Appendix B Applying Present and Future Values QUICK STUDIES Quick Study B-1 10 minutes 1... First Annuity Future Payment Number of Periods Interest Rate Table B.1 Value Amount Bo
Trang 1Appendix 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
Trang 2Quick 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)
Trang 3Exercise 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)
Trang 4Exercise 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
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
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
Trang 5Exercise 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)
Trang 6Exercise 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
Trang 7Exercise 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.]