5) Amortization tables are useful for each of the following reasons EXCEPT ________.
A) determining the principal balance due if the loan is being paid off early
B) determining how much of a total payment is interest and how much is principal for tax
purposes
C) determining the regular periodic total payment
D) All of these are useful purposes of an amortization table.
6) Your firm intends to finance the purchase of a new construction crane. The cost is $2,500,000.
What is the size of the annual ordinary annuity payment if the loan is amortized over a ten-year
period at a rate of 7.50%?
A) $228,611.56
B) $364,214.82
C) $3,391,475.16
D) There is not enough information to answer this question.
7) Your firm intends to finance the purchase of a new construction crane. The cost is $2,500,000.
What is the size of the first payment if the crane is financed with an interest-only loan at an
annual rate of 7.50%?
A) $187,500.00
B) $127,500.00
C) $3,391,475.16
D) There is not enough information to answer this question.
8) Your firm intends to finance the purchase of a new construction crane. The cost is $2,500,000.
How large is the payment at the end of year ten if the crane is financed at a rate of 7.50% as a
discount loan?
A) $5,152,578.91
B) $4,158,364.87
C) $3,391,475.16
D) There is not enough information to answer this question.
9) You have a choice among three types of loan and wish to pay the LEAST total cash flows. An
amortized loan will result in fewer dollars paid out than a discount or an interest-only loan for
the same amount, positive interest rate, and time period.
10) The first interest payment on a 5-year, 8%, $100,000, fully-amortized loan with annual
payments will be less than the last interest payment.
11) The last interest payment on a 12-year, 6%, $138,000, fully-amortized loan with annual
payments will be less than the first interest payment.
12) Once you begin making payments on an amortization schedule for a loan such as a mortgage
or car loan, most contracts clearly state that you may NOT pay off the loan early.
13) Complete the equal-payments three-year amortization table.
Year
Beginning
Principal
Payment
Interest
Expense
Principal
Reduction
Ending
Principal
1
$6,000.00
$480.00
$4,151.80
2
$2,328.20
$1,996.06
3
$2,155.74
Year
Beginning
Principal
Payment
Interest
Expense
Principal
Reduction
Ending
Principal
1
$6,000.00
$2,328.20
$480.00
$1,848.20
$4,151.80
2
$4,151.80
$2,328.20
$332.14
$1,996.06
$2,155.74
3
$2,155.74
$2,328.20
$172.46
$2,155.74
$0.00
There is more than one way to complete the table, but here is one solution. BP second year is
equal to the EP from the first year. All three payments are equal to $2,328.20. The interest
expense in year two is the difference between the year two payment and the principal reduction.
The EP in year two is equal to the BP in year three. The principal reduction in year three is equal
to the BP in year three. The interest expense in year three is the difference between the year three
payment and the principal reduction. The EP in year three is $0.00. The annual interest expense
may also be found by dividing the first year’s interest expense by the BP to determine that the
annual interest rate is 8%. You can then multiply the rate by the BP to determine the annual
interest expense for years two and three.
Diff: 3
Topic: 4.6 Amortization Schedules
AACSB: Analytical Thinking
LO: 4.6 Build and analyze amortization schedules.
39
Copyright © 2019 Pearson Education, Inc.
4.7 Waiting Time and Interest Rates for Annuities
1) William wishes to save enough money to purchase a retirement lake cabin. He is willing to
spend $200,000 for the cabin and he can save $20,000 per year and invest the money into an
account earning 7.00% per year. If his investments come in the form of equal annual end-of-the-
year cash flows and the first cash flow is in exactly one year, how long will it take him to save
enough money to buy the lake cabin?
A) Between 7 and 8 years
B) Between 9 and 10 years
C) Between 10 and 11 years
D) Exactly 10 years
2) Marie has a $1,200,000 investment portfolio and she wishes to spend $87,500 per year as an
ordinary annuity. If the investment account earns 5% annually, how long will her portfolio last?
Use a calculator to determine your answer.
A) 11.43 years
B) 14.17 years
C) 19.86 years
D) 23.72 years
3) Your parents have an investment portfolio of $450,000, and they wish to take out cash flows
of $60,000 per year as an ordinary annuity. How long will their portfolio last if the portfolio is
invested at an annual rate of 4.50%? Use a calculator to determine your answer.
A) 8.00 years
B) 9.10 years
C) 9.35 years
D) 10.14 years
4) You have saved $44,000 for college and wish to use $12,000 per year. If you use the money as
an ordinary annuity and earn 5.15% on your investment, how many years will your annuity last?
Use a calculator to determine your answer.
A) 4.27 years
B) 4.17 years
C) 3.59 years
D) 3.36 years
5) You need to repay a loan with a future value of $304,071.00 in 17.5 years. If you can make
annual year-end deposits of $12,000 into an account, what annual rate of return would you
require to earn enough money to pay the loan in full at the due date?
A) 7.92%
B) 8.73%
C) 4.39%
D) 4.30%
6) You currently have $67,000 in an interest-earning account. From this account, you wish to
make 10 year-end payments of $8,500 each. What annual rate of return must you make on this
account to meet your objective?
A) 4.16%
B) 4.58%
C) 6.42%
D) 7.32%
7) Solving for an unknown interest rate for annuity cash flows is an iterative (or trial-and-error)
process.
8) Present values and interest rates are inversely related. This means that if you deposit $1,000
into an interest-earning account today, it will take longer to reach a future value of $5,000 at an
interest rate of 6% than at a rate of 4%.
9) Solving for an unknown interest rate given the PV, FV, PMT, and N is an iterative (or trial-
and-error) process.
