Solutions to Textbook Recommended Problems
4-1.
You have just taken out a five-year loan from a bank to buy an engagement ring. The ring costs
$5000. You plan to put down $1000 and borrow $4000. You will need to make annual payments
of $1000 at the end of each year. Show the timeline of the loan from your perspective. How would
the timeline differ if you created it from the bank’s perspective?
0
1
2
3
4
5
4000
–1000
–1000
–1000
–1000
–1000
From the bank’s perspective, the timeline is the same except all the signs are reversed.
4-3.
Calculate the future value of $2000 in
a.
Five years at an interest rate of 5% per year.
b. Ten years at an interest rate of 5% per year.
c.
Five years at an interest rate of 10% per year.
d. Why is the amount of interest earned in part (a) less than half the amount of interest earned
in part (b)?
a.
Timeline:
0
1
2
5
2000
FV= ?
FV5 = 2, 000 × 1.055 = 2, 552.56
b.
Timeline:
0
1
2
10
2000
FV=?
FV10 = 2, 000 × 1.0510 = 3, 257.79
c.
Timeline:
0
1
2000
2
5
FV= ?
FV5 = 2, 000 × 1.15 = 3, 221.02
d.
Because in the last 5 years you get interest on the interest earned in the first 5 years as well as
interest on the original $2,000.
1
4-4.
What is the present value of $10,000 received
a.
Twelve years from today when the interest rate is 4% per year?
b. Twenty years from today when the interest rate is 8% per year?
c.
Six years from today when the interest rate is 2% per year?
a.
Timeline:
0
1
2
3
12
PV=?
PV =
10, 000
12
10,000
= 6, 245.97
1.04
b.
Timeline:
0
1
2
3
20
PV=?
PV =
10, 000
1.08
c.
20
Timeline:
0
10,000
= 2,145.48
1
2
3
4
5
PV=?
PV =
10,000
10, 000
1.02
4-6.
6
6
= 8, 879.71
Consider the following alternatives:
i.
$100 received in one year
ii. $200...