Unit 6 finance
you must invest ____ today at 8% to get $2 in one year
$1.85 $2/(1.08)^1
an investment offers a perpetual cash flow of $100 every year. The required rate of return on this investment is 10%. what's the value of this investment?
$1000
the future value of $100 compounded for 50 years at 10% per year is
$11739.09 100(1.1)^50
The future value of a $100 investment in 4 years compounded at 8% per year equals:
$136.05 100(1.08)^4
Alice has $20,000 in an account that pays 8% per year. Alice wants to withdraw = amounts at the end of the next 10 years. How much will Alice receive each year?
$2980.59 $20,000/[(1-11/1.08^10)]/.08]
You invest $500 at 10% interest per annum. At the end of 2 years with simple interest, you will have _____ and with compound interest you will have _____
$600,$605 Simple interest= 500(.1)=$50 per year x 2 years= 100; $500+ $100= $600 compound interest = $500(1.1)^2= $605
What is the present value of an annuity that makes payments of $100 per year for 10 years if the first payment is made immediately and the discount rate is 10% per year?
$675.9
which of the following is the general formula for the EAR when m is the number of times interest is compounded in a year?
(1+ quoted rate/m)^m -1
If you invest for a single period at an interest rate of r, your money will grow to ______ per dollar invested
(1+r)
formula for the PV of an annuity due is
(1+r)(PV of ordinary annuity)
Different Compounding Periods
-Bonds pay interest semiannually. -Stocks pay dividends quarterly. -Leases often require monthly payments.
growing annuity
-Its cash flows increase at a regular growth rate
which of the following can be used to calculate present value?
-financial calculator -algebraic formula -time value of money table
time value of money tables are not as common as they once were because
-it's easier to use inexpensive financial calculators instead -they're available for only a relatively small number of interest rates
effective annual rates and compounding
-rate is quoted as 10% compounded semiannually - 10% compounded semiannually is = to 10.25% per year
Ways to determine present value
-time value tables -formula -financial calculator
which cannot be evaluated as annuities or annuities due
-tips to waiter -monthly electric bills
why is a dollar received today worth more than a dollar received in the future?
-today's dollar can be reinvested, yielding greater amount in the future -inflation will make a dollar in the future worth less than a dollar today
which of the following is an incorrect keystroke in financial calculator for calculating the future value of $100 today for 2 years at 10% per year?
.1 I/y -the interest rate in a financial calculator is entered as a whole number not a decimal
the present value interest factor for $1 at 5% compounded annually for 5 years is?
.7835 1/(1.05)^5
for a given time period (t) and interest rate (r), the present value factor is ____ the future value factor
1 divided by the reciprocal of
Three Ways to Alter Future Values
1) Increasing the amount of cash you have. 2) Saving for a longer period of time allows savings amount to grow at a faster rate exponentially 3) Locating an investment that earns more interest.
Three Interest Rates to Track
1) Stated Annual Interest Rate: The interest rate stated on an annual basis. 2) Periodic Interest Rate: The interest rate applied each month to the principle. 3) Effective Annual Interest Rate: The interest rate that reflects the effect of compounding over the entire annual period. For the effective annual interest rate, you apply the quarterly interest rate for the number of compounding periods within a year. -So, what you have are two annual rates, one for the nominal rate stated on an annual basis, the other reflecting the effects of compounding. -These two annual rates are connected through the periodic rate.
ways to calculate FV for multiple cash flows
1) compound the accumulated balance forward 1 year at a time 2) calculate FV of each cash flow first and then add these up
ways to calculate PV for multiple cash flows
1) discount back one time period at a time 2) calculate PVs individually and add them up
calculating EARs
1) divide the quoted rate by the number of times that the interest is compounded 2) then add 1 to the result and raise it to the power of number of times the interest is compounded 3) finally, subtract the 1. If you let *m* be the # of times the interest is compounded during the year, then the equation is: EAR= (1+ quoted rate/m)^m
calculating present values -annuities
1) take present value of each cash flow 2) use PV annuity formula 3) use time value tables
EARs concepts
1) the highest quoted rate is not necessarily the best 2) compounding during the year can lead to a significant difference between the quoted rate and the effective rate (what you get or pay for)
which formula represents a present value factor?
