TIME VALUE OF MONEY

1
TIME VALUE OF MONEY

• MONEY HAS TIME VALUE BECAUSE
• PEOPLE WOULD RATHER CONSUME NOW RATHER THAN
  LATER.
• PEOPLE PREFER TO CONSUME MORE RATHER THAN LESS
• PEOPLE CAN BE INDUCED TO CONSUME LESS NOW IF
  PROMISED MORE LATER

2
COMMONLY USED SYMBOLS

• FV FUTURE VALUE
• FVIF FUTURE VALUE INTEREST FACTOR
• PV PRESENT VALUE
• PVIF PRESENT VALUE INTEREST FACTOR

3
MORE SYMBOLS

• PVA PRESENT VALUE OF AN ANNUITY
• PVIFA PRESENT VALUE INTEREST FACTOR FOR AN
  ANNUITY
• FVA FUTURE VALUE OF AN ANNUITY
• FVIFA FUTURE VALUE INTEREST FACTOR FOR AN
  ANNUITY

4
MORE SYMBOLS

• PMT CONSTANT PAYMENT
• k INTEREST RATE
• n NUMBER OF TIME PERIODS
• t A SPECIFIC TIME (e.g., t 1, t 2)
• EAR EFFECTIVE ANNUAL RATE

5
CALCULATOR SETUP
HIT THE 2ND BUTTON THEN THE FORMAT (.)
BUTTON HIT THE 4 BUTTON, THEN THE ENTER
BUTTON HIT THE 2ND BUTTON THEN THE P/Y (I/Y)
BUTTON HIT THE 1 BUTTON, THEN THE ENTER
BUTTON HITTHE 2ND BUTTON, THEN THE CLR TVM (FV)
BUTTON
6
IMPORTANT!
BEFORE BEGINNING A TIME VALUE PROBLEM, CLEAR OUT
THE TIME VALUE KEYS BY HITTING 2ND CLR TVM!
7
FINDING A FUTURE VALUE OF A SINGLE SUM
t
0 1
2 3
100
?
PV 100 k 10
8
FINDING THE FUTURE VALUE OF A SINGLE SUM OF 100
AT t 1
t
0 1
2 3
100
?
FV1 100 (100 X .1) 100 (1 .1)
110
PV 100 k 10
9
FUTURE VALUE OF 100 ATt 2
t
0 1
2 3
110
?
100
(1 .1)
FV2
FV1
110(1 .1) 100(1 .1)(1 .1) 100(1
.1)2
PV 100 k 10
Since 110 100(1 .1)
10
FUTURE VALUE OF SINGLE SUMFORMULA
FVn PV(1 k)n
1. EFFECT OF k 2. EFFECT OF n
FVIF
11
EXAMPLE
PV 500, n 10, k 6
FV10 500(1 .06)10 895.42
0
10
500
895.42
12
CALCULATOR SOLUTION FVn PV(FVIF, n, k) FV10
500 (FVIF, 10, 6) 500 PV 10 N I/Y
6 CPT FV
13
CALCULATOR SOLUTION FVn PV(FVIF, n, k) FV10
500 (FVIF, 10, 6) 500 PV 10 N I/Y
6 CPT FV
NOW LETS TRY FINDING THE FV USING A HIGHER
INTEREST RATE. WHAT HAPPENS TO THE FV AND WHY?
14
CALCULATOR SOLUTION FVn PV(FVIF, n, k) FV10
500 (FVIF, 10, 6) 500 PV 10 N I/Y
6 CPT FV
NOW LETS TRY FINDING THE FV USING A HIGHER VALUE
FOR N. WHAT HAPPENS TO THE FV AND WHY?
15
Lets work some problems

• Problem 4.4 page on 172 cases A and E

16
Problem 4.4 Case A
FV PV(1 K)N 200(1 .05)20 FV
200(FVIF, 20, 5) 530.66 Interpretation of
Answer? 200 PV 20 N 5 I/Y CPT FV
17
PROBLEM 4.4 CASE E
FV PV(1 K)N 37,000(1 .11)5 FV
37,000(FVIF, 5, 11) 62,347.15 37,000 PV
5 N 11 I/Y CPT FV
18
To understand present values, remember!
1 X
Y
THE BIGGER X IS, THE SMALLER Y IS.
19
PRESENT VALUE FORMULA
SINCE FVn PV(1 k)n THEN

