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1
TIME VALUE OF MONEY
FACULTY OF BUSINESS AND ACCOUNTANCY
Week 5
2
Based on positive time preference~ a ringgit today is worth more than a ringgit expected in the future
TVM tools are used to;
Calculate deposits required to accumulate a future sum
Amortize loans by calculating loan payments schedules
Determine interest or growth rates of money streams
Evaluate perpetuities
Find the required rate of return
3
Basic Concepts Time Lines
Future Values
Present Values
Perpetuities
Single Sum
Annuity
Nominal Rate Periodic Rate
Effective Annual Rate
Required Rate of Return
Compounding Periods
Amortization
Types of Interest Rates
4
TMV Solution Methods
1. Numerical – using regular calculator w/o financial functions
2. Interest Tables - given with the text book a. Present Value Interest Factor b. Present Value Interest Factor for Annuity c. Future Value Interest Factor d. Future Value Interest Factor for Annuity
3. Financial Calculator
4. Worksheet
5
Time Lines
Show the timing of cash flows.
Tick marks occur at the end of periods, so Time 0 is today; Time 1 is the end of the first period (year, month, etc.) or the beginning of the second period.
CF0 CF1 CF3CF2
Time 0 1 2 3
i%
End of period 2 & beginning
of period 3
6
Time line illustrations
100 100100
0 1 2 3i%
100
0 1 2
5%
RM100 lump sum due in 2 years
End of period 2PV
FV
3 year RM100 ordinary annuity (fixed pmts)
10%
7
100 50 75
0 1 2 3
i%
-50
Uneven cash flow stream
CF0 CF1CF2 CF3
8
8
Key Description
Clear all data
No of payment per year
No of year
Annual interest rate
Present value
Future value
(No keyed in) x (P/YR)
Begin End
Calculates amortization table
C ALL
P/YR
PV
FV
I/YR
N
xP/YR
BEG/END
AMORT
9
Future and Present Values
10
Future Value & Present Value
Future Value - Ending amount of your account at the end of n periods
Present Value – Beginning amount in your account
In determining the final value of a cash flow or series of cash flows, compound interest will be applied.
What is compound interest? Is it the same thing as simple interest?
The process of going from today’s values, or PV to future value is called compounding.
11
Simple interest;
105 110
2nd period; (Principal) [(2 x 0.05) + 1 ] = RM110 or, [100 (1.05) - 100] + 100(1.05) = RM110
0 1 2
5%
100
0 1 2
5%
Compounding interest;
100 105 110.25
2nd period; (Principal + interest)(1 + i) (RM100 + RM5) (1 + 0.05) = RM110.25
12
Future Value : One period case
Case 1: Given that a car dealer offers a car for RM20,000 in cash or RM25,000 on credit for one year. Given an annual i.r. of 10%, which payment is better for you & which for the car dealer?
0 1i% = ?
20,000 25,000
Given RM20,000 now, in 1 year at ir of 10%, the money deposited will be ?
20,000
0 110%
FV = ?
13
FV1 = PV + INT = PV + PV (i)
= PV ( 1 + i )
Numerical Solution (N/S) ;
FV1 = PV ( 1 + i ) = 20,000 ( 1 + 0.1) = RM22,000
Future Value Interest Factor for i & n (FVIFi,n)~ the future value of RM1 left on deposit for n periods at a rate of i percent per period
~ where ( 1 + i)n = FVIFi,n
Tabular Solution (T/B) ;
FV1 = PV (FVIFi,n) = 20,000 ( 1.1000) = RM22,000
1414
Find the FV of RM20,000 given an interest rate of 10% in one year.
Data Key
Clear all data
1No of payment
per year
1 No of year
10Annual interest
rate
20,000 Present value
22,000.00
C All
P/YR
PV
FV
I/YR
N
+ / -
15
Present Value : One period case
FV1 = PV ( 1 + i ) , so PV = FV1
(1 + i)
C2 : Given the annual ir of 10%, at what amount of cash would the car dealer be indifferent to receiving RM25,000 at time 1?
0 1
PV = ?
10%
25,000
16
nn,i )i1(
1)PVIF(
Numerical solution ;
PV = FV1 / (1 + i) = 25,000 = RM22,727.27 1 + 0.01
Tabular Solution ;
Present Value Interest Factor for i & n (PVIFi,n)~ the present value of RM1 due n periods in the future discounted at i percent per period
PV = FV (PVIFi,n) = 25,000 (0.9091) = RM 22,727.50
~ where;
17
Find the PV of RM25,000 given an interest rate of 10% in one year.
