization means …
repaying part of a loan in a lump sum
Number of pending payments means
duration of loan
The excel formula to calculate the number of payments is
nper
The excel formula to calculate the rate is
IRR
The excel formula to calculate the installment is
PMT
In a loan contract, a borrower initially receives __________ from a lender, and is obligated to repay ___________ + ____________________.
initially an amount of money (called principal)
an equal amount of money to the lender at a later time (amortization of the loan), plus an additional sum of money, which is the interest of the loan.
Principal is …
an initial amount of money received by a borrower
Amortization of a loan is …
an amount of money equal to the principal lent to a borrower, which is repaid to the lender at a later time
The interest of a loan is …
an additional sum of money paid to the lender at the time of amortization
The two types of loans are ___________ and ____________ . Which is used depends on ______.
Single-payment loans
Loans repaid by annuities
how the borrower repays the principal
Single-payment loans are …
Loans that require the repayment of the entire principal
sum at the end of its duration and the interests is paid either periodically or not.
Loans repaid by annuities are …
loans where the principal and interest of the loan is repaid by an annuity but the interest is calculated on the unpaid balance.
Single-payment loans are also known as …
bullet loans
Bullet loans are ….
loans that does not amortize over time and must be repaid with a single large payment (also called a balloon payment) at the end of the term of the loan.
A single large payment is also called a
balloon payment
We can differentiate two types of single-payment loans: __________ and _______________.
- When the interests are also paid at the end of the term of the loan (as part of the bullet payment)
- When the interests are paid periodically during the term of the loan.
Single-payment loans are typically ________ loans.
short-term loans
We use the single payment method for _________
bonds and other fixed-income securities.
Two amortization methods are ….
- Single Payment Method
2. Annuities
In the single payment method, for bullet payment, Cn = -C0(1+i)^n
True
** negative because we pay
In the single payment method, for the loans where the interest is paid during the term of the loan, I = C0i% and Cn = C0(1+i)
True
Annuity-amortized loans are normally just called …
Amortized loans
Amortized loans are …
loans with scheduled periodic payments or installments that are composed of two parts:
- the principal repayment
- the interest payment
“As” is called the
principal payment
The two parts of an installment are …
- Principal Payment
2. Interest Payment
The principal repayment (𝑨𝒕) is …
the amount of money the borrower pays to reduce the outstanding loan amount.
The interest payment (𝑰𝒕) is …
the amount of money calculated over the outstanding loan amount, which the borrower pays in concept of interests.
The total amount paid by the lender or installment (𝒂𝒕), is
the sum of the principal repayment and the interest payment.
At = at-It
True because at = At + It
𝑪𝒕 is …
the outstanding loan amount (the unpaid balance) at the moment t.
𝑪𝟎 is …
the amount of money the borrower receives from the lender (the principal of the loan).
True or False, when all the principal repayments are paid, the loan is fully amortized.
True
Because a loan is fully amortized when all the principal repayments are made, the sum of all the principal repayments is equal to the principal.
True
𝐶0 = ∑𝐴t
We can compute the unpaid balance at a given moment, Ct (that is, the part of the principal which has not been paid yet) as the unpaid balance at the previous period minus
the principal repayment of the period.
True
𝐶𝑡 = 𝐶𝑡−1 − 𝐴t = debt yesterday - debt today
the unpaid balance at a given moment t is called
the part of the principal which has not been paid yet
The unpaid balance at a given moment t can be also calculated as the principal of the loan minus all the paid principal repayments or the sum of all the principal repayments to be paid in the future
True
C𝑡 = 𝐶0 − ∑𝐴t
or,
Ct =∑C
In addition to the principal repayments, the borrower must pay the interests.
True
In annuity amortized loans, the interest paid are calculated as the rate of interest of the loan multiplied by the unpaid balance at the beginning of the period
True
It = i%*Ct-1
The interest payments can be paid with the same periodicity as the principal payments, or more frequently than the interest payments.
True
In annuity amortized loans, the interest is always computed over the unpaid balance.