PV FVn FVn 1
(1 k)n (1
K)n
1. EFFECT OF k 2. EFFECT OF n
PVIF
20
FIND PV FV 500, k 6, n 10
0
PV 500 ___1____ (1.06)10
10
279.20
?
500
What is the interpretation of this PV?
21
CALCULATOR SOLUTION
PV 500(PVIF, 10, 6) 500 FV 10 N
6 I/Y CPT PV
22
CALCULATOR SOLUTION
PV 500(PVIF, 10, 6) 500 FV 10 N
6 I/Y CPT PV
NOW, LETS FIND THE PRESENT VALUE USING A HIGHER
INTEREST RATE, E.G., 10. WHAT HAPPENS TO THE
PV AND WHY?
23
CALCULATOR SOLUTION
PV 500(PVIF, 10, 6) 500 FV 10 N
6 I/Y CPT PV
NOW, LETS FIND THE PRESENT VALUE USING A HIGHER
VALUE FOR N, E.G., 20 YEARS. WHAT HAPPENS TO
THE PV AND WHY?
24
Lets work some problems

• Problem 4-10, cases B and C

25
4-10 CASE B
PV FVN 28,000
(1 K)N (1 .08)20 PV
FV(PVIF, N, K) PV 28,000(PVIF, 20, 8)
6,007.35 28,000 FV 20 N
8 I/Y CPT PV
26
4-10 CASE C
PV FVN 10,000
(1 K)N
(1 .14)12
PV 10,000(PVIF, 12, 14) 2,075.59 10,000
FV 12 N 14 I/Y CPT PV
27
COMPOUNDING MORE THAN ONCE PER YEAR

• SUPPOSE YOU INVEST 1,000 INTO A ONE YEAR CD AT
  10 COMPOUNDED SEMIANNUALLY. HOW MUCH WILL YOU
  HAVE AT THE END OF THE YEAR?

1
6 MOS.
0
HALF YEARS INTEREST COMPUTED HERE
HALF YEARS INTEREST COMPUTED HERE TOO
28

• FV 6 MOS 1,000(1 .10/2) 1,050
• FV 1 YEAR 1,050(1 .10/2)
• 1,000(1 .10/2)(1
  .10/2)
• 1,102.50

29
COMPARE

• COMPARE THIS TO THE INTEREST YOU WOULD HAVE
  GOTTEN IF INTEREST WERE COMPOUNDED ONCE PER YEAR
• FV 1,000(1.10) 1,100
• THE 2.50 DIFFERENCE IS THE INTEREST ON
• 50 INTEREST (50 x .05) 2.50

30
SOLUTION

• FV PV(1 K/M)NXM
• N Number of years
• M COMPOUNDINGS PER YEAR
• FV 1,000 (1 .1/2)1x2 1,102.50 OR

31
USING CALCULATOR

• FV PV(FVIF, N, K) (C/Y M)
• FV 1,000(FVIF, 1, 10) (C/Y 2)
• 1,102.50
• SEE NEXT SLIDE FOR BUTTON SEQUENCE

32
CALCULATOR APPROACH - USING THEC/Y OPTION

• HIT 2ND P/Y
• P/Y 1 ENTER
• HIT DOWN ARROW
• C/Y 2 ENTER
• 2ND QUIT
• PV 1,000
• I/Y 10
• N 1 CPT FV

33
A PROBLEM FOR PRACTICE SUPPOSE YOU CAN INVEST
2,000 AT A BANK PAYING INTEREST OF 4 PER YEAR
COMPOUNDED QUARTERLY. HOW MUCH WILL YOU HAVE AT
THE END OF 10 YEARS?
FV PV(1 K/M)NXM 2,000(1
.04/4)4X10 CALCULATOR APPROACH FV PV(FVIF,
N, K) C/Y M C/Y 4 (2ND P/Y, DOWN
ARROW, 4, ENTER, 2ND QUIT) FV
2,000(FVIF,10, 4) 2,977.73
34
BUTTON SEQUENCE FORPREVIOUS SLIDE