Data Key
Clear all data
1Payment per year
1
10Annual interest
rate
25,000
-22727.27273
C ALL
P/YR
FV
PV
I/YR
N
18
Future Value & Present Value : Multi – period case
Important terms;
Compound interest – interest earned on the principal & on the accumulated interest
Discount interest rate – the rate that will make the future value equivalent to the present value
Fair (Equilibrium) Value – the price at which investors are indifferent btw buying or selling a security
0 1 2
discounting
5%
compounding
19
The discount rate is often also referred to as the opportunity cost, the required return, and the cost of capital.
20
C3 : Find the FV o RM100 left for 3 years in an account paying 10 percent, annual compounding;
FV = ?
0 1 2 3
10%
100
FV1 = PV + INT = PV + PV (i)
= PV ( 1 + i )
FV2 = FV1 (1 + i) = PV ( 1 + i ) (1 + i) = PV (1 + i)2
FV3 = PV (1 + i)3
N/S;
FV3 = 100 (1.10)3 = 133.10
2121
Data Key
1
3
10
-100
133.10
C ALL
P/YR
PV
FV
I/YR
N
FVn = PV (1 + i)n = PV (FVIFi,n)
= 100 (1.10)3 = 100 (1.3310) = RM133.10
+/-
22
C4 : Find the PV of RM100 to be received in 3 years if the appropriate ir is 10 percent, compounded annually:
100
0 1 2 3
10%
PV = ?
PVn = FV (1 + i)n
PV3 = FV (1 + i)3
N/S;
PVn = FVn/ (1 + i)n = FVn 1 n = FVn(PVIFi,n) 1 + i
= 100 (1/1.10)3 = 100 (0.7513) = RM75.13
T/S;
23
Data Key
1
3
10
100
-75.13
C ALL
P/YR
FV
PV
I/YR
N
24
n (periods)
and
i (interest rate)
25
Solving for n in TVM problems
C5: How long will it take a firm’s sales to double, if sales are growing at a 15% rate?
0 15%n = ?n - 1
RM1 RM2
FVn = PV (1 + i)n
2 = 1 (1.15)n
2 = (1.15)n
FVn = PV (FVIFi,n)(FVIFi,n) = FV / PV = 2 / 1 = 2
T/S;
Look in FVIF Table for
(FVIF15%,n) = 2
n 5 periods
N/S;
26
0 15%n = ?n - 1
RM1 RM2
Financial Calculator Solution ;
Data Key
1
1
15
2
4.96
C ALL
P/YR
FV
PV
I/YR
N
+/-
27
Solving for interest rate
C6: What annual ir will cause RM100 to grow to RM125.97 in 3 years?
125.97
0 1 2 3
i = ?
100
T/S;
100 (1 + i) 100 (1 + i)2 100 (1 + i)3
100 (1 + i)3 = 125.97100 (FVIFi,3) = 125.97 FVIFi,3 = 1.2597
Look at Row 3 of FVIF Table.1.2597 is in the 8% column
28
Annuities & Perpetuities
29
Annuities
An annuity is a series of equal payments made at fixed intervals for a specific number of periods
Ordinary annuity - payments occur at the end of each period - eg. Students loan
Annuity due – payments are made at the beginning of each period - eg. Mthly rentals, insurance premiums
30
What is the difference between an ordinary annuity and an annuity due? Both are 3-yr annuities ( 3 pmts)
Ordinary Annuity
PMT PMTPMT
0 1 2 3i%
PMT PMT
0 1 2 3i%
PMT
Annuity Due
31
Future Value of an Ordinary Annuity
C7: What is the future value of an ordinary annuity of RM100 per period for 3 yrs if the ir is 10 percent, compounded annually?
Time line approach;
0 1 2 310%
100 100 100
110
121
331
100(1 + i)2
100(1 + i)+
Twice compounding
32
N/S; FVA3 = PMT (1 + i) + PMT (1 + i)1 + PMT (1 + i)2
= 100 (1) + 100 (1.10) + 100 (1.21) = RM331
T/S;FVAn = PMT (FVIFAi,n)FVA3 = 100 (FVIFA10%,3) = 100 (3.3100) = RM331
FC;
= 331.00
10 3-100
Make sure no BGN sign
PMT I/YR N FVP/YR
1
33
Future Value of an Annuity Due
C8: What is the future value of RM100 payments made at beginning of each year for 3 yrs in a saving account that pays 10 percent, compounded annually?
Time line approach;
0 1 2 310%
100 100 0
110
121
133.10100(1 + i)2
100(1 + i)+
Triple compounding
100
100 (1 + i)3
364.10
34
N/S; FVAD3 = PMT (1 + i)3 + PMT (1 + i)2 + PMT (1 + i)1 = 100 (1.331) + 100 (1.21) + 100 (1.10) = RM364.10
T/S;FVADn = FVA3 (1 + i) or = PMT (FVIFA10%,3) (1 + i) = 331 (1.10) = 100 (3.3100) (1.10) = RM364.10 = 364.10
FC;
= 364.10
10 3-100
Make sure BGN sign
P/YR PMT I/YR N
1
FV
BEG/END
35
Present Value of an Ordinary AnnuityC9: What is the PV of an annuity of RM100 per period for 3
years if the ir is 10 percent annually?
Time line approach;
0 1 2 310%
100 100
100 /(1 + i)2
100 / (1 + i)
Triple discounting
0
100 / (1 + i)3
90.91
82.64
75.13
248.68
+
100
36
Present Value of an Annuity Due
C10: How much lump sum today to make it equivalent with a 3 year annuity paying RM100 at beginning of each year?
Time line approach;
0 1 2 310%
100 100
100 /(1 + i)2
100 / (1 + i)
Double discounting
100
90.91
82.64
273.55
+
Make sure BGN sign
37
An annuity due will always be greater than
an otherwise equivalent ordinary annuity
because interest will compound for an
additional period.
38
Perpetuities
- is a stream of equal payments expected to continue
forever- a type of annuity
PV (Perpetuity) = payment = PMT interest rate i
the current price
39
C11: A perpetual bond promised to pay RM100 per year in perpetuity. What would the bond’s worth today if the opportunity cost, or discount rate was 5 percent
PV (Perpetuity) = RM100 = RM2000 0.05
As the interest rate increases, the perpetuity’s value will drop.
When ir = 10%;
PVp = 100 = RM1000 0.1
40
Uneven Cash Flow Stream
Payment (PMT) - equal cash flows at regular intervals
Cash flow (CF) - uneven cash flows
Examples of uneven cash flows;
- common stock’s dividend - returns from fixed asset investments ~ production income ~ rentals
41
Present Value of an Uneven Cash Flow Stream
C12: Find PV of the following cash flows stream, discounted at 10%
0 1 2 3 410%
0 100 300 300 -50
PV = CF0 1 0 + CF1 1 1 + CF2 1 2
1 + i 1 + i 1 + i
+ CF3 1 3 + CF4 1 4 1 + i 1 + i
CF0 CF1 CF2 CF3 CF4
42
For cash flow calculation ;
Key
Clear all
No of periods per year
Cash flow j
No of consecutive times CFj occurs
Internal rate of return per year
Net present value
C ALL
P/YR
Nj
CFj
IRR/YR
NPV
43
Key
0
100
300
300
50
10
530.09
C ALL
I/YR
CFj
NPV
CFj
CFj
CFj
+/-
Key
0
100
300
2
50
10
530.09
C ALL
I/YR
CFj
NPV
CFj
CFj
Nj
+/-CFj CFj
44
0 1 2 3 4 510%
0 100 50 200 200 200
C13: Find the PV of the following c/f discounted at 10%
497.38 200 (PVIFA10%,3)= 200 (2.4869)
100(1/1 + i)1
50(1/1 + i)2
497.38(1/1 + i)2 or
200 (PVIFA10%,3) or 200 (1/1 + i)3
200 (PVIFA10%,4) or 200 (1/1 + i)4
200 (PVIFA10%,5) or 200 (1/1 + i)5
90.91
41.32
411.03
543.26
150.26
136.60
124.18
45
Future Value of an Uneven Cash Flow Stream
C14: Find FV of the following cash flows stream,compounded at 10%
0 1 2 3 4 510%
0 100 50 200 200 200
FV = CF5 (1 + i)0 + CF4 (1 + i)1 + CF3 (1 + i)2
+ CF2 (1 + i)3 + CF1 (1 + i)
4 + CF0 (1 + i)5
CF0 CF1 CF2 CF3 CF4 CF5
46
0 1 2 3 4 510%
0 100 50 200 200 200
420 ( 1 + i)
200 (FVIFA10%,2) = 200 (2.1)
200 (1 + i)2
200 (1 + i)
50 (1 + i)3 = 50 (1.331)
100 (1 + i)4 = 100 (1.4641)
220
242
66.55
146.41NFV = 874.96
462
462
47
0 1 2 3 4 510%
0 100 50 200 200 200
Data Key
1
0
100
50
200
3
C ALL
P/YR
I/YR
CFj
CF0 CF1 CF2 CF3 CF4 CF5
NFV=?
Data Key
10
543.28
5
0
847.93
CFj
Nj
CFj
NPV
N
PMT
FVCFj
Using formula; NFV = NPV ( 1 + i)n
= 543.26 (1 + 0.1)5
= 874.93
Different Compounding Periods
- annually / semiannually / quarterly / monthly / daily compounding
- the quoted interest rate is normally the annual one.
- If bank promised 10% annual interest rate semiannually
what does it means ? ~ interest will be added each 6 months but will the interest be 10% as quoted or more/less?
Say that you want to deposit your money in the bank which offer you the highest return. As you shopped around, you come up with these rates:
Bank A : 15 percent, compounded daily
Bank B : 15.5 percent, compounded quarterly
Bank C : 16 percent, compounded annually
Which one has the best rates for deposits?
C15: A bank declares that it pays a 6% annual ir semiannually & you want to deposit RM 100. What is FV at the end of 3rd year?
P/YR 1
PV (-)100
n 3
I% 6
FV 119.1
P/YR 1 2
PV (-)100 (-)100
N 6 6
I% 6/2 6
FV 119.41
119.41
0 1 2 36%
Annual compounding
Semiannual compounding0 1 2 3 4 5 6i%
FV3 = PV (1 + i)3
= 100 (1 + 0.06)3 = RM119.10
-100 FV = ?
-100 FV = ?
FV6 = PV (1 + i)6
= 100 (1 + 0.03)6
= RM119.41
i% = 6% /2 = 3%
n = 3 x 2 = 6
Different compounding periods are used for different types of investment
In order to compare securities with different compounding periods, need to put them on a common basis.
Types of interest rates; Nominal or quoted interest rates
Annual percentage rates (APR)
Effective annual rates (EAR)
1. Nominal or Quoted interest rates , inom
Is the contracted, or stated, or declared ir.
The rate which is given by the bank or issuer.
Annual Percentage Rate (APR)
The interest rate charged per period multiplied by the number of periods per year.
C16: If a bank is charging 1.2% per month on car loans, what is the APR?
APR = 1.2% x 12 = 14.4%
It is the nominal rates for loan that some government requires the bank to display to customers.
Periodic rate is the nominal rate at each period; where m is the no of compounding periods per year
Eg: 6% compounded quarterly. periodic rate, iper = inom / m = 6% / 4 = 1.5%
Periodic Rate
mi
i nomper
So periodic rate is the rate charged by a lender or paid by a borrower in each period.
C17: A bank charges 18% annual interest rates monthly on credit card loans, what is the periodic rate?
iper = inom / m = 18% / 12 = 1.5%
Bank will charge 1.5% of interest monthly or per month
So if we delayed paying our credit card debt for a year, will the debt be the same as we take a loan of the same amount at 18% annual interest?
Notice that iper is the rate that is shown on time lines and used in certain calculations, not the annual rate.
C18: How much would you have at the end of the 2nd year when you make RM100 deposit in an account that pays 12% interest rate semiannually.
0 1/2 1 1/2 2 (x2) = N
6%
-100 FV = ?
For calculation of FV given only PV, must use this rate not the annual rate given in this case. AND maintain P/YR = 1.
2. Effective Annual Rates (EAR) or (EFF)
The rate which would produce the same ending (future) value if annual compounding has been used. ~ (the interest rate expressed as if it were compounded once per year)
0 1 2 36%
Annual compounding
Semiannual compounding
0 1 2 3 4 5 63%
-100 119.41
-100 119.10
0 3i = ?
-100 119.41
EAR ;The annual rate that produces the same FV as if we had compounded at a given periodic rate m times per year
An investor would be indifferent between an investment offering a 10.25% annual return and one offering a 10% annual return, compounded semiannually.
Why?
C19: EFF% or EAR for 10% semiannual investment.
%EFF
10.25%
12
0.101
1mi
1 EAR or EFF%
2
mnom
C20: What is the FV of RM100 compounded semiannually for 3 years if inom = 10%? Would it be different if it were compounded quarterly?
Quarterly compounding
Semiannual compounding
0 1 2 3 5%
-100 FV = ?
0 1 2 3
-100 FV = ?
2.5%
134.01
134.49
FVn = PV 1 + inom mn
m FV3 = 100 1 + 0.1 2(3)
2 = 100(1.05)6
= 134.01
EAR = ( 1 + inom / m )m - 1
= ( 1 + 0.10 / 2 )2 – 1
= 10.25%
Semiannual compounding
Quarterly compoundingFVn = PV 1 + inom mn
m FV3 = 100 1 + 0.1 4(3)
4 = 100(1.025)12
= 134.49
EAR = ( 1 + inom / m )m - 1
= ( 1 + 0.10 / 4 )4 – 1
= 10.38%
F/C ;
Given annual i.r. of 10%, compounded semiannually;
10.25
To find APR, given the EAR of 10.25%;
10.00
The APR formula;
APR = 1 + EFF 1/m - 1 x m x 100 100
NOM%10
2 P/YR
EFF% EARNOM%
P/YR
EFF%10.25
2
Compounding More Frequently than Annually
• Compounding more frequently than once a year results in a higher effective interest rate because you are earning on interest on interest more frequently.
• As a result, the effective interest rate is greater than the nominal (annual) interest rate.
• Furthermore, the effective rate of interest will increase the more frequently interest is compounded.
Nominal & Effective Rates
The nominal interest rate is the stated or contractual
rate of interest charged by a lender or promised by a
borrower.
The effective interest rate is the rate actually paid or
earned.
The effective rate > nominal rate whenever
compounding occurs more than once per yearEAR > inom
EAR = inom = iper
If compounding occurs only once a year, then;
Nominal & Effective Rates
C21: What is the effective rate of interest on your credit card if the nominal rate is 18% per year, compounded monthly?
EAR = (1 + .18/12) 12 -1
EAR = 19.56%
Why is it important to consider effective rates of return?
An investment with monthly payments is different from one with quarterly payments. Must put each return on an EFF% basis to compare rates of return. Must use EFF% for comparisons. See the following values of EFF% rates at various compounding levels.
EARANNUAL 10.00% EARQUARTERLY 10.38% EARMONTHLY 10.47% EARDAILY (365)
10.52%
Fractional Time Periods
Before, payments only occur at beginning or end of periods.
What if, payments occur at some date within a period?
0 1st 2nd month 20th day month
1%
-100 FV = ?
C22: Deposits RM100 in a bank that pays 12% ir compounded monthly. How much the amount will be then in 1 month and 20 days?
N/S;
FVn = PV (1 + i)n
= PV (1 + i)1+ 20/30
= 100(1 + 0.1)1.67
= RM101.68
F/C ;
N 20÷30+1
I/YR 1
PV (-)100
P/YR 1
FV 101.67
If use 360-day year;
iper = 0.12 /360 = 0.00033333 per day
No of days deposited; = 50 days
FVn = PV (1 + iper)n
= 100 ( 1.0003333)50
= RM 101.68
Note of Caution;
Rule 1: Money saved/deposited/invested should be in negative sign. Money withdrawn/received should be in positive sign.
C23: RM1000 is deposited today for a semiannual payment of RM300 for 3 years. Given an interest rate of 10% semiannually, how much would be left in the account in 3 years time?
0 1 2 3 5%
-1000 300 300 300 300 300 300 FV = ?
Rule 2 : If there is only PV & no PMT, either;a. If use periodic ir, keep P/YR = 1. b. If use nominal rate, change P/YR
accordingly. C24: RM1000 is deposited today. Given an interest rate of 10%
semiannually, how much would be in the account in 3 years time?
0 1 2 3 5%
-100 FV = ?
