Exercise C-7 (LO C-3)
Annuity
payment
Annual
Rate
Interest
compounded
Period
invested
Future value
of annuity
$2,000 13% Annually 30 years $586,398.43a
Exercise C-8 (LO C-3)
Annuity
payment
Annual
Rate
Interest
compounded
Period
invested
Present value
of annuity
Option 1 $35,000 12% Annually Today $35,000.00a
Option 2 4,000 12% Quarterly 3 years 39,816.02b
a $35,000 × Present value of annuity; n = 0; i = 12%
Problem C-1A (LO C-2)
Person Age
Initial
investment
Accumulated
investment by
retirement
(age 65)
Alec 55 $11,000 $28,531.17a
Daniel 45 $11,000 $74,002.50b
William 35 $11,000 $191,943.42c
Stephen 25 $11,000 $497,851.81d
a $11,000 × Future value of $1; n = 10; i = 10%
PROBLEMS: SET A
Problem C-2A (LO C-2, C-3)
Annuity
payment
Discount
Rate
Interest
compounded
Period
invested
Present value
of annuity
Years 1-6 $100,000 11% Annually 6 years $423,053.79a
Future
value
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 7 $110,000 11% Annually 7 years $ 52,982.43a
Year 8 120,000 11% Annually 8 years 52,071.18d
Year 9 130,000 11% Annually 9 years 50,820.22c
Year 10 140,000 11% Annually 10 years 49,305.83d
Year 10 1,300,000 11% Annually 10 years 457,839.82e
$663,019.48
a $110,000 × Present value of $1; n = 7; i = 11%
b $120,000 × Present value of $1; n = 8; i = 11%
Bruce should purchase the restaurant. With a discount rate of 11%, the current cost of
Problem C-3A (LO C-2, C-3)
Camera 1:
Annuity
payment
Discount
Rate
Interest
compounded
Period
invested
Present value
of annuity
Years 1-8 $300 9% Annually 8 years $1,660.45a
Future
value
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 8 $300 9% Annually 8 years $150.56a
Total cost of camera 1 = $6,000.00 (purchase price)
Camera 2:
Future
payment
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 3 $ 900 9% Annually 3 years $ 694.97a
Year 5 900 9% Annually 5 years 584.94b
Year 7 1,000 9% Annually 7 years 547.03c
$1,826.94
a $900 × Present value of $1; n = 3; i = 9%
Total cost of camera 2 = $5,500.00 (purchase price)
By comparing the total cost of camera 1 ($7,509.89) to the total cost of camera 2
Problem C-1B (LO C-3)
Requirements 1 and 2
Person
Annuity
Payment
Type of
account
Expected
Annual
Return
Four-year
accumulated
investment
Maximum
home
purchasee
Mary Kate $4,000 Savings 2% $16,486.43a$65,945.72
Ashley $5,000 CDs 4% $21,232.32b$84,929.28
Dakota $6,000 Bonds 7% $26,639.66c$106,558.64
Elle $6,000 Stocks 11% $28,258.39d$113,033.56
a $4,000 × Future value of annuity; n = 4; i = 2%
b $5,000 × Future value of annuity; n = 4; i = 4%
PROBLEMS: SET B
Problem C-2B (LO C-2, C-3)
Annuity
payment
Discount
Rate
Interest
compounded
Period
invested
Present value
of annuity
Years 1-20 $60,000 9% Annually 20 years $547,712.74a
Future
value
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 20 $600,000 9% Annually 20 years $107,058.53a
If Woody wants to make at least 9% on his investment, the most he would pay for the
Problem C-3B (LO C-2, C-3)
Option 1:
Present value = $1,600,000
Option 2:
Annuity
payment
Discount
Rate
Interest
compounded
Period
invested
Present value
of annuity
Years 1-10 $150,000 8% Annually 10 years $1,006,512.21a
Option 3:
Annuity
payment
Discount
Rate
Interest
compounded
Period
invested
Present value
of annuity
Years 1-10 $250,000 8% Annually 10 years $1,677,520.35a
Option 4:
Future
payment
Discount
rate
Interest
compounded
Period
invested
Present
Value
Year 5 $2,300,000 8% Annually 5 years $1,565,341.35a
The lowest cost alternative for Star Studios is option 4.