• 2,000 PV
• 10 N
• 4 I/Y
• CPT FV

35
NOTICE!
THE MORE FREQUENTLY INTEREST IS COMPOUNDED THE
HIGHER THE FV WILL BE. WHY?
AT THE EXTREME, INTEREST CAN BE CALCULATED
CONTINUOUSLY.
36
FUTURE VALUES AND CONTINUOUS COMPOUNDING
WHEN INTERST IS COMPOUNDED CONTINUOUSLY THE
FUTURE VALUE CAN BE FOUND USING THE FOLLOWING
FORMULA FV PV(ekxt)
37
CONTINUOUS COMPOUNDING EXAMPLE
FIND THE FUTURE VALUE OF 1,000 IN 5 YEARS WHEN
ITS INVESTED AT 6 COMPOUNDED CONTINUOUSLY. FV
PV(ekxt) 1,000(e.06x5) 1,349.86 ENTER
.30 2ND ex X 1,000
38
LETS WORK A PROBLEM
LOOK AT PROBLEM 4-34, CASE D ON PAGE 181. FV
2,500(e.12 x 4) Punch in .48 Hit 2nd ex X
2,500 4,040.19
39
ANNUITIES AND TIME VALUE

• AN ANNUITY IS AN EQUAL SUM PAID OR RECEIVED OVER
  EQUAL INCREMENTS OF TIME.
  
• 0 1 2 3 4
  5

100
100
100
100
100
40
FINDING THE FUTURE VALUE OF AN ANNUITY
EFFECT OF N EFFECT OF K
FVA PMT (1 k)n - 1
k
FVIFA k 10
0 1 2 3
4 5
100
100
100
100 100
41
THE FUTURE VALUE ANNUITY FORMULA FINDS THE FVA AT
THE LAST ANNUITYPAYMENT. IN THE NEXT PROBLEM,
THEFUTURE VALUE WE FIND WILL BE ITS VALUE AT
TIME 5
42
SETTING UP FOR CALCULATOR
FVA PMT(FVIFA, N, K) 100(FVIFA,
5, 10) 610.51
0 1 2 3
4 5
100
100
100
100 100
43
CALCULATOR SOLUTION
FVA PMT(FVIFA, N, K) 100(FVIFA,
5, 10) 610.51
100 PMT 5 N ( OF PAYMENTS) 10
I/Y CPT FV
44
ANOTHER EXAMPLE
0 1 2
3 10
400 400
400 400
FVA 400(FVIFA, 10, 10) 6,374.97
PMT 400 N 10 ( OF PAYMENTS)
I/Y 10 CPT FV
45
Lets work Some Problems!
Problem 4-17, cases A and B
46
Problem 4-17, Case A
0 1 2 3
10
. . .
2,500 2,500 2,500 2,500

• PMT
• 10 N
• 8 I/Y
• CPT FV

FVA PMT(FVIFA, N, K) FVA 2,500(FVIFA, 10,
8) FVA 36,216.41
47
PROBLEM 4-17, CASE B
0 1 2 3
4 5 6
500 500 500 500
500 500
FVA 500(FVIFA, 6, 12) 4,057.59
48
Retirement Planning
Jerry is 25 years old and can save 250 per month
toward His retirement at age 65. If Jerry can
invest his money to Earn 10 per year, how much
will he have saved by the Time he is 65?
49
Retirement Planning
1ST mo 2nd mo 3rd mo
480th mo
0
. . .
250 250 250
250

FVA?

K 10
50
SINCE JERRY WILL BE MAKING MONTHLY PAYMENTS, WE
NEED TO MAKE SOME ADJUSTMENTS TO THE FUTURE VALUE
ANNUITY FORMULA FVA PMT(1 K/M)NXM 1
K/M P/Y M WHERE M
OF PAYMENTS PER YEAR
FVA PMT(FVIFA, NXM, K)
P/Y
12 FVA 250(FVIFA, 12X40, 10) 1,581,019.90
51
CALCULATOR APPROACH

• 2ND P/Y
• ENTER
• 2ND QUIT
• PMT
• N
• I/Y
• CPT FV 1,581,019.90

52
WHAT IF?
WHAT IF JERRY COULD EARN A SLIGHTLY HIGHER RETURN
OF 12 BY TAKING JUST A LITTLE MORE RISK? HOW
MUCH MORE WOULD HE HAVE SAVED UP FOR HIS
RETIREMEN?
P/Y M FVA PMT(FVIFA, NXM, K)
P/Y 12 FVA
250(FVIFA, 12X40, 12) 2,941,193.13 FVA
250(FVIFA, 12X40, 10) 1,581,019.90
INCREASE
1,360,173.23

