T12-1
REVIEW EXERCISES | CHAPTER 12—SECTION I
Use Table 12-1 to calculate the future value of the following ordinary annuities:
Annuity
Payment
1. $1,000
2. $2,500
3. $10,000
4.
$200
5. $1,500
Payment
Frequency
every
every
every
every
every
3 months
6 months
year
month
3 months
Time
Nominal
Interest
Period (years) Rate (%) Compounded
4
5
10
2
7
8
10
9
12
16
quarterly
semiannually
annually
monthly
quarterly
Future Value
of the Annuity
$18,639.29
$31,444.73
$151,929.30
$5,394.69
$74,951.37
Use Table 12-1 to calculate the future value of the following annuities due:
Annuity
Payment
6. $400
7. $1,000
8.
$50
9. $2,000
10. $4,400
Payment
Frequency
every
every
every
every
every
6 months
3 months
month
year
6 months
Time
Nominal
Interest
Period (years) Rate (%) Compounded
12
3
2 12
25
8
10
8
18
5
6
semiannually
quarterly
monthly
annually
semiannually
Future Value
of the Annuity
$18,690.84
$13,680.33
$1,905.09
$100,226.90
$91,351.00
1. R 5 2% P 5 16 F 5 18.6329
Future value 5 1,000 3 18.6329 5 $18,632.90
6. R 5 5% P 5 24 1 1 5 25 F 5 47.72710 2 1.00000 5 46.72710
Future value 5 400 3 4672710 5 $18,690.84
T12-2
REVIEW EXERCISES | CHAPTER 12—SECTION I
Solve the following exercises by using Table 12-1:
11. Liberty Savings & Loan is paying 6% interest compounded monthly. How much will
$100 deposited at the end of each month be worth after 2 years?
1
R 5 % P 5 24 F 5 25.43196
2
Annuity 5 25.43196 3 100 5 $2,543.20
12. Emory Distributors, Inc., deposits $5,000 at the beginning of each 3-month period for
6 years in an account paying 8% interest compounded quarterly.
a. How much will be in the account at the end of the 6-year period?
R 5 2% P 5 24 1 1 5 25 F 5 32.03030 2 1.00000
Account value 5 31.03030 3 5,000 5 $155,151.50
b. What is the total amount of interest earned in this account?
Total investment 5 5,000.00 3 24 5 120,000.00
Interest earned 5 155,151.50 2 120,000.00 5 $35,151.50
13. When Chuck Darwin was born, his parents began depositing $500 at the beginning of
every year into an annuity to save for his college education. If the account paid 7%
interest compounded annually for the first 10 years and then dropped to 5% for the
next 8 years, how much is the account worth now that Chuck is 18 years old and is
ready for college?
Amount $500.00 R 5 7% P 5 10 1 1 5 11 F 5 15.78360 2 1.00000
500.00 3 14.78360 5 $7,391.80 First 10 years
Amount $7,391.80 R 5 5% P 5 8 F 5 1.47746 (Table 11-1)
$7,391.80 3 1.47746 5 $10,921.09 First 10 years compounded 8 more years
Amount $500.00 R 5 5% P 5 8 1 1 5 9 F 5 11.02656 2 1.00000
500.00 3 10.02656 5 5,013.28 Next 8 years
$10,921.09 1 $5,013.28 5 $15,934.37 Total after 18 years
REVIEW EXERCISES
|
CHAPTER 12—SECTION I
1
years?
2
FV 5 (1 1 .01) 3 81,669.67 5 $82,486.37 Annuity due
c. (Optional) Use the formula for an annuity due to calculate how much would be in
the account after 5 years if it had been an annuity due.
P 5 60
(1 1 .01) 60 2 1
FV 5 1,000
5 $81,669.67 Ordinary annuity
.01
R 5 1%
b. (Optional) Use the formula for an ordinary annuity to calculate how much would
be in the account if the owner saved for 5 years.
