Appendix B - Time Value of Money
Appendix B
Time Value of Money
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 amount17.2920 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 Borroweda. / $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
FuturePayment / 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
FuturePayment / 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...... / $ 5,000Number 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...... / $ 7,500Number 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...... / $13,000Number 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...... / $13,000Number 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...... / $13,000Number 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 investment75.4013 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.]
B-1