• SET P/Y TO 12
• 250 PMT
• N
• 1/Y
• CPT FV

53
LESSON
A SMALL DIFFERENCE IN RETURN ADDS UP TO A LOT OF
MONEY OVER A LONG PERIOD OF TIME. WHILE YOURE
YOUNG, INVEST AGGRESSIVELY FOR THE HIGHER RETURNS
THESE INVESTMENTS OFFER. AS YOU AGE, GRADUALLY
TRANSFER FUNDS INTO MORE CONSERVATIVE
INVESTMENTS.
54
More Retirement Planning
Sue is 25 years old and plans to retire at age
65. She would Like to save 2,000,000 by the
time she retires. What monthly Payment must she
make each month to achieve this goal if She can
invest her money to return 10 per year?
0
1ST mo 2nd mo 3rd mo
480th mo
. . .
PMT PMT PMT
PMT

2,000,000
K 12
55
CALCULATOR SOLUTIONTO SUES RETIREMENT PROBLEM

P/Y 12 2,000,000 PMT(FVIFA, 40X12,
10) PMT 316.25 2ND
P/Y 12 ENTER 2ND
QUIT 2,000,000 FV
10 I/Y 480
N CPT PMT
56
WHAT CAN SUE DO TO REDUCE HER MONTHLY PAYMENT BUT
STILL SAVE UP 2,000,000?
ONE WAY FOR SUE TO REDUCE HER MONTHLY PAY- MENTS
IS TO SEEK INVESTMENTS WITH HIGHER RETURNS, BUT
ALSO HIGHER RISKS. HOW MUCH WOULD SUES MONTHLY
PAYMENT FALL IF SHE COULD INVEST HER MONEY TO
EARN 12 RATHER THAN 10?
57
REDUCTION IN SUES PAYMENT

P/Y M FVA PMT(FVIFA, NXM, K)
P/Y
12 2,000,000 PMT(FVIFA, 40X12, 12)
170.00 2,000,000 FV 480
N PAYMENT _at_ 10
316.25 12 I/Y
PAYMENT _at_ 12 170.00 CPT PMT
PAYMENT REDUCTION 146.25
58
LESSON
THE HIGHER THE RETURN, THE LOWER THE
PAYMENT NEEDED TO ACHIEVE A GIVEN FINANCIAL GOAL.
59
PRESENT VALUE OF AN ANNUITY
PVA PMT PMT . . . PMT PMT (1
1/(1K)N) (1 k)1 (1 k)2
(1 k)n K



1. Effect of K Calculator Approach
2. Effect of N PVA PMT(PVIFA, N
K)
60
Example
How much would you pay today for the right to Get
100 per year for 5 years if your required
return Is 10
0 1 2
3 4 5
100 100 100
100 100
379.08
61
Example, Cont
PVA PMT(PVIFA, N, K) PVA 100(PVIFA, 5,
10) 379.08
100 PMT 5 N 10 I/Y
CPT PV
62
PRESENT VALUE ANNUITY FORMULA

• FINDS THE VALUE OF AN ANNUITY ONE PERIOD BEFORE
  THE START OF THE ANNUITY.
• REMEMBER THIS!!!

63
SUPPOSE I OFFER YOU 200 FOR 5 YEARS. IF YOU
WANT TO EARN 5 ON YOUR MONEY, HOW MUCH AT MOST
WOULD YOU BE WILLING TO PAY ME NOW?
200 200 200 200
200
865.90

