This document discusses time value of money concepts including future value, present value, rates of return, and amortization. It provides examples of cash flow timelines and formulas for calculating future and present value using a financial calculator or spreadsheet. It also covers the differences between nominal interest rates, periodic interest rates, and effective annual rates when interest is compounded more frequently than annually.
For full text article go to : https://www.educorporatebridge.com/financial-modeling/financial-modeling-technique/ This Financial Modeling Technique will help you to understand some important techniques like color coding, circular reference, compilation of historical data, things needs to be considered before making an assumption etc in order to make a financial model easy to understand.
time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
For full text article go to : https://www.educorporatebridge.com/financial-modeling/financial-modeling-technique/ This Financial Modeling Technique will help you to understand some important techniques like color coding, circular reference, compilation of historical data, things needs to be considered before making an assumption etc in order to make a financial model easy to understand.
time value of money
,
concept of time value of money
,
significance of time value of money
,
present value vs future value
,
solve for the present value
,
simple vs compound interest rate
,
nominal vs effective annual interest rates
,
future value of a lump sum
,
solve for the future value
,
present value of a lump sum
,
types of annuity
,
future value of an annuity
Investment Decision — Capital Budgeting Techniques — Pay Back Method — Accounting Rate Of Return — NPV — IRR — Discounted Pay Back Method — Capital Rationing — Risk Adjusted Techniques Of Capital Budgeting. — Capital Budgeting Practices
The Cash Flow Statement translates earnings in the Income Statement into cash inflows. Explained in detail above as a part of the topic “Financial accounting”, is brought to you by Welingkar’s Distance Learning Division.
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What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
BREAKING DOWN 'Time Value of Money - TVM'
Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value.
BREAKING DOWN 'Compound Interest'
Compound Interest Formula
Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.
Investment Decision — Capital Budgeting Techniques — Pay Back Method — Accounting Rate Of Return — NPV — IRR — Discounted Pay Back Method — Capital Rationing — Risk Adjusted Techniques Of Capital Budgeting. — Capital Budgeting Practices
The Cash Flow Statement translates earnings in the Income Statement into cash inflows. Explained in detail above as a part of the topic “Financial accounting”, is brought to you by Welingkar’s Distance Learning Division.
For more such innovative content on management studies, join WeSchool PGDM-DLP Program: http://bit.ly/SlideshareFaccounting
Join us on Facebook: http://www.facebook.com/welearnindia
Follow us on Twitter: https://twitter.com/WeLearnIndia
Read our latest blog at: http://welearnindia.wordpress.com
Subscribe to our Slideshare Channel: http://www.slideshare.net/welingkarDLP
What is the 'Time Value of Money - TVM'
The time value of money (TVM) is the idea that money available at the present time is worth more than the same amount in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. TVM is also referred to as present discounted value.
BREAKING DOWN 'Time Value of Money - TVM'
Money deposited in a savings account earns a certain interest rate. Rational investors prefer to receive money today rather than the same amount of money in the future because of money's potential to grow in value over a given period of time. Money earning an interest rate is said to be compounding in value.
BREAKING DOWN 'Compound Interest'
Compound Interest Formula
Compound interest is calculated by multiplying the principal amount by one plus the annual interest rate raised to the number of compound periods minus one.The total initial amount of the loan is then subtracted from the resulting value.
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Making Your IEP System Work for You: 5 Questions to Ask About Your IEP SystemAccelify
An effective IEP system should accommodate your workflow, not determine it. If you and your staff are bending over backward to make your IEP system work for you, it may not be doing its job. And with limited options on the market, of which many lack sufficient flexibility, it may seem like demanding that your current system do more or migrating from one IEP system to another, may not be worthwhile. But reevaluating your IEP system can be disruptive in a good way too. Demanding more from your IEP system can lead to better tools that help you and your staff more efficiently manage the IEP process and the data needed to manage compliance along the way.
