Chapter 4 Solutions
2.
To find the FV of a lump sum, we use:
FV = PV(1 +
r
)
t
a.
FV = $1,000(1.06)
10
= $1,790.85
b.
FV = $1,000(1.09)
10
= $2,367.36
c.
FV = $1,000(1.06)
20
= $3,207.14
d.
Because interest compounds on the interest already earned, the interest earned in part
c
is more than twice the interest earned in part
a
. With compound interest, future values
grow exponentially.
3.
To find the PV of a lump sum, we use:
PV = FV / (1 +
r)
t
PV = $15,451 / (1.07)
6
= $10,295.65
PV = $51,557 / (1.15)
9
= $14,655.72
PV = $886,073 / (1.11)
18
= $135,411.60
PV = $550,164 / (1.18)
23
= $12,223.79
4.
To answer this question, we can use either the FV or the PV formula. Both will give the
same answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 +
r
)
t
Solving for
r
, we get:
r
= (FV / PV)
1 /
t
– 1
FV = $307 = $242(1 +
r
)
2
;
r
= ($307 / $242)
1/2
– 1
= 12.63%
FV = $896 = $410(1 +
r
)
9
;
r
= ($896 / $410)
1/9
– 1
= 9.07%
FV = $162,181 = $51,700(1 +
r
)
15
;
r
= ($162,181 / $51,700)
1/15
– 1
= 7.92%
FV = $483,500 = $18,750(1 +
r
)
30
;
r
= ($483,500 / $18,750)
1/30
– 1
= 11.44%
5.
To answer this question, we can use either the FV or the PV formula. Both will give the
same answer since they are the inverse of each other. We will use the FV formula, that is:
FV = PV(1 +
r
)
t
Solving for
t
, we get:
t
= ln(FV / PV) / ln(1 +
r
)
FV = $1,284 = $625(1.06)
t
;
t
= ln($1,284/ $625) / ln 1.06
= 12.36 years
FV = $4,341 = $810(1.13)
t
;
t
= ln($4,341/ $810) / ln 1.13
= 13.74 years
FV = $402,662 = $18,400(1.32)
t
;
t
= ln($402,662 / $18,400) / ln 1.32 = 11.11 years
FV = $173,439 = $21,500(1.16)
t
;
t
= ln($173,439 / $21,500) / ln 1.16 = 14.07 years
9.
A consol is a perpetuity.
To find the PV of a perpetuity, we use the equation:
PV =
C
/
r
PV = $120 / .057
PV = $2,105.26
11.
To solve this problem, we must find the PV of each cash flow and add them. To find the PV
of a lump sum, we use:
PV = FV / (1 +
r)
t
PV@10% = $1,200 / 1.10 + $730 / 1.10
2
+ $965 / 1.10
3
+ $1,590 / 1.10
4
= $3,505.23
PV@18% = $1,200 / 1.18 + $730 / 1.18
2
+ $965 / 1.18
3
+ $1,590 / 1.18
4
= $2,948.66
PV@24% = $1,200 / 1.24 + $730 / 1.24
2
+ $965 / 1.24
3
+ $1,590 / 1.24
4
= $2,621.17
13.
To find the PVA, we use the equation: