The document covers fundamental concepts of engineering economics such as the time value of money, present worth, future worth, and various financial formulas used to evaluate investment decisions. It discusses college cost inflation, retirement savings strategies, and the implications of loans and credit card debt, while highlighting the importance of understanding financial factors for making sound economic choices. Key points include break-even analysis, payback periods, and the significant rise in the cost of education over time.

1. 10/31/19
1
EE 200: Engineering Economics 2
Time Value of Money
2
2
136 ENGINEERING ECONOMICS
ENGINEERING ECONOMICS
Factor Name Converts Symbol Formula
Single Payment
Compound Amount to F given P (F/P, i%, n) (1 + i)
n
Single Payment
Present Worth to P given F (P/F, i%, n) (1 + i)
–n
Uniform Series
Sinking Fund to A given F (A/F, i%, n) ( ) 11 + ni
i
Capital Recovery to A given P (A/P, i%, n)

2. ( )
( ) 11
1
+
+
n
n
i
ii
Uniform Series
Compound Amount to F given A (F/A, i%, n)
( )
i
i n 11 +
Uniform Series
Present Worth to P given A (P/A, i%, n)
( )
( )n
n
ii
i
+
+
1

3. 11
Uniform Gradient
Present Worth to P given G (P/G, i%, n)
( )
( ) ( )nn
n
ii
n
ii
i
++
+
11
11
2
Uniform Gradient †
Future Worth to F given G (F/G, i%, n)
( )
i
n
i
i n+
2
11

4. Uniform Gradient
Uniform Series to A given G (A/G, i%, n) ( ) 11
1
+ ni
n
i
NOMENCLATURE AND DEFINITIONS
A �������������Uniform amount per interest period
B �������������Benefit
BV �����������Book value
C �������������Cost
d��������������In ation ad usted interest rate per
interest period
Dj ������������Depreciation in year j
EV �����������Expected value
F �������������Future worth, value, or amount
f �������������� eneral in ation rate per interest
period
G �������������Uniform gradient amount per interest
period
i ��������������Interest rate per interest period
ie �������������Annual effective interest rate
MARR ����Minimum acceptable/attractive rate of return
m �������������Number of compounding periods per
year
n��������������Number of compounding periods; or
the expected
life of an asset
P �������������Present worth, value, or amount
r ��������������Nominal annual interest rate
Sn ������������Expected salvage value in year n

5. Subscripts
j ����������� at time j
n����������� at time n
†����������� F/G = (F/A – n)/i = (F/A) × (A/G)
Risk
Risk is the chance of an outcome other than what is planned to
occur or expected in the analysis�
NON-ANNUAL COMPOUNDING
i m
r1 1e
m
= + -b l
BREAK-EVEN ANALYSIS
By altering the value of any one of the variables in a situation,
holding all of the other values constant, it is possible to find a
value for that variable that makes the two alternatives equally
economical� This value is the break-even point�
Break-even analysis is used to describe the percentage of
capacity of operation for a manufacturing plant at which
income will ust cover expenses.
The payback period is the period of time required for the profit
or other benefits of an investment to equal the cost of the
investment�
Time Value of Money Relating Future and
Present Worth Shows Unreasonable Costs
3
� is Future Worth � is Present Worth � is the
number of compounding periods

6. � is Uniform Amount per interest period (Payment) � is
the interest rate per period
3
10/31/19
2
College Costs Have Historically Increased Faster
than Inflation: Compound Interest Model
• Umich: Total Annual Cost
o 1980: $3,500
o 2020: $30,000
o At 3% annual inflation
o Should be: $11,417
o From � = � 1 + � )
§ � = $3,500
§ � = 0.03 = 3% annual
inflation
§ � = 40 years
• Effective Umich Inflation rate
• Given �, �, �; Find �
• Rearranging: � = � 1 + � )
o � = 2
3
4

7. 5 − 1
o � = 0.0055 = 5.5%
4
Probably a bit high
ee200.m Part A
4
Fred Wilma Barney Betty Dino Description
Age 35 30 25 20 20 Age starting retirement savings
n yrs 20 20 15 10 45 Years making deposit of A k$
N yrs 30 35 40 45 45 Years of investing (65 – Age)
A k$ 10 7.5 5 5 2 Annual lump sum deposit
Retirement Savings Analysis Drives Strategy
You Should Adopt Upon Graduation
• 5 Cases shown below
• Assumptions
o Stock market average annual rate
of return is 10%
o Contribute same annual amount
for � years starting at ���
• Assumptions (cont.)
o Investments compound after that

8. for N − � years to Age 65
o Determine projected retirement
account value at Age 65
7
7
10/31/19
3
136 ENGINEERING ECONOMICS
ENGINEERING ECONOMICS
Factor Name Converts Symbol Formula
Single Payment
Compound Amount to F given P (F/P, i%, n) (1 + i)
n
Single Payment
Present Worth to P given F (P/F, i%, n) (1 + i)
–n
Uniform Series
Sinking Fund to A given F (A/F, i%, n) ( ) 11 + ni
i
Capital Recovery to A given P (A/P, i%, n)

9. ( )
( ) 11
1
+
+
n
n
i
ii
Uniform Series
Compound Amount to F given A (F/A, i%, n)
( )
i
i n 11 +
Uniform Series
Present Worth to P given A (P/A, i%, n)
( )
( )n
n
ii
i
+
+
1

10. 11
Uniform Gradient
Present Worth to P given G (P/G, i%, n)
( )
( ) ( )nn
n
ii
n
ii
i
++
+
11
11
2
Uniform Gradient †
Future Worth to F given G (F/G, i%, n)
( )
i
n
i
i n+
2
11

11. Uniform Gradient
Uniform Series to A given G (A/G, i%, n) ( ) 11
1
+ ni
n
i
NOMENCLATURE AND DEFINITIONS
A �������������Uniform amount per interest period
B �������������Benefit
BV �����������Book value
C �������������Cost
d��������������In ation ad usted interest rate per
interest period
Dj ������������Depreciation in year j
EV �����������Expected value
F �������������Future worth, value, or amount
f �������������� eneral in ation rate per interest
period
G �������������Uniform gradient amount per interest
period
i ��������������Interest rate per interest period
ie �������������Annual effective interest rate
MARR ����Minimum acceptable/attractive rate of return
m �������������Number of compounding periods per
year
n��������������Number of compounding periods; or
the expected
life of an asset
P �������������Present worth, value, or amount
r ��������������Nominal annual interest rate
Sn ������������Expected salvage value in year n

12. Subscripts
j ����������� at time j
n����������� at time n
†����������� F/G = (F/A – n)/i = (F/A) × (A/G)
Risk
Risk is the chance of an outcome other than what is planned to
occur or expected in the analysis�
NON-ANNUAL COMPOUNDING
i m
r1 1e
m
= + -b l
BREAK-EVEN ANALYSIS
By altering the value of any one of the variables in a situation,
holding all of the other values constant, it is possible to find a
value for that variable that makes the two alternatives equally
economical� This value is the break-even point�
Break-even analysis is used to describe the percentage of
capacity of operation for a manufacturing plant at which
income will ust cover expenses.
The payback period is the period of time required for the profit
or other benefits of an investment to equal the cost of the
investment�
Time Value of Money To Get Future Worth from
Payments (A) and the 2 Equations
8
� is Future Worth � is Present Worth � is the
number of compounding periods

13. � is Uniform Amount per interest period (Payment) � is
the interest rate per period
1. �: from portion of time making investment deposits
2. �; from portion of time investments compound
8
Analysis
Solution
Derived from Time Value
of Money Equations
�: = �
1 + � ) − 1
�
�; = �: 1 + � <=)
= �
1 + � ) − 1
�

14. 1 + � <=)
• Future Value from
o Annual deposits of �
o For � years
• Investment compounding
o Of present value �:
o For N − � years
9
9
10/31/19
4
Lesson: Save Money When You’re Young!
• Corollary:
o Don’t borrow
o Except for a house

15. 12
12
136 ENGINEERING ECONOMICS
ENGINEERING ECONOMICS
Factor Name Converts Symbol Formula
Single Payment
Compound Amount to F given P (F/P, i%, n) (1 + i)
n
Single Payment
Present Worth to P given F (P/F, i%, n) (1 + i)
–n
Uniform Series
Sinking Fund to A given F (A/F, i%, n) ( ) 11 + ni
i

16. Capital Recovery to A given P (A/P, i%, n)
( )
( ) 11
1
+
+
n
n
i
ii
Uniform Series
Compound Amount to F given A (F/A, i%, n)
( )
i
i n 11 +
Uniform Series
Present Worth to P given A (P/A, i%, n)

17. ( )
( )n
n
ii
i
+
+
1
11
Uniform Gradient
Present Worth to P given G (P/G, i%, n)
( )
( ) ( )nn
n
ii
n

18. ii
i
++
+
11
11
2
Uniform Gradient †
Future Worth to F given G (F/G, i%, n)
( )
i
n
i
i n+
2
11
Uniform Gradient

19. Uniform Series to A given G (A/G, i%, n) ( ) 11
1
+ ni
n
i
NOMENCLATURE AND DEFINITIONS
A �������������Uniform amount per interest period
B �������������Benefit
BV �����������Book value
C �������������Cost
d��������������In ation ad usted interest rate per
interest period
Dj ������������Depreciation in year j
EV �����������Expected value
F �������������Future worth, value, or amount
f �������������� eneral in ation rate per interest
period
G �������������Uniform gradient amount per interest
period
i ��������������Interest rate per interest period
ie �������������Annual effective interest rate
MARR ����Minimum acceptable/attractive rate of return

20. m �������������Number of compounding periods per
year
n��������������Number of compounding periods; or
the expected
life of an asset
P �������������Present worth, value, or amount
r ��������������Nominal annual interest rate
Sn ������������Expected salvage value in year n
Subscripts
j ����������� at time j
n����������� at time n
†����������� F/G = (F/A – n)/i = (F/A) × (A/G)
Risk
Risk is the chance of an outcome other than what is planned to
occur or expected in the analysis�
NON-ANNUAL COMPOUNDING
i m
r1 1e
m

21. = + -b l
BREAK-EVEN ANALYSIS
By altering the value of any one of the variables in a situation,
holding all of the other values constant, it is possible to find a
value for that variable that makes the two alternatives equally
economical� This value is the break-even point�
Break-even analysis is used to describe the percentage of
capacity of operation for a manufacturing plant at which
income will ust cover expenses.
The payback period is the period of time required for the profit
or other benefits of an investment to equal the cost of the
investment�
Loan Payments and Interest Paid Analysis
13
� is Future Worth � is Present Worth � is the
number of compounding periods
� is Uniform Amount per interest period (Payment) � is
the interest rate per period
13

22. 10/31/19
5
Loans Can be Very Costly
• CSULB: Total Annual Cost
o 2020: $25,000
o Loan Payment
o � = � > :?>
5
:?> 5=:
= $290.30
§ � = $25,000
§ � =
B.BC
:;
for 7% annual interest

23. § � = 10 ⋅ 12 = 120 months
o Cumulative Interest Paid
o �> = � ⋅ � − � = $9,833
• Calculations in Matlab
o ee200.m Part C
o Also in Excel: LoanAmort.xlsx
14
14
Credit Cards Are Very Bad
Trap: Min Payment is Negative Amortization
• Causes principal owed to
grow
o Assumed Principal: $20,000
o Interest: � = B.:H
:;
for 18%
annual interest

24. o � = � > :?>
5
:?> 5=:
= $360.38
o Min Pmt of � = $50
o Debt grows rapidly
• Calculations in Excel
o LoanAmort.xlsx
• See also home mortgage
example
o Interest: � = B.BJ
:;
for 5% annual
interest
o � = � > :?>
5
:?> 5=:

25. = $2,684.12
o 30-year term
15
15
10/31/19
6
136 ENGINEERING ECONOMICS
ENGINEERING ECONOMICS
Factor Name Converts Symbol Formula
Single Payment
Compound Amount to F given P (F/P, i%, n) (1 + i)
n
Single Payment

26. Present Worth to P given F (P/F, i%, n) (1 + i)
–n
Uniform Series
Sinking Fund to A given F (A/F, i%, n) ( ) 11 + ni
i
Capital Recovery to A given P (A/P, i%, n)
( )
( ) 11
1
+
+
n
n
i
ii
Uniform Series

27. Compound Amount to F given A (F/A, i%, n)
( )
i
i n 11 +
Uniform Series
Present Worth to P given A (P/A, i%, n)
( )
( )n
n
ii
i
+
+
1
11
Uniform Gradient
Present Worth to P given G (P/G, i%, n)

28. ( )
( ) ( )nn
n
ii
n
ii
i
++
+
11
11
2
Uniform Gradient †
Future Worth to F given G (F/G, i%, n)
( )
i

29. n
i
i n+
2
11
Uniform Gradient
Uniform Series to A given G (A/G, i%, n) ( ) 11
1
+ ni
n
i
NOMENCLATURE AND DEFINITIONS
A �������������Uniform amount per interest period
B �������������Benefit
BV �����������Book value
C �������������Cost
d��������������In ation ad usted interest rate per
interest period
Dj ������������Depreciation in year j

30. EV �����������Expected value
F �������������Future worth, value, or amount
f �������������� eneral in ation rate per interest
period
G �������������Uniform gradient amount per interest
period
i ��������������Interest rate per interest period
ie �������������Annual effective interest rate
MARR ����Minimum acceptable/attractive rate of return
m �������������Number of compounding periods per
year
n��������������Number of compounding periods; or
the expected
life of an asset
P �������������Present worth, value, or amount
r ��������������Nominal annual interest rate
Sn ������������Expected salvage value in year n
Subscripts
j ����������� at time j
n����������� at time n
†����������� F/G = (F/A – n)/i = (F/A) × (A/G)
Risk

31. Risk is the chance of an outcome other than what is planned to
occur or expected in the analysis�
NON-ANNUAL COMPOUNDING
i m
r1 1e
m
= + -b l
BREAK-EVEN ANALYSIS
By altering the value of any one of the variables in a situation,
holding all of the other values constant, it is possible to find a
value for that variable that makes the two alternatives equally
economical� This value is the break-even point�
Break-even analysis is used to describe the percentage of
capacity of operation for a manufacturing plant at which
income will ust cover expenses.
The payback period is the period of time required for the profit
or other benefits of an investment to equal the cost of the
investment�
These Formulas Form the Basis of Engineering
Economic Trade-offs and Decision Making

32. 18
� is Future Worth � is Present Worth � is the
number of compounding periods
� is Uniform Amount per interest period (Payment) � is
the interest rate per period
18
%% A. Inflation Analysis on College Costs
clc; cla; clf; clear; close all; % Initial Clean-up for multiple
tries
format short; format compact; % Set preferences
i = 0.03; % 3% annual average inflation
P = 3.5; % Annual cost in 1980 (k$)
n = 40; % Years from 1980 to 2020
Fi = P*(1+i)^(n) % Projected annual cost based on inflation
Fa = 30; % Actual annual cost in 2020 (k$)
ia = (Fa/P)^(1/n) - 1; % Effective average inflation rate for
annual college costs
iap = ia*100 % Effective average inflation rate in
percent

33. %% B. Retirment Savings Comparison of 1 Fred, 2 Wilma, 3
Barney, 4 Betty, 5 Dino
clc; cla; clf; clear; close all; % Initial Clean-up for multiple
tries
format short; format compact; % Set preferences
i = 0.1 % 10% annual interest compounded annually
N = [ 30 35 40 45 45 ]; % Years invested prior to age 65
n = [ 20 20 15 10 45 ]; % Years providing deposits
A = [ 10 7.5 5 5 2 ]*1e-3; % Annual deposit to retirement
(M$)
disp(' Fred Wilma Barney Betty Dino in M$')
F = A.*( ( (1+i).^(n) - 1 ) / i ).*(1+i).^(N-n)
%% C. Loan Calc in k$
clc; cla; clf; clear; close all; % Initial Clean-up for multiple
tries
format compact; % Set preferences
P = 25 % Loan amount in k$
i = 0.07/12 % loan interest rate for 7% interest with monthly
payments
n = 10*12 % Term is 10 years with monthly payments
FoP = (1+i)^n; % F/P equation

34. A = P*( ( i*FoP ) / ( FoP - 1 ) ) % Monthly Payments
Ci = n*A - P % Cumulative interest paid (no
time value adjustment)
Loan EqsIntint/mon mosPrincipalPmtCum
Int7.00%0.5833%120$25,000.00$290.28$9,833.60Student
Loan5.00%0.4167%180$500,000.00$3,953.97$211,714.6015-
year Home
Mortgage5.00%0.4167%360$500,000.00$2,684.11$466,279.603
0-year Home
Mortgage18.00%1.5000%120$20,000.00$360.38$23,245.60Cred
it Card 10-year payoff
Credit Card Min PaymentMonth
kIntint/moPmt[k]Int'[k]PP[k]Bal[k]Months018.00%1.5000%$50
.00$20,000.00Loan Amount
(P)360118.00%1.5000%$50.00$300.00-
$250.00$20,250.00218.00%1.5000%$50.00$303.75-
$253.75$20,503.75318.00%1.5000%$50.00$307.56-
$257.56$20,761.31418.00%1.5000%$50.00$311.42-
$261.42$21,022.73518.00%1.5000%$50.00$315.35-
$265.35$21,288.08618.00%1.5000%$50.00$319.33-
$269.33$21,557.41718.00%1.5000%$50.00$323.37-
$273.37$21,830.78818.00%1.5000%$50.00$327.47-

35. $277.47$22,108.25918.00%1.5000%$50.00$331.63-
$281.63$22,389.881018.00%1.5000%$50.00$335.85-
$285.85$22,675.731118.00%1.5000%$50.00$340.14-
$290.14$22,965.871218.00%1.5000%$50.00$344.49-
$294.49$23,260.361318.00%1.5000%$50.00$348.91-
$298.91$23,559.271418.00%1.5000%$50.00$353.39-
$303.39$23,862.661518.00%1.5000%$50.00$357.94-
$307.94$24,170.601618.00%1.5000%$50.00$362.56-
$312.56$24,483.161718.00%1.5000%$50.00$367.25-
$317.25$24,800.411818.00%1.5000%$50.00$372.01-
$322.01$25,122.421918.00%1.5000%$50.00$376.84-
$326.84$25,449.262018.00%1.5000%$50.00$381.74-
$331.74$25,781.002118.00%1.5000%$50.00$386.72-
$336.72$26,117.722218.00%1.5000%$50.00$391.77-
$341.77$26,459.492318.00%1.5000%$50.00$396.90-
$346.90$26,806.392418.00%1.5000%$50.00$402.10-
$352.10$27,158.49$8,358.49-$7,158.49
Mortgage AmortMonth
kIntint/moPmt[k]Int'[k]PP[k]Bal[k]Months05.00%0.4167%$2,6
84.12$500,000.00Loan Amount
(P)36015.00%0.4167%$2,684.12$2,083.34$600.78$499,399.222
5.00%0.4167%$2,684.12$2,080.84$603.28$498,795.9435.00%0.
4167%$2,684.12$2,078.32$605.80$498,190.1445.00%0.4167%$
2,684.12$2,075.80$608.32$497,581.8255.00%0.4167%$2,684.1
2$2,073.26$610.86$496,970.9665.00%0.4167%$2,684.12$2,070

36. .72$613.40$496,357.5675.00%0.4167%$2,684.12$2,068.16$615
.96$495,741.6085.00%0.4167%$2,684.12$2,065.59$618.53$495
,123.0795.00%0.4167%$2,684.12$2,063.02$621.10$494,501.97
105.00%0.4167%$2,684.12$2,060.43$623.69$493,878.28115.00
%0.4167%$2,684.12$2,057.83$626.29$493,251.99125.00%0.41
67%$2,684.12$2,055.22$628.90$492,623.09135.00%0.4167%$2
,684.12$2,052.60$631.52$491,991.57145.00%0.4167%$2,684.1
2$2,049.97$634.15$491,357.42155.00%0.4167%$2,684.12$2,04
7.33$636.79$490,720.63165.00%0.4167%$2,684.12$2,044.67$6
39.45$490,081.18175.00%0.4167%$2,684.12$2,042.01$642.11$
489,439.07185.00%0.4167%$2,684.12$2,039.33$644.79$488,79
4.28195.00%0.4167%$2,684.12$2,036.65$647.47$488,146.8120
5.00%0.4167%$2,684.12$2,033.95$650.17$487,496.64215.00%
0.4167%$2,684.12$2,031.24$652.88$486,843.76225.00%0.4167
%$2,684.12$2,028.52$655.60$486,188.16235.00%0.4167%$2,6
84.12$2,025.79$658.33$485,529.83245.00%0.4167%$2,684.12$
2,023.05$661.07$484,868.76255.00%0.4167%$2,684.12$2,020.
29$663.83$484,204.93265.00%0.4167%$2,684.12$2,017.53$66
6.59$483,538.34275.00%0.4167%$2,684.12$2,014.75$669.37$4
82,868.97285.00%0.4167%$2,684.12$2,011.96$672.16$482,196
.81295.00%0.4167%$2,684.12$2,009.16$674.96$481,521.85305
.00%0.4167%$2,684.12$2,006.35$677.77$480,844.08315.00%0.
4167%$2,684.12$2,003.52$680.60$480,163.48325.00%0.4167%
$2,684.12$2,000.69$683.43$479,480.05335.00%0.4167%$2,684
.12$1,997.84$686.28$478,793.77345.00%0.4167%$2,684.12$1,

37. 994.98$689.14$478,104.63355.00%0.4167%$2,684.12$1,992.11
$692.01$477,412.62365.00%0.4167%$2,684.12$1,989.22$694.9
0$476,717.72375.00%0.4167%$2,684.12$1,986.33$697.79$476,
019.93385.00%0.4167%$2,684.12$1,983.42$700.70$475,319.23
395.00%0.4167%$2,684.12$1,980.50$703.62$474,615.61405.00
%0.4167%$2,684.12$1,977.57$706.55$473,909.06415.00%0.41
67%$2,684.12$1,974.63$709.49$473,199.57425.00%0.4167%$2
,684.12$1,971.67$712.45$472,487.12435.00%0.4167%$2,684.1
2$1,968.70$715.42$471,771.70445.00%0.4167%$2,684.12$1,96
5.72$718.40$471,053.30455.00%0.4167%$2,684.12$1,962.73$7
21.39$470,331.91465.00%0.4167%$2,684.12$1,959.72$724.40$
469,607.51475.00%0.4167%$2,684.12$1,956.70$727.42$468,88
0.09485.00%0.4167%$2,684.12$1,953.67$730.45$468,149.6449
5.00%0.4167%$2,684.12$1,950.63$733.49$467,416.15505.00%
0.4167%$2,684.12$1,947.57$736.55$466,679.60515.00%0.4167
%$2,684.12$1,944.50$739.62$465,939.98525.00%0.4167%$2,6
84.12$1,941.42$742.70$465,197.28535.00%0.4167%$2,684.12$
1,938.33$745.79$464,451.49545.00%0.4167%$2,684.12$1,935.
22$748.90$463,702.59555.00%0.4167%$2,684.12$1,932.10$75
2.02$462,950.57565.00%0.4167%$2,684.12$1,928.97$755.15$4
62,195.42575.00%0.4167%$2,684.12$1,925.82$758.30$461,437
.12585.00%0.4167%$2,684.12$1,922.66$761.46$460,675.66595
.00%0.4167%$2,684.12$1,919.49$764.63$459,911.03605.00%0.
4167%$2,684.12$1,916.30$767.82$459,143.21615.00%0.4167%
$2,684.12$1,913.10$771.02$458,372.19625.00%0.4167%$2,684

38. .12$1,909.89$774.23$457,597.96635.00%0.4167%$2,684.12$1,
906.66$777.46$456,820.50645.00%0.4167%$2,684.12$1,903.42
$780.70$456,039.80655.00%0.4167%$2,684.12$1,900.17$783.9
5$455,255.85665.00%0.4167%$2,684.12$1,896.90$787.22$454,
468.63675.00%0.4167%$2,684.12$1,893.62$790.50$453,678.13
685.00%0.4167%$2,684.12$1,890.33$793.79$452,884.34695.00
%0.4167%$2,684.12$1,887.02$797.10$452,087.24705.00%0.41
67%$2,684.12$1,883.70$800.42$451,286.82715.00%0.4167%$2
,684.12$1,880.37$803.75$450,483.07725.00%0.4167%$2,684.1
2$1,877.02$807.10$449,675.97735.00%0.4167%$2,684.12$1,87
3.65$810.47$448,865.50745.00%0.4167%$2,684.12$1,870.28$8
13.84$448,051.66755.00%0.4167%$2,684.12$1,866.89$817.23$
447,234.43765.00%0.4167%$2,684.12$1,863.48$820.64$446,41
3.79775.00%0.4167%$2,684.12$1,860.06$824.06$445,589.7378
5.00%0.4167%$2,684.12$1,856.63$827.49$444,762.24795.00%
0.4167%$2,684.12$1,853.18$830.94$443,931.30805.00%0.4167
%$2,684.12$1,849.72$834.40$443,096.90815.00%0.4167%$2,6
84.12$1,846.24$837.88$442,259.02825.00%0.4167%$2,684.12$
1,842.75$841.37$441,417.65835.00%0.4167%$2,684.12$1,839.
25$844.87$440,572.78845.00%0.4167%$2,684.12$1,835.72$84
8.40$439,724.38855.00%0.4167%$2,684.12$1,832.19$851.93$4
38,872.45865.00%0.4167%$2,684.12$1,828.64$855.48$438,016
.97875.00%0.4167%$2,684.12$1,825.08$859.04$437,157.93885
.00%0.4167%$2,684.12$1,821.50$862.62$436,295.31895.00%0.
4167%$2,684.12$1,817.90$866.22$435,429.09905.00%0.4167%

39. $2,684.12$1,814.29$869.83$434,559.26915.00%0.4167%$2,684
.12$1,810.67$873.45$433,685.81925.00%0.4167%$2,684.12$1,
807.03$877.09$432,808.72935.00%0.4167%$2,684.12$1,803.37
$880.75$431,927.97945.00%0.4167%$2,684.12$1,799.70$884.4
2$431,043.55955.00%0.4167%$2,684.12$1,796.02$888.10$430,
155.45965.00%0.4167%$2,684.12$1,792.32$891.80$429,263.65
975.00%0.4167%$2,684.12$1,788.60$895.52$428,368.13985.00
%0.4167%$2,684.12$1,784.87$899.25$427,468.88995.00%0.41
67%$2,684.12$1,781.13$902.99$426,565.891005.00%0.4167%$
2,684.12$1,777.36$906.76$425,659.131015.00%0.4167%$2,684
.12$1,773.58$910.54$424,748.591025.00%0.4167%$2,684.12$1
,769.79$914.33$423,834.261035.00%0.4167%$2,684.12$1,765.
98$918.14$422,916.121045.00%0.4167%$2,684.12$1,762.16$9
21.96$421,994.161055.00%0.4167%$2,684.12$1,758.31$925.81
$421,068.351065.00%0.4167%$2,684.12$1,754.46$929.66$420,
138.691075.00%0.4167%$2,684.12$1,750.58$933.54$419,205.1
51085.00%0.4167%$2,684.12$1,746.69$937.43$418,267.72109
5.00%0.4167%$2,684.12$1,742.79$941.33$417,326.391105.00
%0.4167%$2,684.12$1,738.86$945.26$416,381.131115.00%0.4
167%$2,684.12$1,734.93$949.19$415,431.941125.00%0.4167%
$2,684.12$1,730.97$953.15$414,478.791135.00%0.4167%$2,68
4.12$1,727.00$957.12$413,521.671145.00%0.4167%$2,684.12$
1,723.01$961.11$412,560.561155.00%0.4167%$2,684.12$1,719
.01$965.11$411,595.451165.00%0.4167%$2,684.12$1,714.99$9
69.13$410,626.321175.00%0.4167%$2,684.12$1,710.95$973.17

40. $409,653.151185.00%0.4167%$2,684.12$1,706.89$977.23$408,
675.921195.00%0.4167%$2,684.12$1,702.82$981.30$407,694.6
21205.00%0.4167%$2,684.12$1,698.73$985.39$406,709.23121
5.00%0.4167%$2,684.12$1,694.63$989.49$405,719.741225.00
%0.4167%$2,684.12$1,690.50$993.62$404,726.121235.00%0.4
167%$2,684.12$1,686.36$997.76$403,728.361245.00%0.4167%
$2,684.12$1,682.21$1,001.91$402,726.451255.00%0.4167%$2,
684.12$1,678.03$1,006.09$401,720.361265.00%0.4167%$2,684
.12$1,673.84$1,010.28$400,710.081275.00%0.4167%$2,684.12
$1,669.63$1,014.49$399,695.591285.00%0.4167%$2,684.12$1,
665.40$1,018.72$398,676.871295.00%0.4167%$2,684.12$1,661
.16$1,022.96$397,653.911305.00%0.4167%$2,684.12$1,656.90
$1,027.22$396,626.691315.00%0.4167%$2,684.12$1,652.62$1,
031.50$395,595.191325.00%0.4167%$2,684.12$1,648.32$1,035
.80$394,559.391335.00%0.4167%$2,684.12$1,644.00$1,040.12
$393,519.271345.00%0.4167%$2,684.12$1,639.67$1,044.45$39
2,474.821355.00%0.4167%$2,684.12$1,635.32$1,048.80$391,4
26.021365.00%0.4167%$2,684.12$1,630.95$1,053.17$390,372.
851375.00%0.4167%$2,684.12$1,626.56$1,057.56$389,315.291
385.00%0.4167%$2,684.12$1,622.15$1,061.97$388,253.321395
.00%0.4167%$2,684.12$1,617.73$1,066.39$387,186.931405.00
%0.4167%$2,684.12$1,613.28$1,070.84$386,116.091415.00%0.
4167%$2,684.12$1,608.82$1,075.30$385,040.791425.00%0.416
7%$2,684.12$1,604.34$1,079.78$383,961.011435.00%0.4167%
$2,684.12$1,599.84$1,084.28$382,876.731445.00%0.4167%$2,

41. 684.12$1,595.32$1,088.80$381,787.931455.00%0.4167%$2,684
.12$1,590.79$1,093.33$380,694.601465.00%0.4167%$2,684.12
$1,586.23$1,097.89$379,596.711475.00%0.4167%$2,684.12$1,
581.66$1,102.46$378,494.251485.00%0.4167%$2,684.12$1,577
.06$1,107.06$377,387.191495.00%0.4167%$2,684.12$1,572.45
$1,111.67$376,275.521505.00%0.4167%$2,684.12$1,567.82$1,
116.30$375,159.221515.00%0.4167%$2,684.12$1,563.17$1,120
.95$374,038.271525.00%0.4167%$2,684.12$1,558.50$1,125.62
$372,912.651535.00%0.4167%$2,684.12$1,553.81$1,130.31$37
1,782.341545.00%0.4167%$2,684.12$1,549.10$1,135.02$370,6
47.321555.00%0.4167%$2,684.12$1,544.37$1,139.75$369,507.
571565.00%0.4167%$2,684.12$1,539.62$1,144.50$368,363.071
575.00%0.4167%$2,684.12$1,534.85$1,149.27$367,213.801585
.00%0.4167%$2,684.12$1,530.06$1,154.06$366,059.741595.00
%0.4167%$2,684.12$1,525.25$1,158.87$364,900.871605.00%0.
4167%$2,684.12$1,520.43$1,163.69$363,737.181615.00%0.416
7%$2,684.12$1,515.58$1,168.54$362,568.641625.00%0.4167%
$2,684.12$1,510.71$1,173.41$361,395.231635.00%0.4167%$2,
684.12$1,505.82$1,178.30$360,216.931645.00%0.4167%$2,684
.12$1,500.91$1,183.21$359,033.721655.00%0.4167%$2,684.12
$1,495.98$1,188.14$357,845.581665.00%0.4167%$2,684.12$1,
491.03$1,193.09$356,652.491675.00%0.4167%$2,684.12$1,486
.06$1,198.06$355,454.431685.00%0.4167%$2,684.12$1,481.07
$1,203.05$354,251.381695.00%0.4167%$2,684.12$1,476.05$1,
208.07$353,043.311705.00%0.4167%$2,684.12$1,471.02$1,213

42. .10$351,830.211715.00%0.4167%$2,684.12$1,465.96$1,218.16
$350,612.051725.00%0.4167%$2,684.12$1,460.89$1,223.23$34
9,388.821735.00%0.4167%$2,684.12$1,455.79$1,228.33$348,1
60.491745.00%0.4167%$2,684.12$1,450.67$1,233.45$346,927.
041755.00%0.4167%$2,684.12$1,445.53$1,238.59$345,688.451
765.00%0.4167%$2,684.12$1,440.37$1,243.75$344,444.701775
.00%0.4167%$2,684.12$1,435.19$1,248.93$343,195.771785.00
%0.4167%$2,684.12$1,429.99$1,254.13$341,941.641795.00%0.
4167%$2,684.12$1,424.76$1,259.36$340,682.281805.00%0.416
7%$2,684.12$1,419.51$1,264.61$339,417.671815.00%0.4167%
$2,684.12$1,414.25$1,269.87$338,147.801825.00%0.4167%$2,
684.12$1,408.95$1,275.17$336,872.631835.00%0.4167%$2,684
.12$1,403.64$1,280.48$335,592.151845.00%0.4167%$2,684.12
$1,398.31$1,285.81$334,306.341855.00%0.4167%$2,684.12$1,
392.95$1,291.17$333,015.171865.00%0.4167%$2,684.12$1,387
.57$1,296.55$331,718.621875.00%0.4167%$2,684.12$1,382.17
$1,301.95$330,416.671885.00%0.4167%$2,684.12$1,376.74$1,
307.38$329,109.291895.00%0.4167%$2,684.12$1,371.29$1,312
.83$327,796.461905.00%0.4167%$2,684.12$1,365.82$1,318.30
$326,478.161915.00%0.4167%$2,684.12$1,360.33$1,323.79$32
5,154.371925.00%0.4167%$2,684.12$1,354.81$1,329.31$323,8
25.061935.00%0.4167%$2,684.12$1,349.28$1,334.84$322,490.
221945.00%0.4167%$2,684.12$1,343.71$1,340.41$321,149.811
955.00%0.4167%$2,684.12$1,338.13$1,345.99$319,803.821965
.00%0.4167%$2,684.12$1,332.52$1,351.60$318,452.221975.00

43. %0.4167%$2,684.12$1,326.89$1,357.23$317,094.991985.00%0.
4167%$2,684.12$1,321.23$1,362.89$315,732.101995.00%0.416
7%$2,684.12$1,315.56$1,368.56$314,363.542005.00%0.4167%
$2,684.12$1,309.85$1,374.27$312,989.272015.00%0.4167%$2,
684.12$1,304.13$1,379.99$311,609.282025.00%0.4167%$2,684
.12$1,298.38$1,385.74$310,223.542035.00%0.4167%$2,684.12
$1,292.60$1,391.52$308,832.022045.00%0.4167%$2,684.12$1,
286.81$1,397.31$307,434.712055.00%0.4167%$2,684.12$1,280
.98$1,403.14$306,031.572065.00%0.4167%$2,684.12$1,275.14
$1,408.98$304,622.592075.00%0.4167%$2,684.12$1,269.27$1,
414.85$303,207.742085.00%0.4167%$2,684.12$1,263.37$1,420
.75$301,786.992095.00%0.4167%$2,684.12$1,257.45$1,426.67
$300,360.322105.00%0.4167%$2,684.12$1,251.51$1,432.61$29
8,927.712115.00%0.4167%$2,684.12$1,245.54$1,438.58$297,4
89.132125.00%0.4167%$2,684.12$1,239.54$1,444.58$296,044.
552135.00%0.4167%$2,684.12$1,233.52$1,450.60$294,593.952
145.00%0.4167%$2,684.12$1,227.48$1,456.64$293,137.312155
.00%0.4167%$2,684.12$1,221.41$1,462.71$291,674.602165.00
%0.4167%$2,684.12$1,215.32$1,468.80$290,205.802175.00%0.
4167%$2,684.12$1,209.20$1,474.92$288,730.882185.00%0.416
7%$2,684.12$1,203.05$1,481.07$287,249.812195.00%0.4167%
$2,684.12$1,196.88$1,487.24$285,762.572205.00%0.4167%$2,
684.12$1,190.68$1,493.44$284,269.132215.00%0.4167%$2,684
.12$1,184.46$1,499.66$282,769.472225.00%0.4167%$2,684.12
$1,178.21$1,505.91$281,263.562235.00%0.4167%$2,684.12$1,

44. 171.94$1,512.18$279,751.382245.00%0.4167%$2,684.12$1,165
.64$1,518.48$278,232.902255.00%0.4167%$2,684.12$1,159.31
$1,524.81$276,708.092265.00%0.4167%$2,684.12$1,152.96$1,
531.16$275,176.932275.00%0.4167%$2,684.12$1,146.58$1,537
.54$273,639.392285.00%0.4167%$2,684.12$1,140.17$1,543.95
$272,095.442295.00%0.4167%$2,684.12$1,133.74$1,550.38$27
0,545.062305.00%0.4167%$2,684.12$1,127.28$1,556.84$268,9
88.222315.00%0.4167%$2,684.12$1,120.79$1,563.33$267,424.
892325.00%0.4167%$2,684.12$1,114.28$1,569.84$265,855.052
335.00%0.4167%$2,684.12$1,107.73$1,576.39$264,278.662345
.00%0.4167%$2,684.12$1,101.17$1,582.95$262,695.712355.00
%0.4167%$2,684.12$1,094.57$1,589.55$261,106.162365.00%0.
4167%$2,684.12$1,087.95$1,596.17$259,509.992375.00%0.416
7%$2,684.12$1,081.30$1,602.82$257,907.172385.00%0.4167%
$2,684.12$1,074.62$1,609.50$256,297.672395.00%0.4167%$2,
684.12$1,067.91$1,616.21$254,681.462405.00%0.4167%$2,684
.12$1,061.18$1,622.94$253,058.522415.00%0.4167%$2,684.12
$1,054.42$1,629.70$251,428.822425.00%0.4167%$2,684.12$1,
047.63$1,636.49$249,792.332435.00%0.4167%$2,684.12$1,040
.81$1,643.31$248,149.022445.00%0.4167%$2,684.12$1,033.96
$1,650.16$246,498.862455.00%0.4167%$2,684.12$1,027.08$1,
657.04$244,841.822465.00%0.4167%$2,684.12$1,020.18$1,663
.94$243,177.882475.00%0.4167%$2,684.12$1,013.25$1,670.87
$241,507.012485.00%0.4167%$2,684.12$1,006.28$1,677.84$23
9,829.172495.00%0.4167%$2,684.12$999.29$1,684.83$238,144

45. .342505.00%0.4167%$2,684.12$992.27$1,691.85$236,452.4925
15.00%0.4167%$2,684.12$985.22$1,698.90$234,753.592525.00
%0.4167%$2,684.12$978.14$1,705.98$233,047.612535.00%0.4
167%$2,684.12$971.04$1,713.08$231,334.532545.00%0.4167%
$2,684.12$963.90$1,720.22$229,614.312555.00%0.4167%$2,68
4.12$956.73$1,727.39$227,886.922565.00%0.4167%$2,684.12$
949.53$1,734.59$226,152.332575.00%0.4167%$2,684.12$942.3
1$1,741.81$224,410.522585.00%0.4167%$2,684.12$935.05$1,7
49.07$222,661.452595.00%0.4167%$2,684.12$927.76$1,756.36
$220,905.092605.00%0.4167%$2,684.12$920.44$1,763.68$219,
141.412615.00%0.4167%$2,684.12$913.09$1,771.03$217,370.3
82625.00%0.4167%$2,684.12$905.71$1,778.41$215,591.97263
5.00%0.4167%$2,684.12$898.30$1,785.82$213,806.152645.00
%0.4167%$2,684.12$890.86$1,793.26$212,012.892655.00%0.4
167%$2,684.12$883.39$1,800.73$210,212.162665.00%0.4167%
$2,684.12$875.89$1,808.23$208,403.932675.00%0.4167%$2,68
4.12$868.35$1,815.77$206,588.162685.00%0.4167%$2,684.12$
860.79$1,823.33$204,764.832695.00%0.4167%$2,684.12$853.1
9$1,830.93$202,933.902705.00%0.4167%$2,684.12$845.56$1,8
38.56$201,095.342715.00%0.4167%$2,684.12$837.90$1,846.22
$199,249.122725.00%0.4167%$2,684.12$830.21$1,853.91$197,
395.212735.00%0.4167%$2,684.12$822.49$1,861.63$195,533.5
82745.00%0.4167%$2,684.12$814.73$1,869.39$193,664.19275
5.00%0.4167%$2,684.12$806.94$1,877.18$191,787.012765.00
%0.4167%$2,684.12$799.12$1,885.00$189,902.012775.00%0.4

46. 167%$2,684.12$791.26$1,892.86$188,009.152785.00%0.4167%
$2,684.12$783.38$1,900.74$186,108.412795.00%0.4167%$2,68
4.12$775.46$1,908.66$184,199.752805.00%0.4167%$2,684.12$
767.50$1,916.62$182,283.132815.00%0.4167%$2,684.12$759.5
2$1,924.60$180,358.532825.00%0.4167%$2,684.12$751.50$1,9
32.62$178,425.912835.00%0.4167%$2,684.12$743.45$1,940.67
$176,485.242845.00%0.4167%$2,684.12$735.36$1,948.76$174,
536.482855.00%0.4167%$2,684.12$727.24$1,956.88$172,579.6
02865.00%0.4167%$2,684.12$719.09$1,965.03$170,614.57287
5.00%0.4167%$2,684.12$710.90$1,973.22$168,641.352885.00
%0.4167%$2,684.12$702.68$1,981.44$166,659.912895.00%0.4
167%$2,684.12$694.42$1,989.70$164,670.212905.00%0.4167%
$2,684.12$686.13$1,997.99$162,672.222915.00%0.4167%$2,68
4.12$677.81$2,006.31$160,665.912925.00%0.4167%$2,684.12$
669.45$2,014.67$158,651.242935.00%0.4167%$2,684.12$661.0
5$2,023.07$156,628.172945.00%0.4167%$2,684.12$652.62$2,0
31.50$154,596.672955.00%0.4167%$2,684.12$644.16$2,039.96
$152,556.712965.00%0.4167%$2,684.12$635.66$2,048.46$150,
508.252975.00%0.4167%$2,684.12$627.12$2,057.00$148,451.2
52985.00%0.4167%$2,684.12$618.55$2,065.57$146,385.68299
5.00%0.4167%$2,684.12$609.95$2,074.17$144,311.513005.00
%0.4167%$2,684.12$601.30$2,082.82$142,228.693015.00%0.4
167%$2,684.12$592.62$2,091.50$140,137.193025.00%0.4167%
$2,684.12$583.91$2,100.21$138,036.983035.00%0.4167%$2,68
4.12$575.16$2,108.96$135,928.023045.00%0.4167%$2,684.12$

47. 566.37$2,117.75$133,810.273055.00%0.4167%$2,684.12$557.5
5$2,126.57$131,683.703065.00%0.4167%$2,684.12$548.69$2,1
35.43$129,548.273075.00%0.4167%$2,684.12$539.79$2,144.33
$127,403.943085.00%0.4167%$2,684.12$530.85$2,153.27$125,
250.673095.00%0.4167%$2,684.12$521.88$2,162.24$123,088.4
33105.00%0.4167%$2,684.12$512.87$2,171.25$120,917.18311
5.00%0.4167%$2,684.12$503.83$2,180.29$118,736.893125.00
%0.4167%$2,684.12$494.74$2,189.38$116,547.513135.00%0.4
167%$2,684.12$485.62$2,198.50$114,349.013145.00%0.4167%
$2,684.12$476.46$2,207.66$112,141.353155.00%0.4167%$2,68
4.12$467.26$2,216.86$109,924.493165.00%0.4167%$2,684.12$
458.02$2,226.10$107,698.393175.00%0.4167%$2,684.12$448.7
5$2,235.37$105,463.023185.00%0.4167%$2,684.12$439.43$2,2
44.69$103,218.333195.00%0.4167%$2,684.12$430.08$2,254.04
$100,964.293205.00%0.4167%$2,684.12$420.69$2,263.43$98,7
00.863215.00%0.4167%$2,684.12$411.26$2,272.86$96,428.003
225.00%0.4167%$2,684.12$401.79$2,282.33$94,145.673235.00
%0.4167%$2,684.12$392.28$2,291.84$91,853.833245.00%0.41
67%$2,684.12$382.73$2,301.39$89,552.443255.00%0.4167%$2
,684.12$373.14$2,310.98$87,241.463265.00%0.4167%$2,684.1
2$363.51$2,320.61$84,920.853275.00%0.4167%$2,684.12$353.
84$2,330.28$82,590.573285.00%0.4167%$2,684.12$344.13$2,3
39.99$80,250.583295.00%0.4167%$2,684.12$334.38$2,349.74$
77,900.843305.00%0.4167%$2,684.12$324.59$2,359.53$75,541
.313315.00%0.4167%$2,684.12$314.76$2,369.36$73,171.95332

48. 5.00%0.4167%$2,684.12$304.89$2,379.23$70,792.723335.00%
0.4167%$2,684.12$294.97$2,389.15$68,403.573345.00%0.4167
%$2,684.12$285.02$2,399.10$66,004.473355.00%0.4167%$2,6
84.12$275.02$2,409.10$63,595.373365.00%0.4167%$2,684.12$
264.99$2,419.13$61,176.243375.00%0.4167%$2,684.12$254.91
$2,429.21$58,747.033385.00%0.4167%$2,684.12$244.78$2,439
.34$56,307.693395.00%0.4167%$2,684.12$234.62$2,449.50$53
,858.193405.00%0.4167%$2,684.12$224.41$2,459.71$51,398.4
83415.00%0.4167%$2,684.12$214.17$2,469.95$48,928.533425.
00%0.4167%$2,684.12$203.87$2,480.25$46,448.283435.00%0.
4167%$2,684.12$193.54$2,490.58$43,957.703445.00%0.4167%
$2,684.12$183.16$2,500.96$41,456.743455.00%0.4167%$2,684
.12$172.74$2,511.38$38,945.363465.00%0.4167%$2,684.12$16
2.28$2,521.84$36,423.523475.00%0.4167%$2,684.12$151.77$2
,532.35$33,891.173485.00%0.4167%$2,684.12$141.22$2,542.9
0$31,348.273495.00%0.4167%$2,684.12$130.62$2,553.50$28,7
94.773505.00%0.4167%$2,684.12$119.98$2,564.14$26,230.633
515.00%0.4167%$2,684.12$109.30$2,574.82$23,655.813525.00
%0.4167%$2,684.12$98.57$2,585.55$21,070.263535.00%0.416
7%$2,684.12$87.80$2,596.32$18,473.943545.00%0.4167%$2,6
84.12$76.98$2,607.14$15,866.803555.00%0.4167%$2,684.12$6
6.12$2,618.00$13,248.803565.00%0.4167%$2,684.12$55.21$2,
628.91$10,619.893575.00%0.4167%$2,684.12$44.25$2,639.87$
7,980.023585.00%0.4167%$2,684.12$33.26$2,650.86$5,329.16
3595.00%0.4167%$2,684.12$22.21$2,661.91$2,667.253605.00

49. %0.4167%$2,678.37$11.12$2,667.25$0.00$466,277.45$500,000
.00
Loan Payments and BalanceIntint/mon mosPmt[500.0k$] Bal[36
mos] Bal[60 mos] Int Only
Pmt4.00%0.3333%360$2,387.08$472,494.33$452,238.23$1,666.
674.25%0.3542%360$2,459.70$473,600.35$454,038.58$1,770.8
44.50%0.3750%360$2,533.43$474,673.55$455,790.21$1,875.00
4.75%0.3958%360$2,608.24$475,712.61$457,491.77$1,979.175
.00%0.4167%360$2,684.11$476,718.31$459,143.98$2,083.345.
25%0.4375%360$2,761.02$477,691.54$460,747.69$2,187.505.5
0%0.4583%360$2,838.95$478,633.27$462,303.83$2,291.675.75
%0.4792%360$2,917.87$479,542.88$463,811.84$2,395.846.00
%0.5000%360$2,997.76$480,421.53$465,272.93$2,500.006.25
%0.5208%360$3,078.59$481,268.87$466,686.81$2,604.176.50
%0.5417%360$3,160.35$482,087.72$468,056.35$2,708.346.75
%0.5625%360$3,243.00$482,876.27$469,379.93$2,812.507.00
%0.5833%360$3,326.52$483,635.91$470,659.01$2,916.677.25
%0.6042%360$3,410.89$484,367.95$471,895.08$3,020.847.50
%0.6250%360$3,496.08$485,072.27$473,088.19$3,125.007.75
%0.6458%360$3,582.07$485,750.21$474,239.85$3,229.178.00
%0.6667%360$3,668.83$486,401.69$475,350.21$3,333.348.25
%0.6875%360$3,756.34$487,027.99$476,420.74$3,437.508.50
%0.7083%360$3,844.57$487,629.06$477,451.65$3,541.678.75
%0.7292%360$3,933.51$488,207.34$478,445.59$3,645.849.00
%0.7500%360$4,023.12$488,761.49$479,401.51$3,750.00