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32) George and Barbara will be retiring in four years and would like to buy a lake house. They
estimate that they will need $150,000 at the end of four years to buy this house. They want to
make four equal annual payments into an account at the end of each year. If they can earn 16%
on their money, compounded annually, over the next four years, how much must they invest at
the end of each year for the next four years to have accumulated $150,000 by retirement?
A) $25,523
B) $29,606
C) $46,212
D) $43,500
E) $37,500
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
33) You have been accepted to study gourmet cooking at Le Cordon Bleu Culinary Institute in
Paris, France. You will need $15,000 every six months (beginning six months from now) for the
next three years to cover tuition and living expenses. Mom and Dad have agreed to pay for your
education. They want to make one deposit now in a bank account earning 6% interest,
compounded semiannually, so that you can withdraw $15,000 every six months for the next three
years. How much must they deposit now?
A) $97,026
B) $73,760
C) $90,000
D) $81,258
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
34) Horace and Myrtle want to buy a house. Their banker offered them a fully amortizing
$95,000 loan at a 12% annual rate for 20 years. What will their monthly payment be if they make
equal monthly installments over the next 20 years?
A) $1,046
B) $749
C) $1,722
D) $1,346
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
11
35) Harold Hawkins bought a home for $320,000. He made a down payment of $45,000; the
balance will be paid off over 30 years at a 6.775% rate of interest. How much will Harold's
monthly payments be? Round off to the nearest $1.
A) $1,450
B) $1,788
C) $3,200
D) $1,682
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
36) You buy a race horse, which has a winning streak for four years, bringing in $500,000 per
year, and then it dies of a heart attack. If you paid $1,518,675 for the horse four years ago, what
was your annual return over this four-year period?
A) 8%
B) 33%
C) 18%
D) 12%
Topic: 6.1 Annuities
Keywords: internal rate of return
Principles: Principle 1: Money Has a Time Value
5.116%. What is the quoted rate of interest on the loan?
A) 4.5%
B) 4.75%
C) 5%
D) 6%
Topic: 6.1 Annuities
Keywords: effective annual rate
Principles: Principle 1: Money Has a Time Value
12
38) You deposited $2,000 in a bank account paying 6% on January 1, 2004, and then you made
$2,000 deposits on January 1 in 2005 and 2006. Which of the following expressions will
calculate your bank balance just after the last payment was deposited?
A) FV = $2,000[1.06]-1 + $2,000[1.06]-2 + $2,000[1.06]-3
B) FV = $2,000[1.06]1 + $2,000[1.06]2 + $2,000[1.06]3
C) FV = $2,000[1.06]0 + $2,000[1.06]1 + $2,000[1.06]2
D) FV = $2,000[1.06]-0 + $2,000[1.06]-1 + $2,000[1.06]-2 + $1,000[1.06]-3
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
39) Harry just bought a new four-wheel-drive Jeep Cherokee for his lumber business. The price
of the vehicle was $35,000, of which he made a $5,000 down payment and took out an amortized
loan for the rest. His local bank made the loan at 12% interest for five years. He is to pay back
the principal and interest in five equal annual installments beginning one year from now.
Determine the amount of Harry's annual payment.
A) $8,322
B) $9,600
C) $9,709
D) $6,720
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
40) Your investment goal is to have $3,000,000 in 40 years for retirement. You decide to invest in
a mutual fund today that pays 12% per year compounded monthly. How much must you invest at
the end of each month to meet your investment goal? Round to the nearest $1.
A) $245
B) $255
C) $285
D) $305
E) $315
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
13
15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate the
total amount of interest dollars you will pay the bank over the life of the loan. Round to the
nearest dollar and assume end-of-month payments.
A) $47,451
B) $51,644
C) $54,776
D) $57,798
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
42) You have borrowed $70,000 to buy rental property. You plan to make monthly payments over
a 15-year period. The bank has offered you a 9% interest rate compounded monthly. Calculate
the principal paid to the bank in month two of the loan. Assume end-of-period payments.
A) $184.01
B) $186.38
C) $188.46
D) $190.64
E) $192.73
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
43) A friend of yours plans to begin saving for retirement by depositing $2,000 at the end of each
year for the next 25 years. If she can earn 10% annually on her investment, how much will she
have accumulated at the end of 25 years?
A) $50,000
B) $196,692
C) $100,000
D) $216,361
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
14
44) How much must you deposit at the end of each of the next 10 years in a savings account
paying 5% annually in order to have $10,000 saved by the end of the 10th year?
A) $1,000
B) $1,638
C) $1,500
D) $795
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
45) What is the value today of an investment that pays $500 every year at year-end during the
next 15 years if the annual interest rate is 9%?
A) $4,030.50
B) $7,500.00
C) $3,500.00
D) $7,000.00
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
46) How much would an investor be willing to pay today for an investment that returns $1,000
every year at year-end for five years if he wants to earn a 10% annual return on the investment?
