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
©2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Solutions Manual, Appendix B 1383
,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).
©2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
1384 Financial & Managerial Accounting, 5th Edition
,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.
©2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Solutions Manual, Appendix B 1385
, 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)
a. p = present value of $60,000 at 9% for 4 years
p = $60,000 x 0.7084
p = $42,504
b. p = present value of $15,000 at 8% for 2 years
p = $15,000 x 0.8573
p = $12,859.50
c. There are at least two ways to solve this problem. (1) We can take the
$463 today, compute its future value, and then compare it to the future
value amount of $1,000. (2) We can discount the $1,000 back to the
present and compare it to the $463 today.
The same answer results: choose $463 today
f = future value of $463 at 9% for 10 years
f = $.4224
f = $1096.12 (which implies we’d prefer the $463 today)
p = present value of $1,000 at 9% for 10 years
p = $1,000 x 0.4224
p = $422.40 (which is less than $463 today)
d. f = future value of $90 at 5% for 8 years
Formula: $90 = f x 0.6768; then solve for f
f = $.6768
f = $132.98
e. f = future value of $158,500 at 10% for 8 years
Formula: $158,500 = f x 0.4665; then solve for f
f = $339,764.20
©2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
1386 Financial & Managerial Accounting, 5th Edition
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
©2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Solutions Manual, Appendix B 1383
,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).
©2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
1384 Financial & Managerial Accounting, 5th Edition
,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.
©2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Solutions Manual, Appendix B 1385
, 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)
a. p = present value of $60,000 at 9% for 4 years
p = $60,000 x 0.7084
p = $42,504
b. p = present value of $15,000 at 8% for 2 years
p = $15,000 x 0.8573
p = $12,859.50
c. There are at least two ways to solve this problem. (1) We can take the
$463 today, compute its future value, and then compare it to the future
value amount of $1,000. (2) We can discount the $1,000 back to the
present and compare it to the $463 today.
The same answer results: choose $463 today
f = future value of $463 at 9% for 10 years
f = $.4224
f = $1096.12 (which implies we’d prefer the $463 today)
p = present value of $1,000 at 9% for 10 years
p = $1,000 x 0.4224
p = $422.40 (which is less than $463 today)
d. f = future value of $90 at 5% for 8 years
Formula: $90 = f x 0.6768; then solve for f
f = $.6768
f = $132.98
e. f = future value of $158,500 at 10% for 8 years
Formula: $158,500 = f x 0.4665; then solve for f
f = $339,764.20
©2013 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
1386 Financial & Managerial Accounting, 5th Edition
