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```									CHAPTER 9

3)Money has a time value because funds received today can be reinvested to reach a
greater value in the future. A person would rather receive \$1 today than \$1 in ten years,
because a dollar received today, invested at 6 percent for example, is worth \$1.791 after
ten years.

6) The greater the number of compounding periods, the larger the future value. The
investor should choose daily compounding over monthly or quarterly.

8) Different financial applications of the time value of money:
Equipment purchase or new product decision,
Present value of a contract providing future payments,
Future worth of an investment,
Regular payment necessary to provide a future sum,
Regular payment necessary to amortize a loan,
Determination of value of a bond.

Problems
1) a)\$3,000*1.12 = \$3,360.00
b)\$3,360*1.12 = \$3,763.20
c)\$3,763*1.12 = \$4,214.78
d)\$3000*1.12 = \$4,215.00
2)
a) \$5,247
b) \$12,420
c) \$2,330
d) \$1

3)
a) \$10,692
b) \$19,899
c) \$238,158
d) \$265,113(7%, 50 periods)

19)
FV = PV*FVIF(3%,40periods)
FV = \$20,000*3.262 = \$65,240

22) First alternative present value of \$10,000 received now: \$10,000
Second alternative present value of annuity of \$2,000 for eight years
PV= A*PVIFA
= \$2,000 * PVIFA(11%,8years)
= \$2,000*5.146
= \$10,292
Third alternative present value of \$24,000 received in eight years:
PV = FV*PVIF(11%,8years)
= \$24,000*.434
= \$10,416
Select \$24,000 to be received in eight years.

First alternative present value of \$10,000 received today : \$10,000
Second alternative present value of annuity of \$2,000 for 8 years:
PV = A*PVIFA
= \$2,000*PVIFA(12%,8years)
= \$2,000*4.968
= \$9,936

Third alternative present value of \$24,000 received in 8 years
PV = FV*PVIF(12%,8years)
= \$24,000* PVIF(12%,8years)
= \$24,000*.404
= \$9,696
Select \$10,000 now

28)A=PV/PVIFA(9%,15periods)
=\$180,000/8.061
=\$22,329.74
31)
First find the present value of the first three payments.
PV=FV*PVIF
1)\$2,000*.917=\$1,834
2)3,500*.842= 2,947
3)4,500*.772= 3,474
\$8,255
The value of annuity at the beginning of the fourth year is
PV=A*PVIF(9%,7periods)
= \$5,000*5.033=\$25,165
This value at the beginning of year four (end of year three) must now be discounted back
three years to get the present value of the deferred annuity.
PV=FV*PVIF(9%,3periods)
= \$25,165*.772=\$19,427.38
Finally, find the total present value of first three payments.
Present value of three payments        \$ 8,255.00
Present value of the deferred annuity 19,427.00
\$27,682.38

34)
PVIFA = PV/A(7 periods)
= \$15,618/\$3,000
= 5.206
Interest rate = 8%

35)FV*PV*FVIF(10%,5 periods)
FV=\$10,000*1.611
=\$16,110 amount owed after 5 years

A= PV/PVIFA(11%,12 periods)
= \$16,110/6.492
= \$2,482 Annual payments to retire the loan

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