• PMT
• 5 N
• 5 I/Y
• CPT PV

PVA PMT(PVIFA, n, k) PVA 200(PVIFA, 5, 5)
865.90
64
Lets Work Some Problems

• Problem 4-18 cases A and C
• Problem 4-19-a

65
Problem 4-18 case A
0 1
2 3
12,000 12,000 12,000
31,491.79
PVA PMT(PVIFA, N, K) PVA 12,000(PVIFA, 3,
7) 31,491.79
66
Problem 4-18, Case A, Calculator Solution
12,000 PMT 3 N 7
I/Y CPT PV ANS 31, 491.79
67
Problem 4.18, Case C
0 1 2 3 4
5 6 7 8 9
700 700 700 700 700 700
700 700 700
PVA 700(PVIFA, 9, 20) 2,821.68
68
WHAT IF ANNUITY BEGINS SOMETIME AFTER TIME 1? FOR
EXAMPLE, HOW MUCH AT MOST WOULD YOU BE WILLING
TOPAY NOW FOR THE RIGHT TO GET 100 DURING YEARS
2, 3, 4, AND 5 IF YOU WISH TO EARN 10 ON YOUR
MONEY?
PVIFA BRINGS ANNUITY VALUE BACK ONE PERIOD BEFORE
THE FIRST ANNUITY PAYMENT
0 1 2 3
4 5
100
100
100
100
69
IN THIS EXAMPLE, THE PRESENT VALUE ANNUITY
FORMULA VALUES THE ANNUITY AT END OF TIME 1
WE THEN HAVE TO BRING TIME 1 VALUE BACK TO TIME 0
PVA1 100(PVIFA, 4, 10) 316.99
0 1 2 3
4 5
100
100
100
100
316.99
PVA1
70
TAKING THE ANNUITY BACK ONE MORE YEAR
PV 316.99(PVIF, 1, 10) 288.17
0 1 2 3
4 5
288.17
100
100
100
100
316.99
PVA1
71
There Must Be Another Way!

• There is more later.

72
PERPETUAL ANNUITIES(PERPETUITIES)
PV (PERPETUITY) PMT
k
0 1 2 3
4
. . .
100
100 (FOREVER)
100 100
73
FIND THE PV OF 100 TO BE RECEIVEDFOR EVER. k
10
PV (PERPETUITY) 100 1,000
.1
WHATS THE FUTURE VALUE OF THIS ANNUITY?
74
WHAT IF YOU NEED TO FIND PV OF UNEVEN CASH FLOWS
PV 100 200 400
400 700
(1.08)5
(1.08)3
(1.08)2
(1.08)4
(1.08)1
100(PVIF, 1, 8) 200(PVIF, 2, 8) 400
(PVIF, 3, 8) 400(PVIF, 4, 8)


700(PVIF, 5, 8)
0 1 2 3
4 5
700
100
400
200
400
75
CALCULATOR SOLUTION

• PRESS CF BUTTON
• HIT DOWN ARROW
• PRESS 100 FOR C01 THEN ENTER BUTTON
• HIT DOWN ARROW
• PRESS 1 FOR F01 THEN ENTER BUTTON
• HIT DOWN ARROW

76

• PRESS 200 FOR CF02 THEN PRESS ENTER
• HIT DOWN ARROW
• PRESS 1 FOR F02 THEN PRESS ENTER
• HIT DOWN ARROW
• PRESS 400 FOR CF03 THEN PRESS ENTER
• HIT DOWN ARROW
• PRESS 2 FOR F03 THEN PRESS ENTER

77

• PRESS 700 FOR CF04 THEN PRESS ENTER
• HIT DOWN ARROW
• PRESS 1 FOR F04 THEN PRESS ENTER
• HIT NPV KEY
• ENTER 8 FOR I
• HIT DOWN ARROW
• PRESS CPT
• PV 1,352.01

78

• WASNT I SUPPOSED TO SHOW YOU A BETTER WAY TO
  COMPUTE THE PV OF AN ANNUITY STARTING AFTER TIME
  1?

K 10
0 1 2
3 4
0 0 100
100 100
79

• THE EASY WAY TO DO THIS IS TO
• HIT CF HIT NPV
• CF0 0 I 10
• DOWN ARROW DOWN ARROW
• C01 0 CPT
• DOWN ARROW
• F01 1 ANSWER
  288.17
• DOWN ARROW
• C02 100
• DOWN ARROW
• F02 4

80
ANOTHER EXAMPLE
CASH FLOW A
CASH FLOW B
YEAR
1 100
300 2
400
400 3 400
400 4
400
400 5 300
100
k 8
81
INTEREST RATE PROBLEMS

• WHAT ANNUAL INTEREST RATE WILL CAUSE 100 TO GROW
  TO 125.97 IN THREE YEARS?
• 0 1 2
  3

100
100(1 k)3
125.97 -100(FVIF, 3 , k) IMPLIES k 8
82
ANOTHER INTEREST RATE PROBLEM

• I OFFER TO LEND YOU 575 TODAY IF YOU WILL REPAY
  ME 1,000 IN TEN YEARS. YOU WILL NOT BORROW
  MONEY IF THE RATE EXCEEDS 10. SHOULD YOU TAKE
  THIS LOAN?
• PV FV(PVIF, n, k)
• -575 1,000(PVIF, 10, k)
• ENTER WHAT YOU KNOW, SOLVE FOR k (k 5.7)
  TAKE THE LOAN.