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Time lines
Future value / Present value of lump sum
FV / PV of annuity
Perpetuities
Uneven CF stream
Compounding periods
Nominal / Effective / Periodic rates
Amortization
The time value of money is the concept that money available at the present time is worth more than the identical sum in the future due to its potential earning capacity. This core principle of finance holds that, provided money can earn interest, any amount of money is worth more the sooner it is received. Time Value of Money is also sometimes referred to as present discounted value.
0132994879/.DS_Store
__MACOSX/0132994879/._.DS_Store
0132994879/Appendix.pdf
A-1
Using a Calculator
As you prepare for a career in business, the ability to use a financial calculator is essential,
whether you are in the finance division or the marketing department. For most positions,
it will be assumed that you can use a calculator in making computations that at one time
were simply not possible without extensive time and effort. The following examples let us
see what is possible, but they represent only the beginning of using the calculator in finance.
With just a little time and effort, you will be surprised at how much you can do with
the calculator, such as calculating a stock’s beta, or determining the value of a bond on a
specific day given the exact date of maturity, or finding net present values and internal rates
of return, or calculating the standard deviation. The list is almost endless.
In demonstrating how calculators may make our work easier, we must first decide which
calculator to use. The options are numerous and largely depend on personal preference.
We have chosen the Texas Instruments BA II Plus and the Hewlett-Packard 10BII.
We will limit our discussion to the following issues:
I. Introductory Comments
II. An Important Starting Point
III. Calculating Values for:
A. Future value of $1
B. Present value of $1
C. Future value of an annuity of $1 for n periods
D. Present value of an annuity of $1 for n periods
IV. Calculating Present Values
V. Calculating Future Values (compound sum)
VI. Calculating the Number of Payments or Receipts
VII. Calculating the Payment Amount
VIII. Calculating the Interest Rate
IX. Bond Valuation
A. Computing the value of a bond
B. Calculating the yield to maturity of a bond
X. Computing the Net Present Value and Internal Rate of Return
A. Where future cash flows are equal amounts in each period (annuity)
B. Where future cash flows are unequal amounts in each period
I. Introductory Comments
In the examples that follow, you are told (1) which keystrokes to use, (2) the resulting ap-
pearance of the calculator display, and (3) a supporting explanation.
The keystrokes column tells you which keys to press. The keystrokes shown in a white
box tell you to use one of the calculator’s dedicated or “hard” keys. For example, if + /- is
shown in the keystrokes instruction column, press that key on the keyboard of the calcula-
tor. With the Texas Instruments BA II Plus, to use a function printed in a shaded box above
a dedicated key, always press the shaded key 2nd first, then the function key. The HP 10BII
has two shift keys, one purple (PRP) and one orange (ORG). To use the functions printed
in purple (stats) on the keypad, press the purple button first. To use the functions printed
in orange (shift) on the keypad, press the orange button first.
Appendix A
A-2 Appendix A
I I . A n I m p o r t A n t S t A r t I n g p o I n t - t e x A S I n S t r u m e n t ...
The Time Value of Money Future Value and Present Value .docxchristalgrieg
The Time Value of
Money: Future Value
and Present Value
Computations
"If I deposit $10,000 today, how much will I have for a down payment on a house in five years?"
"Will $2,000 saved a year give me enough money when I retire?"
"How much must I save today to have enough for my children's post-secondary education?"
As introduced in Chapter 1 and used to measure financial opportunity costs in other chapters,
the time value of money, more commonly referred to as interest, is the cost of money that is bor-
rowed or lent. Interest can be compared to rent, the cost of using an apartment or other item.
The time value of money is based on the fact that a dollar received today is worth more than a
dollar that will be received one year from today because the dollar received today can be saved
or invested and will be worth more than a dollar a year from today Similarly, a dollar that will
be received one year from today is currently worth less than a dollar today.