R 5 1% P 5 30 F 5 34.78489
1,000.00 3 34.78489 5 $34,784.89
a. How much will be available for the second store after 2
14. Surfside Hardware has been in business for a few years and is doing well. The owner
has decided to save for a future expansion to a second location. He invests $1,000 at
the end of every month at 12% interest compounded monthly.
T12-3
BUSINESS DECISION
|
CHAPTER 12—SECTION I
251,405.04 2 209,282.37 5 $42,122.67 More
R 5 6% P 5 30 1 1 5 31 F 5 84.80168 2 1.00000
3,000.00 3 83.80168 5 $251,405.04
d. If you found a bank that paid 6% interest compounded annually, rather than 5%,
how much more would you have in the account after 30 years?
R 5 5% P 5 30 1 1 5 31 F 5 70.76079 2 1.00000
3,000.00 3 69.76079 5 $209,282.37
c. When you retire in 30 years, what will be the total worth of the account?
R 5 5% P 5 20 1 1 5 21 F 5 35.71925 2 1.00000
3,000.00 3 34.71925 5 $104,157.75
b. How much would the account be worth after 20 years?
R 5 5% P 5 10 1 1 5 11 F 5 14.20679 2 1.00000
3,000.00 3 13.20679 5 $39,620.37
a. How much would the account be worth after 10 years?
15. As part of your retirement plan, you have decided to deposit $3,000 at the beginning
of each year into an account paying 5% interest compounded annually.
PLANNING YOUR NEST EGG
T12-4
REVIEW EXERCISES
|
CHAPTER 12—SECTION II
$300
$2,000
$1,600
$1,000
$8,500
every
every
every
every
every
6 months
year
3 months
month
3 months
Payment
Frequency
7
20
6
1 34
3
10
7
12
6
16
semiannually
annually
quarterly
monthly
quarterly
Time
Nominal
Interest
Period (years) Rate (%) Compounded
$2,969.59
$21,188.02
$27,096.86
$19,887.98
$79,773.10
Present Value
of the Annuity
6.
7.
8.
9.
10.
$1,400
$1,300
$500
$7,000
$4,000
Annuity
Payment
every
every
every
every
every
year
3 months
month
6 months
year
Payment
Frequency
10
4
2 14
12
18
11
12
18
8
7
annually
quarterly
monthly
semiannually
annually
Time
Nominal
Interest
Period (years) Rate (%) Compounded
$9,151.87
$16,819.32
$11,199.32
$110,997.88
$43,052.88
Present Value
of the Annuity
Use Table 12-2 to calculate the present value of the following annuities due:
1.
2.
3.
4.
5.
Annuity
Payment
Use Table 12-2 to calculate the present value of the following ordinary annuities:
T12-5
9. R 5 4% P 5 23 F 5 14.85684 1 1.00000
Amount 5 7,000.00 3 15.85684 5 $110,997.88
10. R 5 7% P 5 17 F 5 9.76322 1 1.00000
Amount 5 4,000.00 3 10.76322 5 $43,052.88
5. R 5 4% P 5 12 F 5 9.3850
Amount 5 8,500.00 3 9.38507 5 $79,773.10
1
8. R 5 1 % P 5 26 F 5 21.39863 1 1.00000
2
Amount 5 500.00 3 22.39863 5 $11,199.32
3. R 5 3% P 5 24 F 5 16.93554
Amount 5 1,600.00 3 16.93554 5 $27,096.86
1
4. R 5 % P 5 21 F 5 19.88798
2
Amount 5 1,000.00 3 19.88798 5 $19,887.98
7. R 5 3% P 5 15 F 5 11.93794 1 1.00000
Amount 5 1,300.00 3 12.93794 5 $16,819.32
CHAPTER 12—SECTION II
2. R 5 7% P 5 20 F 5 10.59401
Amount 5 2,000.00 3 10.59401 5 $21,188.02
|
6. R 5 11% P 5 9 F 5 5.53705 1 1.00000
Amount 5 1,400.00 3 6.53705 5 $9,151.87
REVIEW EXERCISES
1. R 5 5% P 5 14 F 5 9.89864
Amount 5 300.00 3 9.89864 5 $2,969.59
T12-6
REVIEW EXERCISES
|
CHAPTER 12—SECTION II
R 5 6% P 5 10 2 1 5 9 F 5 6.80169 1 1.00000
Amount 5 2,000.00 3 7.80169 5 $15,603.38
12. Maureen O’Connor wants to receive an annuity of $2,000 at the beginning of each
year for the next 10 years. How much should be deposited now at 6% compounded
annually to accomplish this goal?