83
YET ANOTHER INTEREST RATEPROBLEM

• YOU INVEST 10,000 TODAY. WHAT RATE OF RETURN
  WILL YOU NEED TO EARN TO DOUBLE YOUR MONEY IN 6
  YEARS?
• -10,000 20,000(PVIF, 6, k)
• ENTER KNOWN VARIABLES, SOLVE FOR k
• k 12.25

84
ONE MORE PROBLEM

• YOU HAVE 10,000 WHICH YOU ARE CONFIDENT YOU CAN
  INVEST TO RETURN 10 PER YEAR. HOW LONG WILL IT
  TAKE YOU TO DOUBLE YOUR MONEY
• -10,000 20,000(PVIF, n, 10)
• IMPLIES n 7.3 YEARS

85
EFFECTIVE ANNUAL RATES

• NOMINAL RATE RATE QUOTED BY LENDERS
• NOMINAL RATES CANNOT BE COMPARED WITH ONE ANOTHER
  IF THEIR INTEREST RATES ARE NOT COMPUTED
  (COMPOUNDED) THE SAME NUMBER OF TIMES PER YEAR

86
EXAMPLE

• THE FIRST NATIONAL BANK OF ANNISTON OFFERS YOU A
  RATE OF 8 ON A ONE YEAR CD COMPOUNDED ANNUALLY.
• THE FIRST NATIONAL BANK OF OXFORD OFFERS YOU A
  RATE OF 7.9 ON THE SAME CD COMPOUNDED
  SEMIANNUALLY
• EAR (1 knom/m)m - 1
• knom STATED or NOMINAL RATE
• m COMPOUNDINGS PER YEAR

87
EAR FIRST NATIONAL BANK OF ANNISTON

• EAR (1 .08/1)1 - 1 8

88
EAR FIRST NATIONAL BANK OF OXFORD

• EAR (1 .079/2)2 -1 8.06
• PUT MONEY IN FIRST NATIONAL BANK OF OXFORD
• CALCULATOR 2ND ICONV
• 2ND CLR WORK
• NOM7.9 ENTER
• C/Y2 ENTER
• EFF CPT (ANS. 8.056)

89
EAR WITH CONTINUOUS COMPOUNDING

• EAR ek - 1
• Example Find the EAR of an investment with a
  return of 10 compounded continuously.
• EAR e.10 - 1 10.52

90
EAR WITH CONTINUOUS COMPOUNDING

• HIT .10
• HIT 2ND ex
• SUBTRACT 1
• ANSWER 10.52

91
AMORTIZING LOANS

• AMORTIZED LOAN A LOAN THAT IS PAID IN EQUAL
  PAYMENTS OVER EQUAL INCREMENTS OF TIME.
• EXAMPLE YOU BUY A HOUSE AND BORROW 100,000 AT
  A STATED ANNUAL RATE OF 12. YOU WILL REPAY THE
  LOAN BY MAKING EQUAL MONTHLY PAYMENTS FOR THE
  NEXT 30 YEARS

92
AMORTIZATION SCHEDULE

• A TABLE FOR AN AMORTIZED LOAN SHOWING
• 1. THE EQUAL MONTHLY PAYMENTS
• 2. THE PORTION OF THE PAYMENT GOING TO INTEREST
• 3. THE PORTION OF THE PAYMENT GOING TO PRINCIPAL
• 4. THE BALANCE REMAINING AT THE END OF THE PERIOD

93
SAMPLE AMORTIZATION SCHEDULE
LOAN 100,000 N 12 X 30 360 k
12 P/Y 12 PERIOD PAYMENT INTEREST
PRINCIPAL BAL 0

100,000 1
1,028.61 1,000.00 28.61
99,971.39 2 1,028.61
999.71 28.90
99,942.49 3 1,028.61
999.42 29.19
99,913.30 12 1,028.61
996.69 31.92
99,637.12 120 1,028.61
935.11 93.49
93,418.00 359 1,028.61
20.27 1008.34
1,018.43 360 1,028.61
10.18 1018.43 0