Appendix B
Applying Present and Future Values
QUICK STUDIES
Quick Study B-1 (10 minutes)
1.
2%
2.
12%
3.
3%
4.
1%
Quick Study B-2 (10 minutes)
In Table B.1, where n = 15 and p = $2,745/$10,000 = 0.2745, the i = 9%.
Quick Study B-3 (10 minutes)
In Table B.1, where i = 6% and p = $6,651/$10,000 = 0.6651, the n = 7.
Quick Study B-4 (10 minutes)
In Table B.1, where n = 5 and i = 9%, the p = 0.6499.
Amount willing to pay today: 0.6499 x $140,000 = $90,986
Quick Study B-5 (10 minutes)
In Table B.2, where n = 10 and i = 12%, the f = 3.1058.
Cash proceeds at liquidation:3.1058 x $630,000 = $1,956,654
Quick Study B-6 (10 minutes)
In Table B.3, where n = 6 and i = 7%, the p = 4.7665.
Amount willing to pay for the project:4.7665 x $150,000 = $714,975
Quick Study B-7 (10 minutes)
In Table B.4, where n = 30 and i = 10%, the f = 164.494.
Ending value of the investment program:164.494 x $1,500 = $246,741
EXERCISES
Exercise B-1 (10 minutes)
In Table B.2, where i = 12% and f = $96,463/$10,000 = 9.6463, the n = 20 (implies the investor must wait 20 years before payment).
Exercise B-2 (10 minutes)
In Table B.2, where n = 25 and f = $108,347/$10,000 = 10.8347, the i = 10% (investor must earn 10% interest to achieve investment goal).
Exercise B-3 (10 minutes)
In Table B.3, where n = 8 and p = $57,466/$10,000 = 5.7466, the i = 8% (investor must earn 8% interest to achieve investment goal).
Exercise B-4 (10 minutes)
In Table B.3, where i = 10% and p = $82,014/$10,000 = 8.2014, the n = 18 (investor expects 18 annual payments to be received).
Exercise B-5 (10 minutes)
In Table B.4, where n = 40 and f = $154,762/$1,000 = 154.762, the i = 6% (investor must earn a 6% rate of interest).
Exercise B-6 (10 minutes)
In Table B.4, where i = 8% and f = $303,243/$10,000 = 30.3243, the n = 16 (investor must make 16 annual payments to achieve investment goal).
Exercise B-7 (10 minutes)
Interest rate per period = 12% annual / 12 months per year = 1% per month
Using Table B.3, where n = 40 and i = 1%, the p = 32.8347.This means:
Loan balance......
$16,417.35
(present value of loan = 32.8347 x $500)
Down payment...
6,500.00
(cash)
Total cost...........
$22,917.35
Exercise B-8 (15 minutes)
Semiannual interest payment = $500,000 x 10% x 1/2 = $25,000
Using Table B.1, where n = 30 and i = 4%, the p = 0.3083 (Principal payment)
Using Table B.3, where n = 30 and i = 4%, the p = 17.2920 (Interest payments)
0.3083 x $500,000 =
$154,150
present value of maturity amount
17.2920 x $ 25,000 =
432,300
present value of interest payments
$586,450
cash proceeds
Exercise B-9 (15 minutes)
In Table B.1, where n = 6 and i = 10%, the p = 0.5645.
Present value of investment = $606,773 x .5645 = $342,523
Exercise B-10 (15 minutes)
1.$90,000 x 0.6651 (using Table B.1, i = 6%, n = 7) = $59,859.
2.$20,000 x 2.4869 (using Table B.3, i = 10%, n = 3) = $49,738.
Exercise B-11 (15 minutes)
Amount borrowed =
present value of $20,000 at 10% for 3 years
=
$20,000 x 0.7513 (using Table B.1, i = 10%, n = 3)
=
$15,026
Exercise B-12 (10 minutes)
Single Future Payment
Number of Periods
Interest Rate
Table B.1 Value
Amount Borrowed
a.
$40,000
3
4%
0.8890
$35,560
b.
75,000
7
8
0.5835
$43,763
c.
52,000
9
10
0.4241
$22,053
d.
18,000
2
4
0.9246
$16,643
e.
63,000
8
6
0.6274
$39,526
f.
89,000
5
2
0.9057
$80,607
Exercise B-13 (25 minutes)
1.
