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80) You are comparing two annuities with equal present values. The applicable discount rate is
6.5 percent. One annuity will pay $2,000 annually, starting today, for 20 years. The second
annuity will pay annually, starting one year from today, for 20 years. What is the annual payment
for the second annuity?
A) $2,225
B) $2,075
C) $2,000
D) $2,130
E) $2,405
81) Kay owns two annuities that will each pay $500 a month for the next 12 years. One payment
is received at the beginning of each month while the other is received at the end of each month.
At a discount rate of 7.25 percent, compounded monthly, what is the difference in the present
values of these annuities?
A) $289.98
B) $265.42
C) $299.01
D) $308.00
E) $312.50
82) What is the future value of $845 a year for seven years at an interest rate of 11.3 percent?
A) $6,683.95
B) $6,075.69
C) $8,343.51
D) $8,001.38
E) $8,801.91
83) What is the future value of $3,100 a year for six years at interest rate of 8.9 percent?
A) $20,255.40
B) $26,847.26
C) $27,134.16
D) $23,263.57
E) $24,414.67
84) Janet saves $3,000 a year at an interest rate of 4.2 percent. What will her savings be worth at
the end of 35 years?
A) $229,317.82
B) $230,702.57
C) $230,040.06
D) $234,868.92
E) $236,063.66
85) You plan to save $2,400 a year and earn an average rate of interest of 5.6 percent. How much
more will your savings be worth at the end of 40 years if you save at the beginning of each year
rather than at the end of each year?
A) $17,822.73
B) $18,821.10
C) $18,911.21
D) $19,103.04
E) $18,115.31
86) You borrow $12,600 to buy a car. The terms of the loan call for monthly payments for five
years at an interest rate of 4.65 percent, compounded monthly. What is the amount of each
payment?
A) $253.22
B) $243.73
C) $230.62
D) $235.76
E) $233.04
87) You borrow $199,000 to buy a house. The mortgage rate is 5.5 percent, compounded
monthly. The loan period is 30 years, and payments are made monthly. If you pay for the house
according to the loan agreement, how much total interest will you pay?
A) $218,086
B) $198,161
C) $207,764
D) $211,086
E) $185,059
88) You want to have $20,000 saved in five years. If you can earn 4.5 percent on your savings,
what amount must you save each year if the amount you save each year is the same?
A) $3,775.04
B) $3,798.34
C) $3,801.03
D) $3,655.83
E) $4,038.01
89) On the day she retired, Kate had $101,900 in retirement savings. She expects to earn 4.5
percent, compounded monthly, and live 24 more years. How much can she withdraw from her
savings each month during her retirement if she plans to die on the day she spends her last
penny?
A) $592.07
B) $609.21
C) $539.87
D) $604.86
E) $579.22
90) Donaldson's purchased some property for $1.2 million, paid 25 percent down in cash, and
financed the balance for 12 years at 7.2 percent, compounded monthly. What is the amount of
each monthly mortgage payment?
A) $8,440.01
B) $8,978.26
C) $9,351.66
D) $9,399.18
E) $9,513.67
91) Assume you graduate with $31,300 in student loans at an interest rate of 5.25 percent,
compounded monthly. If you want to have this debt paid in full within three years, how much
must you pay each month?
A) $871.30
B) $873.65
C) $876.79
D) $941.61
E) $980.40
92) You are buying a car for $7,500, paying $900 down in cash, and financing the balance for 24
months at 6.5 percent, compounded monthly. What is the amount of each monthly loan
payment?
A) $318.64
B) $294.01
C) $302.02
D) $264.78
E) $245.09
93) Your parents plan to give you $200 a month for four years while you are in college. At a
discount rate of 6 percent, compounded monthly, what are these payments worth to you when
you first start college?
A) $8,797.40
B) $8,409.56
C) $8,198.79
D) $8,516.06
E) $8,279.32
94) You just won the lottery! As your prize you will receive $1,500 a month for 150 months. If
you can earn 7 percent, compounded monthly, on your money, what is this prize worth to you
today?
A) $137,003.69
B) $149,676.91
C) $137,962.77
D) $148,104.26
E) $150,723.76
95) You want to purchase an annuity that will pay you $1,200 a quarter for 15 years and earn a
return of 5.5 percent, compounded quarterly. What is the most you should pay to purchase this
annuity?
A) $52,988.16
B) $48,811.20
C) $47,455.33
D) $48,450.67
E) $52,806.30
96) A car dealer is willing to lease you a car for $319 a month for 60 months. Payments are due
on the first day of each month starting with the day you sign the lease contract. If your cost of
money is 4.9 percent, compounded monthly, what is the current value of the lease?
A) $17,882.75
B) $17,906.14
C) $17,014.34
D) $16,235.42
E) $16,689.54
97) Sara is the recipient of a trust that will pay her $500 on the first day of each month, starting
immediately and continuing for 40 years. What is the value of this inheritance today if the
applicable discount rate is 7.3 percent, compounded monthly?