10) Derek and his father have an agreement. If Derek can save $15,000, his father will pay the
balance toward a used car (up to a total of $20,000). If Derek can save $3,800 per year, how long
will it take him to reach $15,000 if he invests the money into an account earning an annual rate
of 4.25%? Use a financial calculator.
11) You have $50,000 invested in an account paying 3.50%. If you just finished paying your
total college expenses for the coming year and your college costs $19,000 per year, how many
years will your money last? (Treat your costs like an annuity with the first payment one year
from today.) Use a financial calculator.
1) Arvidas recently won the Central States Lottery of $3,500,000. The lottery pays either a total
of twenty $175,000 payments per year with the first payment today (i.e., an annuity due), or
$2,000,000 today. At what interest rate would Arvidas be financially indifferent between these
two payout choices?
A) 6.04%
B) 6.36%
C) 6.88%
D) 8.00%
2) Jusef has won the $3,800,000 state lottery and intends to save all of the money for his
retirement. He chooses to receive an annual cash flow of $190,000 for twenty years, with the
first payment to be received one year from today. How much money will be in his retirement
account in twenty years if he can reinvest his money at an annual rate of 8.75%?
A) $9,374,989
B) $9,451,909
C) $10,007,801
D) $3,800,000
3) After winning the lottery, you state that you are indifferent between receiving twenty
$500,000 end-of-the-year payments (first payment one year from today), or a lump sum of
$5,297,007 today. What interest rate are you using in your decision-making process such that
you are indifferent between the two choices?
A) 5.00%
B) 6.00%
C) 7.00%
D) 8.00%
4) You have won the lottery and received a check for $1,275,156 today. You invest the lottery
check today at an annual interest rate of 8% and allow it to build for a full ten years. At that point
in time, you shift the money to an account paying only 6% per year. You plan to spend $175,000
per year in retirement (assume equal annual end-of-the-year cash flows) for 30 years, and your
first retirement cash flow is exactly eleven years from today. Will you have enough money to
fully fund your desired retirement? Use a calculator to determine your answer.
A) Yes, because your investment will allow you to spend up to $225,000 per year in retirement.
B) No, because your investment will allow you to spend up to only $158,000 per year in
retirement.
C) Yes, because your investment will allow you to spend up to $200,000 per year in retirement.
D) No, because your investment will allow you to spend up to only $137,000 per year in
retirement.
5) You just won the Publisher’s Clearing House Sweepstakes and the right to 30 after-tax
ordinary annuity cash flows of $123,291.18. Assuming a discount rate of 7.50%, what is the
present value of your lottery winnings? Use a calculator to determine your answer.
A) $2,345,823.18
B) $1,664,670.52
C) $1,456,116.46
D) There is not enough information to answer this question.
6) You have a choice between a lottery lump sum payout of $3,300,000 today or a series of
twenty annual annuity due payments. At a discount rate of 5.00%, how large must the annual
annuity due payments be to make you indifferent between the two choices? Use a calculator to
determine your answer.
A) $381,301.32
B) $351,179.40
C) $312,548.41
D) $252,190.99
7) You have a choice between a lottery lump sum payout of $5,509,253.62 today or a series of
twenty annual annuity payments of $500,000 each (first cash flow one year from today). At what
discount rate are you indifferent between the two choices?
A) 4.50%
B) 5.50%
C) 6.50%
D) 7.50%
8) You have a choice between a lottery lump sum payout of $10,000,000 today or a series of
thirty annual annuity payments (first payment one year from today). At a discount rate of 7.50%,
how large must the annual annuity payments be to make you indifferent between the two
choices?
A) $819,814.81
B) $833,102.77
C) $846,712.36
D) $400,000.00
9) It ALWAYS makes more sense financially to take the lump sum payout from winning a
lottery than taking the annual cash flows.
10) If we discount the annual payments from winning the lottery at 10%, the corresponding
present value is greater than if we discount the annual payments at 12%.
11) The present value of a lottery received as an annuity due is less than the present value of a
lottery whose cash flows are received as an ordinary annuity. (Assume that the interest rate used
to discount the cash flows is positive and equal between the two choices and that the magnitude
and number of cash flows are equal for the two choices. Only the timing of the cash flows differs
between the two choices.)
12) Your family recently won the $10,000,000 lottery and chose to accept the annual payout plan
of $500,000 today plus 19 more year-end cash flows of $500,000. If you discount these cash
flows at an annual rate of 8.0%, what is their present value?
13) At what interest rate would you be indifferent to a lottery payout today of $2,229,389.17, or
25 equal annual end-of-the-year payouts of $200,000?
1) The main variables of the TVM equation are ________.
A) present value, future value, time, interest rate, and payment
B) present value, future value, perpetuity, interest rate, and payment
C) present value, future value, time, annuity, and interest rate
D) present value, future value, perpetuity, interest rate, and principal
2) Present value calculations do which of the following?
A) Compound all future cash flows into the future
B) Compound all future cash flows back to the present
C) Discount all future cash flows back to the present
D) Discount all future cash flows into the future
3) An annuity is a series of ________.
A) variable cash payments at regular intervals across time
B) equal cash payments at regular intervals across time
C) variable cash payments at different intervals across time
D) equal cash payments at different intervals across time
4) Amounts of money can be added or subtracted only if they are at the same point in time.
5) It is fortunate that we have formula, calculator, and spreadsheets as tools to solve for variables
of the TVM equation, because there is no real way to visualize the timing and amount of cash
flows.
6) Discuss the nature and importance of the TVM equation.