The time value of money has two major components: future value and present value. Future
value computations, which are also referred to as compounding, yield the amount to which a
current sum will increase based on a certain interest rate and period of time, Present value,
which is calculated through a process called discounting, is the current value of a future sum
based on a certain interest rate and period of time.
In future value problems, you are given an amount to save or invest and you calculate the
amount that will be available at some future date. With present value problems, you are given the
amount that will be available at some future date and you calculate the current value of that amount
Both future value and present value computations are based on basic interest rate calculations.
FINANCIAL CALCULATORS
Currently, financial calculators, with time value of money functions built in, are widely used to
calculate future value, present values, and annuities, For the following examples, we will use the
Texas Instruments BA II Plus financial calculator, which is recommended by the Canadian
Institute of Financial Planning.
When using the BA II Plus calculator to solve time value of money problems, you will be
working with the TVM keys that include:
CPT — Compute key used to initiate financial calculations once all values are inputted
— Number of periods
— Interest rate per period
— Present value
PMT — Amount of payment, used only for annuities
— Future value
Enter values for PV, PMT, and FV as negative if they represent cash outflows (e.g., investing
a sum of money) or as positive if they represent cash inflows (e.g., receiving the proceeds of an
investment). To convert a positive number to a negative number, enter the number and then
press the +/— key.
37
Part 1 PLANNING YOUR PERSONAL FINANCES
The examples that are shown in this chapter assume that interest is compounded
annually and that there is only one cash flow per p ...
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how to swap pi coins to foreign currency withdrawable.DOT TECH
As of my last update, Pi is still in the testing phase and is not tradable on any exchanges.
However, Pi Network has announced plans to launch its Testnet and Mainnet in the future, which may include listing Pi on exchanges.
The current method for selling pi coins involves exchanging them with a pi vendor who purchases pi coins for investment reasons.
If you want to sell your pi coins, reach out to a pi vendor and sell them to anyone looking to sell pi coins from any country around the globe.
Below is the contact information for my personal pi vendor.
Telegram: @Pi_vendor_247
Empowering the Unbanked: The Vital Role of NBFCs in Promoting Financial Inclu...Vighnesh Shashtri
In India, financial inclusion remains a critical challenge, with a significant portion of the population still unbanked. Non-Banking Financial Companies (NBFCs) have emerged as key players in bridging this gap by providing financial services to those often overlooked by traditional banking institutions. This article delves into how NBFCs are fostering financial inclusion and empowering the unbanked.
how can i use my minded pi coins I need some funds.DOT TECH
If you are interested in selling your pi coins, i have a verified pi merchant, who buys pi coins and resell them to exchanges looking forward to hold till mainnet launch.
Because the core team has announced that pi network will not be doing any pre-sale. The only way exchanges like huobi, bitmart and hotbit can get pi is by buying from miners.
Now a merchant stands in between these exchanges and the miners. As a link to make transactions smooth. Because right now in the enclosed mainnet you can't sell pi coins your self. You need the help of a merchant,
i will leave the telegram contact of my personal pi merchant below. 👇 I and my friends has traded more than 3000pi coins with him successfully.
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Currently pi network is not tradable on binance or any other exchange because we are still in the enclosed mainnet.
Right now the only way to sell pi coins is by trading with a verified merchant.
What is a pi merchant?
A pi merchant is someone verified by pi network team and allowed to barter pi coins for goods and services.
Since pi network is not doing any pre-sale The only way exchanges like binance/huobi or crypto whales can get pi is by buying from miners. And a merchant stands in between the exchanges and the miners.
I will leave the telegram contact of my personal pi merchant. I and my friends has traded more than 6000pi coins successfully
Tele-gram
@Pi_vendor_247
when will pi network coin be available on crypto exchange.DOT TECH
There is no set date for when Pi coins will enter the market.
However, the developers are working hard to get them released as soon as possible.
Once they are available, users will be able to exchange other cryptocurrencies for Pi coins on designated exchanges.
But for now the only way to sell your pi coins is through verified pi vendor.