N 3x2 = 6
I/YR 10÷2 = 5
PV (-)100
PMT 0
P/YR 1
FV 134.01
N 3x2 = 6
I/YR 10
PV (-)100
PMT 0
P/YR 2
FV 134.01
Rule 3: For case with PMT or PMT and PV, N = no of payment made, I/YR = annual interest rate, P/YR = no of payments made per year.
0 1 2 3 8%
-100 -150 -150 -150 -150 -150 -150 FV = ?
C25: Interest is 8% compounded quarterly. Initial deposit is RM100, and regular payments of RM150 will be made every semiannually.
2 P/YR
3x2 = 6
N
8.08 I/YR
(-)100 PV
(-)150 PMT
1122.77
FV
8 NOM%
4 P/YR
8.24 I/YR
8.24 EFF%
2 P/YR
8.08 NOM%
C26: Someone offers to sell you a note calling for the pmt of RM1000, 15 months from today for RM850. You have RM850 in the bank, which pays a 7% nominal rate with daily compounding. Should you buy the note or leave your money in the bank.
An Example of Everything
0 456 days
-850 1,000
iper = 7%/365 = 0.0192%
How to solve this? Have to compare both investments on similar grounds;
Fvnote vs. FVbank PVnote vs. PVbank EARnote vs. EARbank
Fvnote vs. Fvbank
Bank : FV = 850 (1.000192)456 = 927.67Note : FV = 1,000 Buy note (more value in future)
PVnote vs. Pvbank
Bank : PV = RM850Note : PV = 1,000 (1.000192)-456 = 916.27 Buy note (more value now)
EARnote vs. EARbank
Bank : iper = 0.0192%Note : 1,000 = 850 (1 + i)456, solving i = 0.0356% Buy note (higher iper means higher EAR)
C27: Cost of note = RM850 PMT = RM190 quarterly for 5 quarters inom = 7% compounded daily Is this a good investment?
0 91 182 274 366 456 days
-850 190 190 190 190 190
iper for bank = 7% / 365 = 0.0192%
PVAnote = 190 (1.000192)-91 + 190 (1.000192)-182 + … + 190 (1.000192)-456
= 901.68PVApocket = 850 Buy note (more value now)
EARnote ; finding iper;
inom = (iper) (m) = (3.83) (4) = 15.3%
So for daily rate = inom / 365 = 0.0419% Buy note coz iper,note > iper, bank = 0.0192%
-850 CFj
190 CFj
5 Nj
IRR 3.82586
Quarterly iper
Loan Types
1. Pure Discount Loans - the borrower receives money today & repays a single sum at some time in the future - eg. A 1-year, 10% RM100 pure discount loan, would require the borrower to repay RM110 in one year.
2. Interest-Only Loans - a loan that has a repayment plan that calls for the borrower to pay interest each period & repay the entire principal (original loan amount) at some point in the future - eg. With a 3-year, 10%, interest-only loan of RM1000, the borrower would pay RM1000(0.1) = 100 in interest at the end of 1st & 2nd years. At the end of 3rd year, the borrower would return the principal along with RM100 in interest for that year.
3. Amortized Loans
- a loan that is repaid in equal payments over its life.- eg. Car & home loans
C28: Say, borrow RM1,000 at 10% interest and have to pay equally at the end of each of the next 3 years.
0 1 2 3
-1,000 PMT PMT PMT10%
T/S ;
PVAn = PMT (PVIFAi,n)1,000 = PMT(PVIFA10%,3) PMT = 1,000 / (2.4869) = RM402.11
F/C ; 3 N
10 I/YR
-1000 PV
0 FV
PMT 402.11
Constructing an amortization table:Repeat steps 1 – 4 until end of loan
Interest paid declines with each payment as the balance declines.
Year Beginning Balance
(1)
PMT(2)
Interest(3)
PrincipRepmt
(4)
EndBalance
1 RM1,000 RM402 RM100 RM302 RM698
2 698 402 70 332 366
3 366 402 37 366 0
Total 1,206.34 206.34 1,000 -
PVn(1 + i)(2) – (3) (1) – (4)
77
1 P/YR
3 N
10 I/YR
-1000 PV
0 FV
PMT 402.11
1 INPUT
AMORT 1-1
= 302.11 PRIN
= 100.00 INT
= -697.89 BAL
1 INPUT 2
AMORT 1-2
= 634.43 PRIN
= 169.79 INT
= -365.57 BAL