1/(1+r)^t
supposed we invest $100 now and receive $259.37 in 10 years. What rate of interest will we achieve?
10% (259.37/100)^1/10 - 1 = 10
you agree to repay $1200 in 2 weeks for a $1000 payday loan. What is your EAR assuming there are 52 weeks in a year?
11347.55% (1200/1000)^26 -1
you agree to pay back $1,100 in 4 weeks for a $1000 payday loan. Your APR to 2 decimal places is ----%
130 [(1100/1000)-1] (52/4)(100)
a credit card charges 18% interest per year (APR) (1.5% each month). What's the EAR?
19.56% (1.015)^12-1
the correct future value interest factor in a time value of money table for finding the future value of $100 in 10 years at 10% per year interest is _______
2.5937 100(1.1)^10= 259.37 259.37 / .10= 2.5937
if the quoted interest rate is 2% per month (12 months in a year), what is the APR?
24%
you borrow $100 and agree to pay back your payday loan in 2 weeks for 10% interest over that 2 week period. What is your stated annual interest rate?
260%
how long will it take $40 to grow to $240 at an interest rate of 6.53% compounded annually?
28.33 ln($240/40)/.0653= 27.43 ~ 28.33
given an annuity that has a payment of $35 per year, an annual interest rate of 3%, and a present value of $130, it will last for ______ years
4
The present value interest factor for 30-year annuity with an interest rate of 10% per year is ______?
9.4269 [1-(1/1.1^30)]/.1]
the present value interest factor for an annuity with an interest rate of 8% per year over 20 years is____?
9.8181 [1-(1/1.08^20)]/.08]
if you wish to find the FV of $100 invested at 10% for 5 years, which of the following would be the correct excel function?
=FV(.10,5,0,-100)
which of the following is the correct excel function to calculate the present value of $300 due in 5 years at a discount rate of 10%?
=PV(10,5,0,300)
which is the appropriate excel function to convert a quoted rate of 12% compounded quarterly to an EAR?
EFFECT(.12,4)
to convert a quoted rate or an APR to an effective rate in excel use what formula?
EFFECT(nominal_rate,npery) -nominal_rate is quoted rate or APR -npery is # of compounding periods per year
If you invest $100 for 5 years at 10% interest compounded annually, which of the following will be the formula for the future value of your investment
FV= 100(1.1)^5
compound interest
Interest earned on both the initial principal and the interest reinvested from prior periods.
Compound Interest
Interest earned on the accumulated interest added to the principal each period time value calculations used in Finance generally rely on compound interest; the base amount for your calculations change with each period, as interest is added to principal to make a larger amount for interest rates to act upon
Simple Interest
Interest earned on the original principal.
interest on interest
Interest earned on the reinvestment of previous interest payments.
simple interest
Interest earned only on the original principal amount invested.
level annuity
Its cash flows are the same in each period -classified by when their cash flows occur. -An annuity due is cash flow that occurs at beginning of each period.
to convert an EAR to a quoted rate, use what formula on spreadsheet?
NOMINAL(effect_rate,npery) effect_rate is the EAR
growing annuities
PV= C[(1/r-g)-(1/r-g)(1+g/1+r)^t]
if FV= PV(1+r) is the single period formula for FV, which is the single period present value formula?
PV= FV/(1+r)
the basic present value equation is
PV= FVt/ (1+r)^t
Which of the following is the correct formula for calculating the present value of a future amount, expected in t years at r percent interest?
