In April 2013 a pound of apples cost $1.42, while oranges cost $1.06. Three year
ID: 2737108 • Letter: I
Question
Explanation / Answer
a.
Calculate the annual compound rate of growth in the price of apples:
= (Ending value / Beginning value )(1/no.of years)-1
= ($1.42 / $1.21)(1/3)-1
= 5.48%
b.
Calculate the annual compound rate of growth in the price of oranges:
= (Ending value / Beginning value )(1/no.of years)-1
= ($1.06 / $0.92)(1/3)-1
= 4.83%
C.
Calculate the price of apples in 2030:
Year
Interest
Future Value
Begin
$1.21
1
$0.07
$1.28
2
$0.07
$1.35
3
$0.07
$1.42
4
$0.08
$1.50
5
$0.08
$1.58
6
$0.09
$1.67
7
$0.09
$1.76
8
$0.10
$1.85
9
$0.10
$1.96
10
$0.11
$2.06
11
$0.11
$2.18
12
$0.12
$2.30
13
$0.13
$2.42
14
$0.13
$2.55
15
$0.14
$2.69
16
$0.15
$2.84
17
$0.16
$3.00
Totals
$1.79
$3.00
Therefore, the price of apples in 2030 is $3.00.
d.
Calculate the price of oranges in 2030:
Year
Interest
Future Value
Begin
$0.92
1
$0.04
$0.96
2
$0.05
$1.01
3
$0.05
$1.06
4
$0.05
$1.11
5
$0.05
$1.16
6
$0.06
$1.22
7
$0.06
$1.28
8
$0.06
$1.34
9
$0.06
$1.41
10
$0.07
$1.47
11
$0.07
$1.55
12
$0.07
$1.62
13
$0.08
$1.70
14
$0.08
$1.78
15
$0.09
$1.87
16
$0.09
$1.96
17
$0.09
$2.05
Totals
$1.13
$2.05
Therefore, the price of orange in 2030 is $2.05.
Year
Interest
Future Value
Begin
$1.21
1
$0.07
$1.28
2
$0.07
$1.35
3
$0.07
$1.42
4
$0.08
$1.50
5
$0.08
$1.58
6
$0.09
$1.67
7
$0.09
$1.76
8
$0.10
$1.85
9
$0.10
$1.96
10
$0.11
$2.06
11
$0.11
$2.18
12
$0.12
$2.30
13
$0.13
$2.42
14
$0.13
$2.55
15
$0.14
$2.69
16
$0.15
$2.84
17
$0.16
$3.00
Totals
$1.79
$3.00