June 12, 2011
Week 1
Chp 2
9.
a. The cost of a new automobile is $10,000. If the interest rate is 5%, how much would you have
to set aside now to provide this sum in five years?
Answer:
r = 5%
.05 x $10,000 = 500 = $10,500
1
st
year: $10,000 x (1 + .05) = 10,000 x 1.05 = $10,500
2
nd
year: $10,500 x 1.05 = $10,000 x 1.05^2 = $11,025
3
rd
year: $11,025 x 1.05 = $10,000 x 1.05^3 = $11,576.25
4
th
year: $11,576.25 x 1.05 = $10,000 x 1.05^4 = 12,155.06
5
th
year: $12,155.06 x 1.05 = $10,000 x 1.05^5 = 12,762.82
PV = $12,762.82/(1.05)^5 = $10,000
10,000/1.05^5 = $7,840
b. You have to pay $12,000 a year in school fees at the end of each of the next six years. If the
interest rate is 8%, how much do you need to set aside today to cover these bills?
Answer:
N= 6 years
I/yr = 8%
FV= 0
PV= ? 55,474.56
PMT= -12,000
12,000 x 4.623 (6-year annuity factor) =
$55,476
c. You have invested $60,476 at 8%. After paying the above school fees, how much would
remain at the end of six years?
Answer:
Total investment = $60,476
Less payments (55,476)
Remaining FVA due=5,000
FVA due = $5,000(1+I)^yr
$5,000(1.08)^6
=$7934.37