1
R 5 % P 5 24 F 5 22.56287
2
Amount 5 400.00 3 22.56287 5 $9,025.15
11. Transamerica Savings & Loan is paying 6% interest compounded monthly. How much
must be deposited now to withdraw an annuity of $400 at the end of each month for
2 years?
Solve the following exercises by using Table 12-2:
T12-7
REVIEW EXERCISES
|
CHAPTER 12—SECTION II
R 5 7% P 5 4 2 1 5 3 F 5 2.62432 1 1.00000
Amount 5 2,000.00 3 3.62432 5 $7,248.64
14. Andrew Zorich is the grand prize winner in a college tuition essay contest sponsored
by a local scholarship fund. The winner receives $2,000 at the beginning of each year
for the next 4 years. How much should be invested at 7% interest compounded annually to pay the prize?
R 5 2% P 5 4 F 5 3.80773
Amount 5 100,000.00 3 3.80773 5 $380,773.00
13. As the chief accountant for the Wentworth Corporation, you have estimated that the
company must pay $100,000 income tax to the IRS at the end of each quarter this year.
How much should be deposited now at 8% interest compounded quarterly to meet
this tax obligation?
T12-8
T12-9
BUSINESS DECISION | CHAPTER 12—SECTION I I
THE SETTLEMENT
15. Churchill Enterprises has been awarded an insurance settlement of $5,000 at the end
of each 6-month period for the next 10 years.
a. As their accountant, calculate how much the insurance company must set aside now,
at 6% interest compounded semiannually, to pay this obligation to Churchill.
R 5 3% P 5 20 F 5 14.87747
Amount 5 5,000.00 3 14.87747 5 $74,387.35
b. (Optional) Use the present value of an ordinary annuity formula to calculate how
much the insurance company would have to invest now if the Churchill settlement
was changed to $2,500 at the end of each 3-month period for 10 years, and the insurance company could earn 8% interest compounded quarterly.
R 5 2% P 5 40 Amount 5 $2,500.00
1 2 (1.02) 240
1 2 (1 1 i) 2n
PV 5 2,500.00 3
PV 5 PMT 3
i
.02
PV 5 2,500.00 3
1 2 (1 1 .02) 240
.02
2,500.00 3 27.35547924 5 $68,388.70
c. (Optional) Use the present value of an annuity due formula to calculate how
much the insurance company would have to invest now if the Churchill settlement was paid at the beginning of each 3-month period rather than at the end.
R 5 2% P 5 40 Amount 5 $2,500.00
PV annuity due 5 (1 1 i) 3 PV ordinary annuity
PV 5 (1 1 .02) 3 68,388.70 5 $69,756.47
T12-10
REVIEW EXERCISES | CHAPTER 12—SECTION I I I
For the following sinking funds, use Table 12-1 to calculate the amount of the periodic
payments needed to amount to the financial objective (future value of the annuity):
Sinking Fund
Payment
1. $2,113.50
2. $9,608.29
$55.82
3.
$203.93
4.
$859.13
5.