True
In loans with equal frequency for interest and principal payments …
we pay the principal payment and the interest
In annuity amortized loans, if we pay the interest more frequently than principal payments,
We pay the interest one period and the interest + principal payment the other period.
The rule of financial equivalence states that …
The unpaid balance of a loan at any moment k can be calculated as the sum of the discounted value of all the pending installments.
𝑪𝒌 = ∑𝒂𝒕/(1+i)^t, where t = k+1
𝑪𝒌 = ∑𝒂𝒕/(1+i)^t, where t = k+1 is called
The rule of financial equivalence
Principal repayments, As =
as - Is
Unpaid balance, Cs =
debt yesterday - debt today
Cs-1 - As
Repaid balance, Ms =
Ms = C0 - Cs or ∑As
Usually, loans are amortized by immediate annuities, i.e., the payment of the principal starts in the next period to the collection of the principal by the lender.
True
Although loans are amortized by immediate annuities, it is possible to agree to have the payment of the principal paid by a deferred annuity.
True
Immediate annuities means …
the payment of the principal starts in the next period to the collection of the principal by the lender.
The period between the granting of the loan
and the first payment of principal is called …
the grace period.
The two types of graces periods are:
- Interest-only grace period
In an interest-only grace period,
the borrower only pays interests during the grace period
In a no-payment grace period,
the borrower will make no payment during the grace period, but the interests will be compounding.
In a non-payment grace period, Cc-1 =
𝐶𝑐−1 = 𝐶0 (1 + 𝑖)^𝑐−1
You are paying interest on the new compounded amount, and C0 = the new compounded amount
In interest-only grace period, 𝐶𝑛 =
Cn-1 * i%
The installments of an annuity-amortized loan can be computed following different payment plans.
True
The most commonly used plans in an annuity-amortized loan are the following:
- Equal principal payment (AKA straight line method)
- Equal installment loans (AKA French method)
- Varying-installment loans
- Anticipated interest method (less common in Spain)
- Sinking fund method (less common in Spain)
In the straight line method,
all the installments are composed of a constant principal payment 𝐴𝑡 = 𝐴 ∀𝑡 , plus the interest
on the unpaid balance.
Equal principal payment is also known as
(AKA straight line amortization)
Equal installment loans are also known as
(AKA French method)
In the French method,
all the installments are equal 𝑎𝑡 = 𝑎 ∀ 𝑡 .
In varying-installment loans,
the installments vary following an arithmetic progression, 𝑎𝑡 = 𝑎𝑡−1 + 𝑑 ∀ 𝑡 or a geometric progression 𝑎𝑡 = 𝑎𝑡−1 * 𝑞 ∀ 𝑡 .
Most of the loans in Spain are amortized following …
The equal installments method or equal principal payments
Between the equal installments method and the equal principal payments, _____________ is more common
equal installments method
In the straight line method (equal principal payment), to create the amortization schedule,
- Calculate the As (cte principal repayment)
- Calculate all the values of Ct (principal payment in each period)
- Calculate the interest payment, Is
- Calculate the total amount to be paid, as
In equal principal payment method, the constant principal repayment, As =
C0/nper
principal of the loan/number of periods
The total amount to be paid, the installment =
Interest, Is + Principal Repayment, As
The total amount to be paid, the installment (as) =
Interest, Is + Principal Repayment, As
In the equal installments method,
the main feature is both the interest payment and the principal repayment vary but their sum, i.e., the installment, is constant.
The most common amortization method is the equal installments method.
True
In the French method, the main feature is both the interest payment and the principal repayment vary but the installment is constant.
True
In the equal installments method, as = _______.
C0/an)i = C0/PV
To calculate the installment in Excel, we use the function ______
PMT
To compute the value of the constant installment, we can use the rule of financial equivalence
True
To calculate the unpaid balance at any moment, we can use _______________ because …
the rule of financial equivalence
the discounted value of all pending installments is unpaid balance.
In the French method, once the unpaid balance is computed, we can also calculate the interest payment for any period t.