A) $76,811.30
B) $67,557.52
C) $89,204.04
D) $78,192.28
E) $80,006.09
98) Starting today, Alicia is going to contribute $100 a month to her retirement account. Her
employer matches her contribution by 50 percent. If these contributions remain constant, and she
earns a monthly rate of .55 percent, how much will her savings be worth 40 years from now?
A) $399,459.44
B) $300,456.74
C) $349,981.21
D) $299,189.16
E) $354,087.88
99) An annuity costs $70,000 today, pays $3,500 a year, and earns a return of 4.5 percent. What
is the length of the annuity time period?
A) 54.96 years
B) 49.48 years
C) 52.31 years
D) 43.08 years
E) 48.00 years
100) You are borrowing $5,200 at 7.8 percent, compounded monthly. The monthly loan payment
is $141.88. How many loan payments must you make before the loan is paid in full?
A) 30
B) 36
C) 40
D) 42
E) 48
101) You are retired, have $264,500 in your savings, withdraw $2,000 each month, and earn 4.5
percent, compounded monthly. How long will it be until you run out of money?
A) 13.67 years
B) 15.25 years
C) 22.08 years
D) 13.02 years
E) 18.78 years
102) A growing perpetuity is currently valued $6,225.81. The next annuity payment will be $386
and the discount rate is 9 percent. What is the annuity's rate of growth?
A) 2.45 percent
B) 3.10 percent
C) 2.80 percent
D) 2.50 percent
E) 2.95 percent
103) Christina will receive annuity payments of $1,200 a year for five years, with the first
payment occurring at Year 4. What is the value of this annuity to her today at a discount rate of
7.25 percent?
A) $4,209.19
B) $4,774.04
C) $3,961.80
D) $4,887.48
E) $4,111.08
104) Jeanette expects to live 30 years after she retires. At the end of the first year of her
retirement, she wants to withdraw $35,000 from her savings. Each year thereafter, she wants to
increase her annual withdrawal by 3.5 percent. If she can earn 5.5 percent on her savings, how
much does she need to have in retirement savings on the day she retires?
A) $862,001.34
B) $648,909.18
C) $764,458.87
D) $919,028.56
E) $832,004.01
105) Nu-Tools plans to set aside an equal amount of money each year, starting today, so that it
will have $25,000 saved at the end of three years. If the firm can earn 4.7 percent, how much
does it have to save annually?
A) $7,596.61
B) $7,689.16
C) $8,004.67
D) $8,414.14
E) $8,333.33
106) Seven years ago, Carlos took out a mortgage for $185,000 at 5.6 percent, compounded
monthly, for 30 years. He has made all of the monthly payments as agreed. What is his current
loan balance?
A) $ 157,308.74
B) $141,833.33
C) $164,621.06
D) $148,211.09
E) $142,779.47
107) Assume mortgage rates increase to 7.5 percent and you borrow $329,000 for 30 years to
purchase a house. What will your loan balance be at the end of the first 15 years of monthly
payments?
A) $238,854.07
B) $194,311.64
C) $248,153.73
D) $207,308.09
E) $192,938.72
108) Angela borrowed $5,000 for five years at an APR of 6.2 percent. The loan calls for equal,
annual principal payments. Interest will also be paid annually. What will be her loan payment in
Year 2?
A) $1,248
B) $1,310
C) $1,016
D) $1,274
E) $1,157
109) A small craft store located in a kiosk expects to generate annual cash flows of $6,800 for
the next three years. At the end of the three years, the business is expected to be sold for
$15,000. What is the value of this business at a discount rate of 15 percent?
A) $30,100.07
B) $29,408.27
C) $25,388.67
D) $17,409.09
E) $19,477.67
110) TH Manufacturers expects to generate cash flows of $129,600 for the next two years. At the
end of the two years the business will be sold for an estimated $3.2 million. What is the value of
this business at a discount rate of 14 percent?
A) $2,704,655
B) $2,284,644
C) $2,675,703
D) $2,848,392
E) $2,900,411
111) Jenni's Diner has expected net annual cash flows of $16,200, $18,600, $19,100, and
$19,500 for the next four years, respectively. At the end of the fourth year, the diner is expected
to be worth $57,900 cash. What is the present value of the diner at a discount rate of 11.6
percent?
A) $93,090.25
B) $87,492.16
C) $101,016.38
D) $104,998.02
E) $98,411.20
112) Explain the net present value formula and also explain what the net present value
represents.
NPV = −Cost + PV
113) Marlene and Darlene are each the recipient of an annuity that pays $1,000 at the end of each
year for twelve years. They both received their first payment on the same day. Explain how
Marlene and Darlene could have different NPVs for their annuities.
114) There are multiple factors that affect the value of an annuity. Explain what these four
factors are and discuss how a change in each factor will impact both the present value and the
future value of the annuity.
115) Tobi owns a perpetuity that will pay $1,500 a year, starting one year from now. He offers to
sell you all the payments remaining after the first 25 payments have been paid. What price
should you offer him today for payments 26 onward if the discount rate is 8 percent? What does
your offer price illustrate about the value of perpetuities?
116) What is the difference between an ordinary annuity and an annuity due? What value can be
used to quickly convert both the present value and the future value of an ordinary annuity into
annuity due values?
