Chapter 5: The Time Value 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? 6 Percent
Which of the following are valid interest compounding periods? Daily, monthly, annually,
weekly, continuously, quarterly, and semiannually.
Real-world investments often involve many payments received or paid over time. Managers
refer to this as a: stream of cash flows
Match the financial calculator keys on the left below with their correct functions listed on the
right.
N – number of periods
I – interest rate
PV – present value
FV – future value
PMT – constant recurring payment
Which of the following is perpetuity? A constant stream of cash flows period.
The real interest rate can be defined as: the real change in value of an investment (or real cost
of a loan) after adjustment of inflation
Which of the following is the correct formula for the discount factor? 1/(1+r)t
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.
The interest rate per period is most properly defined as: the interest rate that is applied to the
current balance every compounding period.
The value in t years of an investment made today at interest rate r is called the future value of
your investment.
Which of the following are annuities? Installment loan payments and monthly rent payments in
a lease.
A traditional (non-growing) annuity consists of a fixed stream of cash flows for a fixed period of
time.
The best known price index used by economists who measure inflation is: the consumer price
index (CPI)
Compound growth means that value increases after t periods by: (1 + growth rate)t
Present value represents what an amount of money promised or expected in the future is
worth: today
Which of the following statements are true regarding the present value of a stream of cash
payments? Real cash payments should be discounted using a real interest rate & nominal cash
payments should be discounted using a nominal interest rate.
If the future value is $750 in 3 years and the interest rate is 15 percent, what is the present
value? $750/(1.15)3 = $493.14
For a given FV and t, the value of PV decreases as r increases.
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? .$248.69
A dollar invested today at 7.5 percent interest compounded annually will be worth one year
from now. $1.075 [FV = $1.00(1+0.075)1]
If interest rates go up, the present value of a perpetuity will decrease.
A series of level payments that begins immediately for a specified period of time is called an:
annuity due
If you are promised $100 in one year, $200 in two years, and $300 in 3 years, then those
promises combined equal less than $600 today.
The “t-year annuity factor”, which is used to calculate the present value of a $1.00 annuity for t-
years, is given by which of the following equations? [1/r-1/r(1+r)t]
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
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 rate of this loan? EAR = (1-0.03/12)12 – 1 =
3.04
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 increased since 1981. The inflation-
adjusted price today should be $2.50 if there had been no real growth in the price of a pack.
If interest rates go down, the present value of a perpetuity will increase.
You deposited $250 in a savings account 12 years ago. Today the balance in that account is
$690. What annual rate of interest did you earn? PV = -250, FV = 690, n = 12, PMT = 0, compute
i = 8.88%
Another name for the interest rate used to calculate PV is the discount rate.
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