True
The principal repayment can be computed as the difference between the installment and the interest
payment.
True
In the French method, the principal repayments vary in a geometric fashion with a growth rate of the rate of interest.
True
In the equal installments method, because the principal repayments vary in a geometric fashion with the growth rate of interest, the principal repayments during the first stages of the loan are smaller than the principal repayments during the last stages of the loan.
True
In the French Method, because principal repayments are initially smaller, the installment is constant, and the interest payments will be higher at the first stages and smaller at the last stages.
True
In the French Method, principal repayments are initially smaller, the installment is constant, and the interest payments will be higher at the first stages and smaller at the last stages.
True
The differences between the equal installments method and the straight line method are ….
- In the French method, the installments, as, are cte, and in the straight line method, the installment decreases in an arithmetic progression.
- In the French method, the amortization repayment, At, follows a geometric progression with the rate of growth, i and in the Straight line method, it is cte.
- The interest payment decreases in the equal installments method and decreases with the principal payment in the equal principal payment amortization
- The installment composition is two squares (one for the interest and one for the principal) in the equal installments method and a square and a rectangle (interest and principal respectively) for the equal principal payment amortization.
An installment decreasing in an arithmetic progression means …
the installment is the difference between two
consecutive installments −𝐴*i%
For the same rate of interest and term, the straight line system implies a lower amount of interests paid, but the installments are higher in the first stages of the loan.
True
The excel functions for the equal installments method are:
- PMT (rate;nper) to estimate the installment
- IPMT(rate;nper;pv) to estimate the interest payment
- PPMT(rate;nper;pmt;pv) to estimate the principal repayment
Changes in the rate of interest and the prepayment of
principal can be applied to any type of loan.
True
Changes in the rate of interest and the prepayment of
principal can be applied to _______.
equity installments loan
Equity installments loan …
is the most common loan where changes in the rate of interest and the prepayment of principal occur
In changes in the condition of a loan contract, floating interest loans are quite frequent nowadays.
True
In a floating interest loan, the interest rate of the loan is referred to an interest index (such as the EURIBOR or the LIBOR).
True
The interest of the loan is usually equal to the value of that index plus a certain spread.
True
Since the interest of a loan is usually equal to the value of the index + a spread,
the interest rate of the loan will be similar to the normal rates of interest in the financial markets in any moment
Usually, floating interest loans include an interest revision plan.
True
In an interest revision plan,
the borrower and the lender agree to the period for revision (a year, a half-year, a quarter…).
In an interest revision plan, at the beginning of every
period, the interest rate for that period is calculated as ___________ plus ________.
the value of the reference index
the spread
The interest rate in an interest revision plan will work as a fixed rate during that revision period, but it may change for the next revision period.
True
EURIBOR stands for …
The Euro Interbank Offered Rate
EURIBOR is …
a daily reference rate, published by the European
Money Markets Institute.
EURIBOR is based on the averaged interest rates at which Eurozone banks offer to lend unsecured funds to other banks in the euro wholesale money market (or interbank market).
True
EURIBOR is based on the averaged interest rates at which Eurozone banks offer to lend unsecured funds to other banks in the euro wholesale money market (or interbank market).
True
Eurozone banks offer to lend unsecured funds to other banks in the euro wholesale money market (or interbank market) at an average interest rate.
True
In the prepayment of principal, loan contracts usually include a clause that allows the borrower to make non-periodical payments to reduce the unpaid balance, but the lenders usually charges a commission when the borrower makes such prepayments.
True
Non-periodical payments to reduce the unpaid balance are called …
These payments are known as “prepayment of principal”.
Given that the prepayments of principal modify the unpaid balance, it is necessary to recalculate
the amortization schedule.
True
Prepayments of principal modify the unpaid balance.
True
There are two options to recalculate the unpaid balance, which are:
Option 1: keeping the same installment, but modifying the maturity
Option 2: keeping the maturity, but reducing the installment
When recalculating the unpaid balance, if we keep the installment the same but modify the maturity, this means that …
the lender can decide to keep paying the same installment but, as the unpaid balance is smaller after the prepayment of principal, the number of installments required to fully payback the loan will be lower.