Payment
Frequency
every
every
every
every
every
Time
Period
(years)
Nominal
Rate (%)
Interest
Compounded
Future Value
(Objective)
8
14
5
1 12
4
10
9
12
12
16
semiannually
annually
quarterly
monthly
quarterly
$50,000
$250,000
$1,500
$4,000
$18,750
6 months
year
3 months
month
3 months
1. R 5 5% P 5 16 FV 5 50,000.00
Table factor 5 23.65749
50,000.00
Payment 5
5 $2,113.50
23.65749
4. R 5 1% P 5 18 FV 5 4,000.00
Table factor 5 19.61475
4,000.00
5 $203.93
Payment 5
19.61475
2. R 5 9% P 5 14 FV 5 250,000.00
Table factor 5 26.01919
250,000
5 $9,608.29
Payment 5
26.01919
5. R 5 4% P 5 16 FV 5 18,750.00
Table factor 5 21.82453
18,750.00
Payment 5
5 $859.13
21.82453
3. R 5 3% P 5 20 FV 5 1,500.00
Table factor 5 26.87037
1,500.00
5 $55.82
Payment 5
26.87037
T12-11
REVIEW EXERCISES | CHAPTER 12—SECTION I I I
You have just been hired as a loan officer at the Eagle National Bank. Your first assignment is to calculate the amount of the periodic payment required to amortize (pay
off) the following loans being considered by the bank (use Table 12-2):
Loan
Payment
6. $4,189.52
$336.36
7.
$558.65
8.
9. $1,087.48
$51.83
10.
Payment
Period
every
every
every
every
every
Term
of Loan
(years)
Nominal
Rate (%)
Present Value
(Amount of Loan)
12
5
134
8
1.5
9
8
18
6
12
$30,000
$5,500
$10,000
$13,660
$850
year
3 months
month
6 months
month
6. R 5 9% P 5 12 PV 5 30,000.00
Table factor 5 7.16073
30,000.00
5 $4,189.52
Payment 5
7.16073
7. R 5 2% P 5 20 PV 5 5,500.00
Table factor 5 16.35143
5,500.00
Payment 5
5 $336.36
16.35143
1
8. R 5 1 % P 5 21 PV 5 10,000.00
2
Table factor 5 17.90014
10,000.00
Payment 5
5 $558.65
17.90014
9. R 5 3% P 5 16 PV 5 13,660.00
Table factor 5 12.56110
13,660.00
Payment 5
5 $1,087.48
12.56110
10. R 5 1% P 5 18 PV 5 850.00
Table factor 5 16.39827
850.00
5 $51.83
Payment 5
16.39827
T12-12
REVIEW EXERCISES | CHAPTER 12—SECTION I I I
11. West Coast Industries established a sinking fund to pay off a $10,000,000 loan for a
corporate jet that comes due in 8 years.
a. What equal payments must be deposited into the fund every 3 months at 6% interest compounded quarterly for West Coast to meet this financial obligation?
R 5 1 12% P 5 32 PV 5 10,000,000.00
Factor 5 40.68829
10,000,000.00
Payment 5
5 $245,770.96
40.68829
b. What is the total amount of interest earned in this sinking fund account?
245,770.96 3 32 5 7,864,670.72
Amount of interest 5 10,000,000.00 2 7,864,670.72
5 $2,135,329.28
12. Tina Woodruff bought a new Toyota Matrix for $15,500. She made a $2,500 down payment and is financing the balance at the Mid-South Bank over a 3-year period at 12%
interest. As her banker, calculate what equal monthly payments will be required by
Tina to amortize the car loan.
R 5 1% P 5 36 PV 5 (15,500.00 2 2,500.00) 5 13,000.00
Factor 5 30.10751
13,000.00
5 $431.79
Payment 5
30.10751
13. Green Thumb Landscaping buys new lawn equipment every 3 years. It is estimated
that $25,000 will be needed for the next purchase. The company sets up a sinking fund
to save for this obligation.
a. What equal payments must be deposited every 6 months if interest is 8% compounded semiannually?
R 5 4% P 5 6 FV 5 25,000.00
Factor 5 6.63298
25,000.00
5 $3,769.04
Payment 5
6.63298
b. What is the total amount of interest earned by the sinking fund?
