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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
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Solutions Manual, Appendix B717
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).
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Financial Accounting, 4th Edition718
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)
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Solutions Manual, Appendix B719
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.
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Financial Accounting, 4th Edition720
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 $35,560b. 75,000 7 8 0.5835 $43,763c. 52,000 9 10 0.4241 $22,053d. 18,000 2 4 0.9246 $16,643e. 63,000 8 6 0.6274 $39,526f. 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 $ 4,717Second payment... 5,000 2 6 0.8900 4,450Third payment....... 5,000 3 6 0.8396 4,198Fourth payment..... 5,000 4 6 0.7921 3,961Fifth payment........ 5,000 5 6 0.7473 3,737Sixth payment....... 5,000 6 6 0.7050 3,525Total borrowed...... $24,588
Second AnnuityFuture Payment
Number of Periods
Interest Rate
Table B.1 Value
Amount Borrowed
First payment........ $7,500 1 6% 0.9434 $ 7,076Second payment... 7,500 2 6 0.8900 6,675Third payment....... 7,500 3 6 0.8396 6,297Fourth payment..... 7,500 4 6 0.7921 5,941Total borrowed...... $25,989
©McGraw-Hill Companies, 2008
Solutions Manual, Appendix B721
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
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Financial Accounting, 4th Edition722
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
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Solutions Manual, Appendix B723
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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Financial Accounting, 4th Edition724
