1 - Interest Rate Measurement Flashcards
(153 cards)
What is the opening quote for this chapter?
The safest way to double your money is to fold it over and put it in your pocket.
What is interest?
The time value of money. In the most common context, interest refers to the consideration or rent paid by a borrower of money to a lender for the use of the money over a period of time.
What does the Federal Reserve Board set?
The “federal funds discount rate”, a target rate at which banks can borrow and invest funds with one another.
What does Libor refer to?
The London Interbank Overnight Rate, which is an international rate charged by one bank to another for very short term loans denominated in US dollars.
How are interest rates typically quoted?
As an annual percentage.
What’s the formula for calculating the accumulated value or future value for compound interest?
Cn = C(1+i)^n
If someone made an initial deposit on January 1st 2018, how would the interest accrue?
He would have interest added to his account on December 31 of 2018 and every December 31st after that for as long as the account remained open.
For accumulated interest, the rate of interest may change from one year to the next. How would we incorporate that into the Cn = C(1+i)^n formula?
If the interest rate is i1 in the first year, i2 in the second year, and so on,
Cn = C(1+i1)(1+i2)…(1+in), where the growth factor for year t is (i+it) and the interest rate for year t is it. Note that “year t” starts at time t-1 and ends at time t.
In practice, interest may be credited or charged more frequently than once per year. What’s the formula for calculating the accumulated value or future value for this compound interest?
Cn = C(1+j)^n after n compounding period.
It is typical to use i to denote an annual rate of interest, and, in this text, j will often be used to denote an interest rate for a period other than a year.
What is the effective annual rate of interest?
The effective annual rate of interest earned by an investment during a one-year period is the percentage change in the value of the investment from the beginning to the end of the year, without regard to the investment behavior at intermediate point in the year.
What are equivalent rates of interest?
Two rates of interest are said to be equivalent if they result in the same accumulated values at each point in time.
When compound interest is in effect, and deposits and withdrawals are occurring in an account, how can the resulting balance at some future point in time be determined?
By accumulating all individual transactions to that future time point.
When compound interest is in effect, and deposits and withdrawals are occurring in an account, the resulting balance at some future point in time can be determined by accumulating all individual transactions to that future time point. how would that look?
Cn = c(1+i)^n + d(1+i)^(n-t) - w(1+i)^(n-t)
where t is the period the deposit or withdrawal was made.
What is the accumulation factor and accumulation amount function?
a(t) is the accumulated value at time t of an investment of 1 made at time 0 and defined as the accumulation factor from time 0 to time t. The notation A(t) will be used to denote the accumulated amount of an investment at time t, so that if the initial investment amount is A(0), the the accumulated value at time t is A(t) = a(0)⋅a(t).
A(t) is the accumulated amount function.
Compound interest accumulation at rate i per period is defined with t as any real positive real number.
What is the formula for Compound Interest Accumulation?
At effective annual rate of interest i per period, the accumulation factor from time 0 to time t is
a(t) = (1+i)^t
In practice, financial transaction can take place at any point in time, and it may be necessary to represent a period which is a fractional part of a year. How is a fraction of a year generally described?
A fraction of a year is generally described in terms of either an integral number of m months, or an exact number of d days. In the case that time is measured in months, it is common in practice to formulate the fraction of the year t in the form t = m/12, even though not all months are exactly 1/12 or a year. In the case that time is measured in days, t is often formulated as t = d/365
When considering the equation X(1+i)^t = Y, given any three of the four variables X, Y, i t, it is possible to find the fourth. If the unknown variable is t, then how do we solve for it?
t = ln(Y/X) / ln(1+i)
When considering the equation X(1+i)^t = Y, given any three of the four variables X, Y, i t, it is possible to find the fourth. If the unknown variable is i, then how do we solve for it?
i = (Y/X)^(1/t) -1
When is simple interest often used?
When calculating interest accumulation over a fraction of a year or when executing short term financial transactions.
What is simple interest accumulation function?
The accumulation function from time 0 to time t at annual simple interest rate i, where t is measured in years is
a(t) = 1+it
How are fractions of years calculated for simple interest?
Like compound interest, t is either m/12 or d/365.
What is a promissory note?
A short-term contract (generally less than one year) requiring the issuer of the note (the borrower) to pay the holder of the note (the lender) a principal amount plus interest on that principal at a specified annual interest rate for a specified length of time. At the end of the time period, the payment (principle and interest) is due.
How are promissory notes calculated?
Promissory notes are calculated on the basis of simple interest. the interest rate earned by the lender is sometimes referred to as the “yield rate” earned on the investment.
What’s an important note about yield rates?
As concepts are introduced throughout this text, we will see the expression “yield rate” used in a number of different investment contexts with differing meanings. In each case it will be important to relate the meaning of the yield rate to the context in which it is being used.