PV=FV/(1+r)^t
Methods for Evaluating Interest Rates
Stated rate: the nominal rate stated on an annual basis Effective rate: includes the effect of compounding.
effective annual rate (EAR)
The interest rate expressed as if it were compounded once per year. ex. the 10.25%, rate that you will earn
stated interest rate
The interest rate expressed in terms of the interest payment made each period. Also quoted interest rate. -what a 10% rate is called
quoted interest rate
The interest rate expressed in terms of the interest payment made each period. Also stated interest rate.
compounding
The process of accumulating interest in an investment over time to earn more interest. -means earning interest on interest
level perpetuities
Those with regular payments that are the same in each time period.
change in interest rates
a change in interest rates can decrease present value if rates increase
Annuities
a finite, regular, cash flow stream -the cash flows involved in the annuity follow a regular pattern. -Rent, salary, pensions, and car payments are all examples of annuities 2 types of annuities: -level -growing
perpetuities
a regular stream of cash flow that is indefinite--it theoretically goes on forever emphasize near term cash flows rather than far-out cash flows 2 types: -level -growing
the interest rate charged per period multiplied by the number of periods per year is the
annual percentage rate -disclose an APR on all consumer loans
an annuity with payments beginning immediately rather than at the end of the period is called an ______
annuity due
to calculate the future value of $100 invested for t years at r interest rate, you enter the present value in your calculator and see a negative number. Why?
because the $100 is an outflow from you which should be negative
future value is the ______ value of an investment at some time in the future
cash
the effective annual rate (EAR) takes into account the ____ of interest that occurs within a year
compounding
the process of accumulating interest in an investment over time to earn more interest is called
compounding
Delaying investments
delaying investments can increase future value because less time periods are discounted
APR vs EAR
difference is small when APR and EAR interest rates are small, but difference is large when interest rates are large. ex. payday loans
the interest rate expressed as if it were compounded equally once per year is called the ______
effective annual rate
In almost all multiple cash flow calculations, it's implicitly assumed that the cash flows occur at the _____ of each period
end
true or false: future value refers to the amount of money an investment is worth today
false
which are the primary ways used to perform financial calculations today?
financial calculator spreadsheet functions
the amount an investment is worth after one or more periods is called the ____ value
future
if the interest rate is greater than 0,. the value of an annuity is always ____ an ordinary annuity
greater than
more frequent compounding leads to
higher EARs
a perpetuity is a constant stream of chas flows for a(n) _____ amount of time
infinite
When finding the present or future value of an annuity using a financial calculator, the ____ ____ should be entered as a percentage
interest rate
The time value factors
interest rates and time periods
an ordinary annuity consists of a(n) ______ stream of cash flows for a fixed period of time
level
given an investment amount and a set rate of interest, the ______ time period, the _____ future value
longer, greater
when entering variables in excel function, the "sign convention" can be critical to achieving a correct answer. Sign convention says that outflows are negative values; inflows positive. Which variables is this a consideration?
payment future value present value
real world examples of annuities
pensions mortgages leases
C/r is the formula for the present value of a(n) _____
perpetuity
if you want to know how much you need to invest today at 12% compounded annually in order to have $4000 in 5 years, you'll need to find a _______ value
present
the current value of a future cash flow discounted at the appropriate rate is called the _____ value
present
an interest rate expressed in terms of the interest payment made each period is called a(n) ______
quoted interest rate, stated interest rate
ordinary annuity
series of constant or level cash flows that occur at the *end* of each period for some fixed number of periods
what is the primary difference between time value or money date entries in your calculator and in a spreadsheet?
the interest rate in your calculator is entered as a whole number while in the spreadsheet function it is entered as a decimal
growing perpetuities
those with payments which increase at a regular rate.
because of ______ and ______, interest rates are often quoted in many different ways
tradition and legislation
the formula for the future value of an annuity factor is [(1+r)^t-1]/r
true
true or false: when calculating the PV of an annuity using the financial calculator, you enter the cash flows of the annuity in the PMT key
true
The first cash flow at the end of week 1 is $100, second at end of month 2 is $100, and 3rd at end of year 3 is $100. Cash flow patter is a(n) _____ type of cash flow
uneven
Suppose you expect to receive $5000 in one year, $4300 in 2 years, and $5000 in 3 years. Discount rate is 17%.
year 1: $5000/1.17= $4273 year 2: $4300/1.17^2= $3141 year 3: $5000/1.17^3= $3121
