Finance Chapter 6
banks are required by law to display the
APR on all consumer loans but not the APY
to use the growing annuity formula, the growth rate
has to be the same every period and cannot equal the periodic rate
annuity due
if an annuity's payments occur at the beginning of each period rent or lease agreements
for an amortized loan, each identical payment consists of
interest and repayment of principal
present value of an ordinary annuity is
the lump sum value of the annuity payments one period before the first payment
the ear is defined as (1 + r)^m - 1
true
the maximum EAR occurs when the number of compounding periods per year is infinite
true
when buying a lottery ticket, you should always choose the cash option if you have a short consumption horizon
False
when r increases the PV increases
false
when solving perpetuity problems, the payment and present value must be consistent, that is, measured over the same interval of time
false
perpetuities
financial assets that pay an infinite number of recurring cash flows
for an amortized loan, the interest component is the largest in the
first period
in order to use the simple perpetuity formula, you must assume the periodic rate is constant forever
true
starting to save for retirement early then stopping can be a better strategy than starting later and continuing when your retire
true
the EAR is not the only effective rate
true
the perpetuity PV formula is a special case of the ordinary annuity PV formula, where the number of payments is infinite instead of countable
true
to apply the growing annuity formula, you must assume the required return is constant for the life of the contract
true
to apply the perpetuity formula, you must assume the periodic rate is constant forever
true
when t increases the fv increases
true
you can take a daily periodic rate and convert it into an effective weekly rate
true
you can take a monthly periodic rate and convert it into an effective quarterly rate
true
difference between APR and ear
EAR takes into account any compounding that takes place throughout the year, while the APR does not
7.7% per annum is an APR
True
as the compounding frequency approaches infinity, the EAR approaches a ceiling
True
when applying the present value of an annuity due formula, the lump sum is when the first payment occurs
True
growing annuity
an annuity whose payments grow at a constant rate for the life of the contract
as the compounding frequency increases, the ear
becomes greater than the APR
the future value of a perpetuity formula gives the lump sum value one period prior to when the last cash flow in the stream occurs
false
the present value of a perpetuity formula gives the lump sum value when the first cash flow in the stream occurs
false
effective rate
compounds up a high frequency low rate to arrive at an equivalent low frequency high rate
the EAR is a special case of an
effective rate
.82 percent per month is an APY
false
2.94% yearly with continuous compounding is an EAR
false
3.11% per year compounded continuously is an APY
false
4 bps per day is an APR
false
7.5% per year compounded monthly is an APY
false
9 bps weekly is an EAR
false
9.4% interest per year with quarterly compounding is an EAR
false
If the payment amount decreases the present value of annuity increases
false
The APY is defined as r x m
false
all else equal, a growing annuity with a positive growth rate will have a smaller future value than an annuity with constant payments
false
an effective rate is a high frequency low rate that is equivalent to a low frequency high interest rate
false
an effective rate is a low frequency low interest rate that is equivalent to a high frequency high rate
false
as the compounding frequency approaches infinity, the APR approaches zero
false
as the compounding frequency approaches infinity, the EAR approaches the APR
false
as the compounding frequency decreases, the EAR increases at a decreasing rate
false
as the compounding frequency increases, the APR increases at a decreasing rate
false
by law, consumer loans must report the APY to the borrower
false
by law, investments must report the APY to the investor
false
by law, investors must report the APR to the investor
false
by law, savings accounts must report the APR to the depositor
false
by law, savings accounts must report the EAR to the depositor
false
by law, savings accounts must report the ear to the depositor
false
given m = 2, the APR is greater than the APY
false
given m = 4, the APY is less than the APR
false
if the periodic rate increases the future value of a growing annuity will decrease, all else equal
false
the EAR is the only effective rate
false
amortized loan
loan where the principal of the loan is paid off over the life of the loan, rather than entirely at the end of the loan term
future value of an ordinary annuity
lump sum value of the payments when you make your last paument
difference between an assets worth and its price
net present value
difference between an ordinary annuity and an annuity due
one extra period of interest
ordinary annuity
payment occurs at the end of the period cars, mortgages
fv of an annuity due
places the lump sum value when the last payment occurs which is a period before that of an ordinary annuity
present value of inflows is greater than present value of outflows
positive NPV and create value
present value of an annuity due
present value of an ordinary annuity times one plus the periodic rate
for annual compounding the APR and the EAR are the
same
annuity
series of equal payments made at fixed intervals for a finite number of periods
for an amortized loan, the repayment of the principal is the
smallest in the first period and increases after that .
financial managers want to know the present value of an asset's cash flows because
that's what the asset is worth today
the difference between the value of a perpetuity whose first annual payment occurs at the end of this year and that of one that begins ten years from now is the value of an ordinary annuity with 9 annual payments
true
the ear is a special case of effective rates in general
true
2.87 percent per year compounded continuously is an APR
true
3 bps per day is a periodic rate
true
3% per year is a periodic rate
true
4.14% yearly with continuous compounding is an APR
true
8% per year with daily compounding is an apr
true
8.2% interest per year with quarterly compounding is an APR
true
9.3% paid annually is an APY
true
By law, consumer loans must report the APR to the borrower
true
In the case of continuous compounding, for a given APR the EAR is maximized
true
all effective rates are annual
true
all else equal, a growing annuity with a positive growth rate will have a larger present value than an annuity with constant payments
true
an effective interest rate is a low frequency rate that is equivalent to a high frequency rate
true
an important difference between an ordinary annuity and a perpetuity is that the lump sum value occurs one period prior to the cash flow in the stream for the annuity, and when the first payment occurs for the perpetuity
true
annual interest of 11.1% is an APY
true
as the compounding frequency approaches infinity, the APY approaches an asymptote
true
as the compounding frequency approaches infinity, the EAR approaches a ceiling
true
as the compounding frequency decreases, the APR remains unchanged
true
as the compounding frequency decreases, the periodic rate increases
true
as the compounding frequency increases, the APY increases at a decreasing rate
true
as the compounding frequency increases, the EAR increases at a decreasing rate
true
as the compounding frequency increases, the periodic rate decreases
true
as the frequency of dividends increases, the value of a preferred stock rises
true
as the periodic rate increases so too does the size of the next dividend to be paid
true
as the periodic rate increases t decreases in the case of continuous compounding
true
as the periodic rate increases the NPV will fall for an investment with a fixed initial cost and cash inflows that follow
true
as the periodic rate increases the future value of an annuity due increases
true
as the periodic rate increases the value of an annuity due falls
true
as the periodic rate increases then you are more likely to take the cash option for a lottery
true
as time increases, the proportion of an amortized loan payment that goes to interest declines
true
assuming a strictly positive growth rate, a growing annuity has no two payments that are the same
true
continuous compounding is when interest is paid/recieved at every infinitesimally small instant of time
true
for an amortized loan, the amount of interest paid in the fifth payment is greater than that of the sixth
true
given PV, FV, and t, you can use the ordinary annuity formula and trial and error to solve for r
true
given a cost of capital and a correct timeline, multiple uneven cash flows have an equivalent lump sum
true
given annual compounding, the periodic rate equals the APR
true
given m = 1, the APR equals the periodic rate
true
given m = 1, the periodic rate equals the ear
true
given m = 2, the APR is less than the EAR
true
given m = 2, the APY is greater than the APR
true
given m = 2, the ear is greater than the apr
true
given m = 2, the periodic rate is less than the APR
true
if the payment amount increases the present value of an annuity due increases
true
if there is a series of cash flows in a stream, and you use a discount rate to convert it to a lump sum at a point of time, you can then get the equivalent value of the stream at any other time
true