Real Estate Finance & Investments, 16e (Brueggeman)
Chapter 3 Mortgage Loan Foundations: The Time Value of Money
1) In order to solve a compounding problem, you must know all four of the variables in order to
solve for the fifth variable.
2) One way to calculate the present value of a single payment is with the following formula: PV
= FV × (1 + i)n.
3) Assuming an interest rate of 6%, the present value of $1 that will be received a year from now
is $0.75.
4) The future value of $800 deposited today would be greater if that deposit earned 8% rather
than 7.75%.
5) You always see an ordinary annuity used in business and never see an annuity due used in
business.
6) The internal rate of return is the good feeling you get inside when you earn a return on your
investment.
7) An investment may have more than one internal rate of return.
8) Assume that an investment, with a single initial cost of $1,000 and a yield of $50 monthly for
10 years, had a 7% IRR in the 60th month and a 7.2% IRR five months later. The IRR can be
6.8% in the 62nd month.
9) The future value of a $1 annuity compounded at 5% annually is greater than the future value
of a $1 annuity compounded at 5% semi-annually.
10) If you deposit $1,000 in an account that earns 5% per year (compounded monthly), what will
the balance in the account be at the end of 5 years?
A) $1,272
B) $1,276
C) $1,280
D) $1,283
11) Ten years ago, you put $150,000 into an interest-earning account. Today it is worth
$275,000. What is the effective annual interest earned on the account?
A) 47.99%
B) 6.00%
C) 6.25%
D) 8.33%
12) Your friend has a trust fund that will pay him $100,000 at the end of 10 years. Your friend,
however, wants his money today. He promises to sign his trust fund over to you if you give him
some money today. You require a 20% interest rate on money you lend to friends. How much
would you be willing to lend under these terms?
A) $16,151
B) $50,000
C) $80,000
D) $0—it would be impossible to earn 20% interest on the loan.
13) A deposit placed in an interest-earning account earning 8% a year will double in value in
________ years.
A) 6
B) 8
C) 9
D) 72
14) At the end of 8 years, your friend wants to have $50,000 saved for a down payment on a
house. He expects to earn 8%—compounded monthly—on his investments over the next 8 years.
How much would your friend have to put in his investment account each month to reach his
goal?
A) $188
B) $374
C) $392
D) $521
15) Your friend just won the lottery. He has a choice of receiving $50,000 a year for the next 20
years or a lump sum today. The lottery uses a 15% discount rate. What would be the lump sum
amount your friend would receive?
A) $312,967
B) $316,426
C) $500,000
D) $1,000,000
16) The future value of a single deposit of $1,000 will be greatest when this amount is
compounded:
A) Annually
B) Semi-annually
C) Quarterly
D) Monthly
17) The future value of $1,000 compounded annually for 8 years at 12% may be calculated with
the following formula:
FV = $1,000 * (1 + 12%)8
If the same $1,000 was compounded quarterly, what formula would you use to calculate the FV?
A) FV = $1,000 * (1 + 3%)8
B) FV = $1,000 * (1 + 12%)32
C) FV = $1,000 * (1 + 3%)32
D) FV = $1,000 * (1 + 12%)2
18) If you saw a table containing the following factors, what kind of interest factor would you be
looking at?
End of Year
6%
1
1.06000
2
1.12360
3
1.19101
4
1.26247
5
1.33822
A) Present value of a single amount
B) Future value of a single amount
C) Present value of an annuity
D) Future value of an annuity
19) Begin with a single sum of money at period 0. First, calculate a future value of that sum at
12.01%. Then discount that future value back to period 0 at 11.99%. In relation to the initial
single sum, the discounted future value:
A) Is greater than the original amount
B) Is less than the original amount
C) Is the same as the original amount
D) Cannot be determined with the information given
20) The future value compound factor given for period (n) at 15%:
A) Would be less than the factor for period (n + 1) at 15%
B) Would be greater than the factor given for period (n + 1) at 15%
C) Would be the same as the factor given for period (n + 1) at 15%
D) Bears no relationship to the factor for period (n + 1) at 15%
21) Which of the following is not a basic component of any compounding problem?
A) An initial deposit
B) An interest rate
C) A period of time
D) A net present value
22) If an investment earns 12% annually:
A) An equivalent monthly investment would have to earn a higher equivalent nominal rate to
yield the same return
B) An equivalent monthly investment would have to earn a lower equivalent nominal rate to
yield the same return
C) An equivalent monthly investment would have to earn the same equivalent nominal rate to
yield the same return
D) A relation cannot be determined between a monthly and annual investment
23) The internal rate of return:
A) Is also known as the investment of investor’s yield
B) Represents a return on investment expressed as a compound rate of interest
C) Is calculated by setting the price of an investment equal to the stream of cash flows it
generates and solving for the interest rate
D) Can be defined by all of the above
24) Using only the information in the table below, what would the IRR be for an investment that
cost $500 in period 0 and was sold for $750 in period 5?
Present Value Factor for Reversion of $1
Period
6%
7%
8%
10%
1
.943396
.934579
.925926
.909091
2
.889996
.873439
.857339
.826446
3
.839619
.816298
.793832
.751315
4
.792094
.762895
.713503
.683013
5
.747258
.712986
.680583
.620921
6
.704961
.666643
.630170
.564474
A) Between 6% and 7%
B) Between 7% and 8%
C) Between 8% and 9%
D) Between 9% and 10%
25) Using only the information in the table below, approximately how much would you pay
today for an investment that pays $0 annual interest, but earns 8% interest over the next four
years and has a face value at maturity of $13,500?
Present Value Factor for Reversion of $1
Period
6%
7%
8%
10%
1
.943396
.934579
.925926
.909091
2
.889996
.873439
.857339
.826446
3
.839619
.816298
.793832
.751315
4
.792094
.762895
.713503
.683013
5
.747258
.712986
.680583
.620921
6
.704961
.666643
.630170
.564474
A) $8,000
B) $9,000
C) $10,000
D) $11,000
26) The name for a series of equal, annual cash flows that are received at the end of each period
is?
A) Ordinary annuity
B) Annuity due
C) Regular annuity
D) Ordinary annuity due
27) An investment that costs $105,000 today is expected to produce the following cash inflows
over each of the next five years: $20,000; $25,000; $23,000; $22,000; $21,000. What is the IRR
(compounded annually) for this investment?
A) 188.6%
B) 18.9%
C) 1.89%
D) −18.9%
28) If Beth make an initial investment of $1,000, how much will it be worth after three years if
her average return is 8.25% (use monthly compounding)?
A) $1,268.48
B) $17,354.20
C) $1,279.74
D) $1,020.77
29) For situations calling for other than annual compounding, each of these factors (when
present) must be adjusted for the number of compounding periods in a year:
A) PV & FV
B) N & i,
C) N, i, & PMT
D) N, i, PV, & PMT
30) How much money does Ted need to invest each month in order to accumulate $10,000 over a
five-year period, if he expects to get a return of 5.625% per year?
A) $144.71
B) $1,787.30
C) $148.94
D) $146.36