6 3 3,769.04 5 22,614.24
Amount of interest 5 25,000.00 2 22,614.24
5 $2,385.76
REVIEW EXERCISES
|
CHAPTER 12—SECTION III
R 5 1.5% P 5 16 FV 5 7,500.00
Factor 5 17.93237
7,500.00
Payment 5
5 $418.24
17.93237
15. Brian and Erin Joyner are planning a safari vacation in Africa in 4 years and will need
$7,500 for the trip. They decide to set up a sinking fund savings account for the vacation. They intend to make regular payments at the end of each 3-month period into
the account that pays 6% interest compounded quarterly. What periodic sinking fund
payment will allow them to achieve their vacation goal?
R 5 12% P 5 25 PV 5 200,000.00
Factor 5 7.84314
200,000.00
Payment 5
5 $25,499.99
7.84314
14. Karen Moore is ready to retire and has saved up $200,000 for that purpose. She wants
to amortize (liquidate) that amount in a retirement fund so that she will receive equal
annual payments over the next 25 years. At the end of the 25 years, there will be no
funds left in the account. If the fund earns 12% interest, how much will Karen receive
each year?
T12-13
T12-14
REVIEW EXERCISES | CHAPTER 12—SECTION I I I
(Optional) Solve the following exercises by using the sinking fund or amortization
formulas:
16. Howard Lockwood purchased a new home for $225,000 with a 20% down payment
and the remainder amortized over a 15-year period at 9% interest.
a. What is the amount of the house that was financed?
225,000.00 3 .2 5 45,000.00
Amount financed 5 225,000.00 2 45,000.00
5 $180,000.00
b. What equal monthly payments are required to amortize this loan over 15 years?
R 5 .75%
P 5 180
PV 5 180,000
Amortization payment 5 PV 3
i
.0075
5
180,000
3
1 2 (1 1 i) 2n
1 2 (1 1 .0075) 2180
5 180,000 3
.0075
5 180,000 3 .010142666
.73945057
Payment amount 5 $1,825.68
c. What equal monthly payments are required if Howard decides to take a 20-year
loan rather than a 15?
R 5 .75%
P 5 240
PV 5 180,000
Amortization payment 5 PV 3
i
.0075
2n 5 180,000 3
1 2 (1 1 i)
1 2 (1 1 .0075) 2240
5 180,000 3
Payment 5 $1,619.51
.0075
5 180,000 3 .00899726
.833587155
REVIEW EXERCISES
|
CHAPTER 12—SECTION III
P 5 60
i
.01
5
1,000,000.00
3
(1 1 i) n 2 1
(1 1 .01) 60 2 1
FV 5 1,000,000.00
60 3 12,244.45 5 734,667.00
Interest earned 5 1,000,000.00 2 734,667.00
5 $265,333.00
b. What is the total amount of interest earned in the account?
.01
Payment 5 1,000,000.00 3
5 $12,244.45
.816696699
Payment 5 FV 3
R 5 1%
a. What equal monthly sinking fund payments are required to accumulate the
needed amount?
17. The Sunset Harbor Hotel has a financial obligation of $1,000,000 due in 5 years. A
sinking fund is established to meet this obligation at 12% interest compounded monthly.
T12-15
T12-16
BUSINESS DECISION | CHAPTER 12—SECTION I I I
DON’T FORGET INFLATION!
18. You are the vice president of finance for Casablanca Enterprises, Inc., a manufacturer
of office furniture. The company is planning a major plant expansion in 5 years. You
have decided to start a sinking fund to accumulate the funds necessary for the project.
Current bank rates are 8% compounded quarterly. It is estimated that $2,000,000 in
today’s dollars will be required; however, the inflation rate on construction costs and
plant equipment is expected to average 5% per year for the next 5 years.
a. Use the compound interest concept from Chapter 11 to determine how much will
be required for the project, taking inflation into account.
From Table 11-1, future value at compound interest,
R 5 5% P 5 5 Factor 5 1.27628
FV 5 2,000,000.00 3 1.27628 5 $2,552,560.00
b. What sinking fund payments will be required at the end of every 3-month period
to accumulate the necessary funds?
R 5 2% P 5 20 FV 5 $2,552,560.00
Factor 5 24.29737
2,552,560.00
FV
Payment 5
5
5 $105,054.99
Factor
24.29737