A) $1,000
B) $3,791
C) $5,000
D) $7,700
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
47) A friend of yours would like you to lend him $5,000 today to be paid back in 5 annual
payments. What would be the equal annual end-of-year payment on this loan if you charge your
friend 7% interest?
A) $869.45
B) $1,000.00
C) $1,219.51
D) $1,350.00
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
15
48) Recently you borrowed money for a new car. The loan amount is $15,000 to be paid back in
equal annual payments which begin today, and will continue to be payable at the beginning of
each year for a total of five years. Interest on the loan is 8%. What is the amount of the loan
payment?
A) $3,756.85
B) $4,200.00
C) $3,478.31
D) $3,000.00
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
49) A friend of yours borrows $19,500 from the bank at 8% annually to be repaid in 10 equal
annual end-of-year installments. The interest paid on this loan in year three is:
A) $1,336.01.
B) $1,560.00.
C) $2,906.11.
D) $1,947.10.
Topic: 6.1 Annuities
Keywords: interest paid
Principles: Principle 1: Money Has a Time Value
50) If a loan of $10,000 is paid back in equal annual end-of-year payments of $2,570.69 during
the next five years, what is the annual interest rate on the loan?
A) 2%
B) 5%
C) 9%
D) 12%
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
16
51) What is the present value of an investment that pays $10,000 every year at year-end for the
next five years and $15,000 every year at year-end for years six through 10? The annual rate of
interest for the investment is 9%.
A) $125,000.00
B) $97,250.00
C) $135,173.00
D) $76,827.50
Topic: 6.1 Annuities
Keywords: present value income stream
Principles: Principle 1: Money Has a Time Value
52) Congratulations. You just won the California State Lottery. The amount awarded is paid in 20
equal annual installments, at the beginning of each year. You can invest your money at 6.6%,
compounded annually. You have calculated that the lottery is worth $20,975,400 today. How
much was the amount awarded?
A) $75,310,294
B) $36,000,000
C) $81,047,770
D) $42,000,000
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
53) If you have $375,000 in an account earning 9% annually, what constant amount could you
withdraw each year and have nothing remaining at the end of 20 years?
A) $7,500
B) $18,750
C) $66,912
D) $5,575
E) $41,080
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
17
54) You wish to borrow $12,000 to be repaid in 60 monthly installments of $257.93. The annual
interest rate is:
A) 10.50%.
B) 12.75%.
C) 15.25%.
D) 6.50%.
E) 8.80%.
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
55) You wish to purchase a condo at a cost of $175,000. You are able to make a down payment of
$35,000 and will borrow $140,000 for 30 years at an interest rate of 7.25%. How much is your
monthly payment?
A) $650
B) $955
C) $1,092
D) $1,023
E) $875
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
56) Suppose that you wish to save for your child's college education by opening up an
educational IRA. You plan to deposit $100 per month into the IRA for the next 18 years. Assume
that you will be able to earn 10%, compounded monthly, on your investment. How much will
you have accumulated at the end of 18 years?
A) $21,600
B) $54,719
C) $33,548
D) $85,920
E) $60,056
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
18
35 years. Deposits to the Roth IRA will be made via a $150 payroll deduction at the end of each
month. Assume that Edward will earn 8.75% annual interest compounded monthly over the life
of the IRA. How much will he have at the end of 35 years?
A) $125,250
B) $250,321
C) $363,000
D) $414,405
Topic: 6.1 Annuities
Keywords: future value of annuity
Principles: Principle 1: Money Has a Time Value
58) What is a series of equal payments for a finite period of time called?
A) A perpetuity
B) An axiom
C) A lump sum
D) An annuity
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
59) Which of the following statements is true?
A) The future value of an annuity would be greater if funds are invested at the beginning of each
period instead of at the end of each period.
B) An annuity is a series of equal payments that are made, or received, forever.
C) The effective annual rate (APR) of a loan is higher the less frequently payments are made.
D) The future value of an annuity would be greater if funds are invested at the end of each period
rather than at the beginning of each period.
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
19
60) What is a series of equal payments to be received at the end of each period, for a finite period
of time, called?
A) A perpetuity
B) An annuity due
C) A cash cow
D) A deferred annuity
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
61) What is a series of equal payments to be received at the beginning of each period, for a finite
period of time, called?
A) A perpetuity
B) An annuity due
C) A cash cow
D) A deferred annuity
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
62) One characteristic of an annuity is that an equal sum of money is deposited or withdrawn
each period.
Topic: 6.1 Annuities
Keywords: annuity
Principles: Principle 1: Money Has a Time Value
63) The present value of an annuity increases as the discount rate increases.
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
64) We can use the present value of an annuity formula to calculate constant annual loan
payments.
Topic: 6.1 Annuities
Keywords: present value of annuity
Principles: Principle 1: Money Has a Time Value
20
