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FINC Ch5 Smartbook
Terms in this set (67)
A dollar invested today at 8.0 percent interest compounded annually will be worth _______ three years from now.
The value in t years of an investment made today at interest rate r is called the ___________ of your investment.
A dollar invested today at 8.0 percent simple annual interest will be worth _________ three years from now.
With simple interest, the bank calculates interest only on the principal investment: $1.00 + $.08 + $.08 + $.08 = $1.24. Do not confuse this with compound interest, which computes interest earned on interest.
When money is invested at compound interest, the growth rate is equal to the __________.
Joseph signs a contract with a company that will pay him $25,000. Following the principles of the time value of money, Joseph would be best off if he received payment:
at the beginning of the project
The time value of money states that a dollar today is worth more than a dollar tomorrow. Therefore, if he received the $25,000 at the beginning of the project, he would have 3 months to invest his money and have it grow.
A dollar invested today at 7.5 percent interest compounded annually will be worth _______ one year from now.
What is the future value of $100 invested for 4 years at 10% interest?
FV = $100 x (1+r)t = $100 x (1+.1)4=$146.41
A dollar invested today at 7.5 percent simple annual interest will be worth _______ one year from now.
FV = $1.00 + $0.075
If you are promised $100 in one year, $200 in two years, and $300 in 3 years, then those promises combined equal ______ $600 today.
This relates to the time value of money concept - $1 is worth more today than it is in the future. Therefore, any funds that you receive in the future will be worth less than they are if you received them today.
Compound growth means that value increases after t periods by:
(1 + growth rate)t
Which of the following is the correct formula for the discount factor?
The time value of money concept states that a dollar today is worth _______ a dollar tomorrow.
At a rate of interest of 10% (r), the present value (PV) or $100 will ___________ as the time period (t) ________________.
Present value will decrease as the time period increases. This follows the time value of money concept that a dollar today is worth more than a dollar tomorrow.
A stream of cash flows means that ________.
payments are made over time
Discounting a future value FV at interest rate r over time t is termed a ______________ calculation.
True or false: the discount factor refers to the present value of a $1 future payment.
This is true. The discount factor measures the present value of $1 received in year t.
If the interest rate (r) increases, what will happen to present value (PV) over time?
PV will decline
If the interest rate increases, the present value will decrease over time.
Today you deposit $1000 in an account paying 6% interest. At the end of years 1, 2 and 3 you will deposit $100 in that account. How much will you have at the end of year 4?
$1000(1.06)4 + $100(1.06)3 + $100(1.06)2 + $100(1.06)1 = $1,599.94
Real-world investments often involve many payments received or paid over time. Managers refer to this as a ___________________.
stream of cash flows
You will receive $100 in 1 year, $200 in 2 years and $300 in 3 years. If you can earn a 7.5% rate of interest, what is the present value of this stream of cash flows? (Please note that you receive nothing immediately - there is no initial payment).
$100/(1.075)^1 + $200/(1.075)^2 + $300/(1.075)^3 = $507.58
You put $100 in the bank now, $200 in the bank a year from now, and $300 in the bank in two years. How much money will you have available 3 years from now if you earn a 7.5% rate of interest? (Calculate the future value of this stream of cash flows. Refer to Example 5.6.)
$100 x (1.075)^3 + $200 x (1.075)^2 + $300 x (1.075) = $677.85
Match the financial calculator keys on the left below with their correct functions listed on the right.
n - number of periods
i - interest rate expressed as a percentage
PV - Present Value
FV - Future Value
PMT - constant recurring payment
True or false: The time value of money functions that are provided by your financial calculator are also available as functions in an Excel spreadsheet.
Which of the following is a perpetuity?
A constant stream of cash flows forever
Today you deposit $1000 in an account paying 6% interest. At the end of years 1, 2 and 3 you will deposit $100 in that account. What is the present value of that stream of cash flows?
$1000 + $100/(1.06)^1 + $100/(1.06)^2 + $100/(1.06)^3 = $1,267.30
The interest rate on the financial calculator is expressed as a
In Excel, cash inflows are recognized as ______ values and cash outflows are recognized as ______ values. Interest rates should be entered as ______.
positive, negative, decimals
How much is $100 at the end of each year forever at 10% interest worth today?
$100/.10 = $1,000
A perpetuity is a constant stream of cash flows for a(n) ______ period of time.
C/r is the formula for the present value of a(n) ____.
A traditional (non-growing) annuity consists of a(n) ________ stream of cash flows for a fixed period of time.
Which of the following is the correct equation for the present value of an annuity with regular payment C for t periods at interest rate r?
PV = C[1/r - 1/r(1+r)^t]
$200 at the end of each year forever at 10% per year is worth how much today?