First Annuity
Future
Payment
Number of Periods
Interest Rate
Table B.1 Value
Amount Borrowed
First payment.......
$5,000
1
6%
0.9434
$4,717
Second payment..
5,000
2
6
0.8900
4,450
Third payment.....
5,000
3
6
0.8396
4,198
Fourth payment...
5,000
4
6
0.7921
3,961
Fifth payment.......
5,000
5
6
0.7473
3,737
Sixth payment......
5,000
6
6
0.7050
3,525
Total borrowed....
$24,588
Second Annuity
Future
Payment
Number of Periods
Interest Rate
Table B.1 Value
Amount Borrowed
First payment.......
$7,500
1
6%
0.9434
$7,076
Second payment..
7,500
2
6
0.8900
6,675
Third payment.....
7,500
3
6
0.8396
6,297
Fourth payment...
7,500
4
6
0.7921
5,941
Total borrowed....
$25,989
Exercise B-13 (Continued)
2.
First Annuity
Payment size...............................
$5,000
Number of payments...................
6
Interest rate................................
6%
Value from Table B.3..................
4.9173
Present value of the annuity.......
$24,587
(difference from part (1) due to rounding)
Second Annuity
Payment size...............................
$7,500
Number of payments...................
4
Interest rate................................
6%
Value from Table B.3..................
3.4651
Present value of the annuity.......
$25,988
(difference from part (1) due to rounding)
Exercise B-14 (30 minutes)
1.Present value of the annuity
Payment size...............................
$13,000
Number of payments...................
4
Interest rate................................
4%
(semiannual)
Value from Table B.3..................
3.6299
Present value of the annuity.......
$47,189
2.Present value of the annuity
Payment size...............................
$13,000
Number of payments...................
4
Interest rate................................
6%
(semiannual)
Value from Table B.3..................
3.4651
Present value of the annuity.......
$45,046
3.Present value of the annuity
Payment size...............................
$13,000
Number of payments...................
4
Interest rate................................
8%
(semiannual)
Value from Table B.3..................
3.3121
Present value of the annuity.......
$43,057
Exercise B-15 (15 minutes)
10 years x 4 quarters = 40 interest periods
8% annual / 4 quarters per year = 2% per quarter
In Table B.2, where n = 40 and i = 2%, the f = 2.2080.
Total accumulation = 2.2080 x $7,200 = $15,897.60
Exercise B-16 (15 minutes)
12% annual / 12 months per year = 1% per month
2.5 years x 12 months per year = 30 total months
In Table B.4, where n = 30 and i = 1%, the f = 34.7849.
Total accumulation = 34.7849 x $50 = $1,739.25
Exercise B-17 (15 minutes)
10 years x 4 quarters per year = 40 total quarters
12% annual / 4 quarters per year = 3% per quarter
In Table B.2, where n = 40 and i = 3%, the f = 3.2620.
In Table B.4, where n = 40 and i = 3%, the f = 75.4013.
3.2620 x $100,000 =
$326,200
future value of initial investment
75.4013 x $50,000=
3,770,065
future value of periodic investments
$4,096,265
future value of fund
Exercise B-18 (15 minutes)
In Table B.2, where n = 9 and i = 7%, the f = 1.8385.
Future value of investment = $163,170 x 1.8385 =$299,988
Exercise B-19 (20 minutes)
a.(1)Present Value of a single amount.
(2)Multiply $10,000 by p from Table B.1.
(3)Use Table B.1, periods = 8 and interest rate = 4%.
OR
(1)Future Value of a single amount.
(2)Divide $10,000 by f from Table B.2.
(3)Use Table B.2, periods = 8 and interest rate = 4%.
b.(1)Future Value of an Annuity.
(2)Divide $10,000 by f from Table B.4.
(3) Use Table B.4, periods = 8 and interest rate = 4%.
OR
(1)Present Value of an Annuity.
(2)Multiply $10,000 by p from Table B.1 and then divide by p from
Table B.3.
(3)Use Tables B.1 and B.3,periods = 8 and interest rate = 4%.
c.(1)Future Value of an Annuity.
(2)Multiply $4,000 by f from Table B.4.
(3)Use Table B.4, periods = 40 and interest = 8%.
d.(1)Present Value of an Annuity.
(2)Multiply $30,000 by p from Table B.3.
(3)Use Table B.3, periods = 20 and interest = 10%.
[Note: Students must recognize the present value of $225,000
received today is $225,000.]
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