When recalculating the unpaid balance, same installment different maturity means …
- smaller unpaid balance after the prepayment of principal
2. lower number of installments required to fully payback the loan
When recalculating the unpaid balance, same maturity, reduced installments means
the borrower decides to keep paying the same number of installments but, as the unpaid balance is smaller, the installments to be paid will be lower
When recalculating the unpaid balance, same maturity, reduced installments means
- same number of installments but lower quantity
2. smaller unpaid balance
In both options used to recalculate an unpaid balance, we use ____________ to calculate the new conditions of the loan.
The financial equivalence rule to calculate the new conditions of the loan
APR stands for ….
Annual percentage rate
The higher the interest rate,
the more expensive the loan would be.
In practice, a loan contract usually presents some additional clauses that imply other payments for the borrower different from the principal and interests.
True
Some additional clauses that may be in a loan contract are:
- Arrangement, origination, or application fee
- Legal and survey fees
- Early prepayment or redemption penalties
- Costs originated by the contracting of linked products
An arrangement, origination, or applicable fee …
covers the administration costs of the lender,
such as issuing complex forms, implementing the transaction, and reserving the funds.
Some administration costs of the lender are …
issuing complex forms, implementing the transaction, and reserving the funds.
Legal and survey fees are for …
loan operations that require the intervention of notaries or the inscription of the operation in some public registries.
Early prepayment or redemption penalties are …
fees that are collected by the lender if the
borrower makes a prepayment of principal.
Costs originated by the contracting of linked products are …
when banks and lenders link the granting of the loan to the contracting of additional products (insurances, bank accounts…), which produce additional costs for the borrower.
Costs originated by the contracting of linked products are …
when you get a loan and the bank or lender includes things like insurance or bank accounts and charge these to the borrower as part of the costs of the loan
The existence of additional costs make the comparison of different loan operations more complex, so we need a measure that allows for the comparison among different loan operations.
True
The measure that compares different loans is the Annual Percentage Rate (APR) of the loan.
True
The APR can be defined as
the interest rate of a hypothetical loan in which the only costs are the interest, but which is equivalent to the loan we are evaluating.
To compute the APR, we use the formula of the financial equivalence, equalling the
dated values of collections and payments.
True
∑ Collections/(1+APR)^t = ∑ Payments/(1+APR)^t
True
To directly get the APR, time must be measured in years.
True
If we use any other time units other than time when measuring the APR, __________. Then, we can get the APR by computing the equivalent annual interest rate to that rate we got.
we will not get the annual percentage rate, but the percentage rate referred to the time unit we used.
We can get the APR by computing the equivalent annual interest rate from that rate we got.
True
Origination fee is a percentage of the principal
True
Effective interest = ik/k
True
To convert yearly rate to quarterly rate
(1+i)^(1/t)-1
Each quarter has 3 months.
True
redemption means to pay the entire debt
True
No grace period means the debt is growing.
True
In a 3 year grace period, the installment is compounded only on the interest.
True
Ms = global debt - amt left to repay
True
In interest-only grace period, we always keep in mind …
- the new interest
- the new debt
- the new number of terms
variable pay market has the price …
sometimes up and sometimes down.
Euribor always gives the nominal rate.
True
We calculate installments like things will never change.
True
Schedules are not cash-flows, they are …
payments.
When the interest changes, it is total periods - periods already paid = period.
True
IRR makes inflows = outflows = 0
True
APR is the cost of the loan in percentage.
True
We always pay interest on the outstanding loan.
True
Installment = interest + amortization
True
Amortization means principal repayment
True
If we have different periods for different interest, we can’t use the PV function.
True
The principal is the amount at the beginning of th loan.
True
Interest is always paid on the debt alive.
True
ik = (1+i)^(1/k)-1
True
Debt today = debt yesterday - principal today
True
Debt today = C0 - sum(C1:Ct)
True