$200/0.10 = $2,000
The present value of $100 paid annually at year end for 20 years at 10% per year is:
100[(1/.10)-(1/(.10(1.10)^20))] = 851.36
The present value formula for a(n) ______ is PV = C/r, where C is the constant and regularly timed cash flow to infinity, and r is the interest rate.
The future value of an annuity that lasts n years is equal to
the present value allowed to grow n years.
A fixed stream of cash flows that ends after a specified number of years is called a(n):
An ordinary annuity is a series of level payments that begin ____.
at the end of one payment period
The present value of an annuity of $1 per period is called the ______________.
What is the present value of an ordinary annuity that pays $100 per year for three years if the interest rate is 10% per year?
100[(1/.10)-(1/(.10(1.10)^3))] = 248.69
The present value of an annuity due is equal to the:
present value of an ordinary annuity x (1+r)
Find the future value of an annuity of $100 per year for 10 years at 10 percent per year.
First, find the PV by using the 10 year annuity factor: PV = $100 x 10 year annuity factor = $100 x [1/.1 - 1/.1x(1.1)^10]= $614.46
To find the future value, multiply $614.46 x (1.1)^10= $1,593.75.
A series of level payments that begins immediately for a specified period of time is called a(n):
What is the present value of an annuity consisting of 100 end of year payments of $50,000 when the interest rate is 6 percent? Use your financial calculator.
n=100,i=6,PMT=50000,fv FV=0, compute FV=830877.31
The effective annual interest rate is also known as the ______________.
annually compounded rate
If the interest rate is greater than zero, the present value of an annuity due is always ______ an ordinary annuity.
Cash flows for annuities due always come one period earlier than the corresponding cash flows for ordinary annuities. Therefore, each is discounted for one less period and the present value for the annuity due increases by a factor of (1+r) over that of the ordinary annuity.
To use your financial calculator to solve annuity problems, you use the _____ key for entry of the constant payment C.
Which of the following is a proper definition for the effective annual interest rate?
the interest rate that is annualized using compound interest
If a bank quotes a loan with an APR of 15 percent, compounded monthly, what is the periodic rate on this loan?
15/12 = 1.25 percent
A mortgage company is advertising a 30 year fixed rate mortgage with monthly payments and an APR of 3.0 percent. What is the effective annual interest rate of this loan?
First, find the monthly interest rate: .03/12= .0025%. Next, convert this to an annually compounded interest rate: 1 + effective annual rate = (1 + monthly rate)12 = (1 + .0025)12= 1.0304. The effective annual interest rate is 3.04%.
Inflation can be defined as:
An overall general rise in prices
Which type of price refers to the of purchasing power of money?
If a bank account pays a monthly interest rate on deposits of 0.5 percent, what is the APR the bank will quote for this account?
12 x 0.5 = 6 percent
In 2013 the CPI was about 2.5 times its level in 1981. If the cost of one semester of college was $5000 in 1981, what should the nominal cost of a semester of college be in 2013 assuming the real price is constant?
2.5 x $5000= $12,500
A bank offers a savings account with an APR of 9 percent with monthly compounding. What is the effective annual interest rate of this investment?
EAR=(1 + 0.09/12)^12 - 1 = 9.38 percent
The best known price index used by economists who measure inflation is ________.
the consumer price index (CPI)
True or false: the nominal interest rate can be defined as an interest rate quoted today by a financial institution on a loan or investment, such as an APR or a periodic rate.
______ dollars refer to the actual number of dollars of the day, whereas ______ dollars refer to the amount of purchasing power.
The Annual Percentage Rate (APR) on a loan or investment is properly defined as:
the interest rate per period multiplied by the number of compounding periods per year
In 2013 the CPI was about 2.5 times its level in 1981. If the price of a pack of cigarettes was $1.00 in 1981 and $5.00 in 2013, then the real price has ______ since 1981. The inflation-adjusted price today should be _______ if there had been no real growth in the price of a pack.
Your neighborhood bank is offering investors a money market account that pays 3.5 percent interest on deposits. If the current annual rate of inflation is 1.2 percent, how much is the exact real rate for this account?
[1.035/1.012] - 1 = 2.27 percent
The real interest rate can be defined as:
the real change in value of an investment (or real cost of a loan) after adjustment for inflation
Which type of interest rate is generally quoted for loans and by banks and other financial institutions?
Which of the following statements are true regarding the present value of a stream of cash payments?
Nominal cash payments should be discounted using a nominal interest rate.
Real cash payments should be discounted using a real interest rate.
The rate quoted by Big Bank on a car loan is 8 percent. The annual rate of inflation is currently 1.5 percent. What is the approximate real interest rate paid by the consumer on this loan?
The equation used to determine the approximate real interest rate is:
real interest rate= nominal interest rate - inflation rate
Real cash flow must be discounted by the
real interest rate.
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