Here is the telegram contact of my personal pi vendor
@Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 50$.
So if you are interested in selling your pi network coins at a high rate tho. Or you can't wait till the mainnet launch in 2026. You can easily trade your pi coins with a merchant.
A merchant is someone who buys pi coins from miners and resell them to Investors looking forward to hold massive quantities till mainnet launch.
I will leave the telegram contact of my personal pi vendor to trade with.
@Pi_vendor_247
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Introduction to Indian Financial System ()Avanish Goel
The financial system of a country is an important tool for economic development of the country, as it helps in creation of wealth by linking savings with investments.
It facilitates the flow of funds form the households (savers) to business firms (investors) to aid in wealth creation and development of both the parties
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
what is the best method to sell pi coins in 2024DOT TECH
The best way to sell your pi coins safely is trading with an exchange..but since pi is not launched in any exchange, and second option is through a VERIFIED pi merchant.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and pioneers and resell them to Investors looking forward to hold massive amounts before mainnet launch in 2026.
I will leave the telegram contact of my personal pi merchant to trade pi coins with.
@Pi_vendor_247
2. 2-2
Time lines show timing of cash flows.
CF0 CF1 CF3CF2
0 1 2 3
i%
Tick marks at ends of periods, so Time 0 is
today; Time 1 is the end of Period 1; or the
beginning of Period 2.
3. 2-3
Time line for a $100 lump sum due at
the end of Year 2.
100
0 1 2 Year
i%
4. 2-4
Time line for an ordinary annuity of
$100 for 3 years.
100 100100
0 1 2 3
i%
5. 2-5
Time line for uneven CFs: -$50 at t = 0
and $100, $75, and $50 at the end of
Years 1 through 3.
100 5075
0 1 2 3
i%
-50
6. 2-6
What’s the FV of an initial $100 after 3
years if i = 10%?
FV = ?
0 1 2 3
10%
Finding FVs (moving to the right
on a time line) is called compounding.
100
8. 2-8
After 3 years:
FV3 = FV2(1+i)=PV(1 + i)2
(1+i)
= PV(1+i)3
= $100(1.10)3
= $133.10.
In general,
FVn = PV(1 + i)n
.
9. 2-9
Three Ways to Find FVs
Solve the equation with a regular
calculator.
Use a financial calculator.
Use a spreadsheet.
10. 2-10
Financial calculator: HP10BII
Adjust display brightness: hold down
ON and push + or -.
Set number of decimal places to
display: Orange Shift key, then DISP
key (in orange), then desired decimal
places (e.g., 3).
To temporarily show all digits, hit
Orange Shift key, then DISP, then =
11. 2-11
HP10BII (Continued)
To permantly show all digits, hit
ORANGE shift, then DISP, then .
(period key)
Set decimal mode: Hit ORANGE shift,
then ./, key. Note: many non-US
countries reverse the US use of
decimals and commas when writing a
number.
12. 2-12
HP10BII: Set Time Value Parameters
To set END (for cash flows occuring
at the end of the year), hit ORANGE
shift key, then BEG/END.
To set 1 payment per period, hit 1,
then ORANGE shift key, then P/YR
13. 2-13
Financial calculators solve this
equation:
There are 4 variables. If 3 are
known, the calculator will solve
for the 4th.
.0
n
i1PVnFV =++
Financial Calculator Solution
14. 2-14
3 10 -100 0
N I/YR PV PMT FV
133.10
Here’s the setup to find FV:
Clearing automatically sets everything
to 0, but for safety enter PMT = 0.
Set: P/YR = 1, END.
INPUTS
OUTPUT
15. 2-15
Spreadsheet Solution
Use the FV function: see spreadsheet
in Ch 02 Mini Case.xls.
= FV(Rate, Nper, Pmt, PV)
= FV(0.10, 3, 0, -100) = 133.10
16. 2-16
10%
What’s the PV of $100 due in 3 years if
i = 10%?
Finding PVs is discounting, and it’s
the reverse of compounding.
