Chapter 13—Solutions to Problems
Problem 1: Solution
Answers found using Excel formulas:
1. Amount invested =
$10,000
$21,589.25
Compounding period =
annually
Number of years =
10
Annual interest rate =
8%
Effective interest rate =
8%
# of periods compounded =
10
2. Amount invested =
$5,000
$8,144.47
Compounding period =
semi-annually
Number of years =
5
Annual interest rate =
10%
Effective interest rate =
5% = 10% / 2
# of periods compounded =
10 = 5 years * 2
3. Amount invested =
$8,000; PV of $8,000 = $7,107.90
Compounding period =
quarterly
Number of years =
4
$12,825.02
Annual interest rate =
12%
Effective interest rate =
3% = 12% / 4
# of periods compounded =
16 = 4 years * 4
Answers found using time value of money tables:
1. Amount invested =
$10,000
=$10,000
×
FVF(.08,10)
Compounding period =
annually
=$10,000
×
2.1589
Number of years =
10
=$21,589.00
Annual interest rate =
8%
Effective interest rate = 8%
# of periods compounded = 10
2. Amount invested =
$5,000
=$5,000
×
FVF(.05,10)
Compounding period =
semi-annually =$5,000
×
1.6289
Number of years =
5
=$8,144.50
Annual interest rate =
10%
Effective interest rate = 5% = 10% / 2
# of periods compounded = 10 = 5 years * 2
3. Amount invested =
$8,000
=8,000
×
FVF(.03,16)
Compounding period =
quarterly
=8,000
×
1.6047
Number of years =
4
=$12,837.60
Annual interest rate =
12%
Effective interest rate=
3% =12% / 4
# of periods compounded=
16 = 4 years
×
4