100
0 1 2 3
PV = ?
17. 2-17
Solve FVn = PV(1 + i )n
for PV:
( )
PV =
FV
1+i
= FV
1
1+i
n
n n
n
( )
PV = $100
1
1.10
= $100 0.7513 = $75.13.
3
18. 2-18
Financial Calculator Solution
3 10 0 100
N I/YR PV PMT FV
-75.13
Either PV or FV must be negative. Here
PV = -75.13. Put in $75.13 today, take
out $100 after 3 years.
INPUTS
OUTPUT
26. 2-26
Ordinary Annuity
PMT PMTPMT
0 1 2 3
i%
PMT PMT
0 1 2 3
i%
PMT
Annuity Due
What’s the difference between an
ordinary annuity and an annuity due?
PV FV
27. 2-27
What’s the FV of a 3-year ordinary
annuity of $100 at 10%?
100 100100
0 1 2 3
10%
110
121
FV = 331
28. 2-28
FV Annuity Formula
The future value of an annuity with n
periods and an interest rate of i can
be found with the following formula:
.331
10.
100 =
−+
=
−+
=
0.10
1)0(1
i
1i)(1
PMT
3
n
29. 2-29
Financial calculators solve this
equation:
There are 5 variables. If 4 are
known, the calculator will solve
for the 5th.
.0
i
1ni)(1PMT
n
i1PVnFV =−++++
Financial Calculator Formula
for Annuities
30. 2-30
3 10 0 -100
331.00
N I/YR PV PMT FV
Financial Calculator Solution
Have payments but no lump sum PV,
so enter 0 for present value.
INPUTS
OUTPUT
32. 2-32
What’s the PV of this ordinary
annuity?
100 100100
0 1 2 3
10%
90.91
82.64
75.13
248.69 = PV
33. 2-33
PV Annuity Formula
The present value of an annuity with n
periods and an interest rate of i can
be found with the following formula:
69.248
10.
100 =
+
=
+
=
0.10
)0(1
1
1-
i
i)(1
1
1-
PMT
3
n
34. 2-34
Have payments but no lump sum FV,
so enter 0 for future value.
3 10 100 0
N I/YR PV PMT FV
-248.69
INPUTS
OUTPUT
Financial Calculator Solution
36. 2-36
Find the FV and PV if the
annuity were an annuity due.
10
0
10
0
0 1 2 3
10%
10
0
37. 2-37
PV and FV of Annuity Due
vs. Ordinary Annuity
PV of annuity due:
= (PV of ordinary annuity) (1+i)
= (248.69) (1+ 0.10) = 273.56
FV of annuity due:
= (FV of ordinary annuity) (1+i)
= (331.00) (1+ 0.10) = 364.1
38. 2-38
3 10 100 0
-273.55
N I/YR PV PMT FV
Switch from “End” to “Begin”.
Then enter variables to find PVA3 =
$273.55.
Then enter PV = 0 and press FV to find
FV = $364.10.
INPUTS
OUTPUT
39. 2-39
Excel Function for Annuities Due
Change the formula to:
=PV(10%,3,-100,0,1)
The fourth term, 0, tells the function
there are no other cash flows. The
fifth term tells the function that it is an
annuity due. A similar function gives
the future value of an annuity due:
=FV(10%,3,-100,0,1)
40. 2-40
What is the PV of this uneven cash
flow stream?
0
100
1
300
2
300
310%
-50
4
90.91
247.93
225.39
-34.15
530.08 = PV
41. 2-41
Financial calculator: HP10BII
Clear all: Orange Shift key, then C All
key (in orange).
Enter number, then hit the CFj key.
Repeat for all cash flows, in order.
To find NPV: Enter interest rate (I/YR).
Then Orange Shift key, then NPV key
(in orange).
42. 2-42
Financial calculator: HP10BII (more)
To see current cash flow in list, hit
RCL CFj CFj
To see previous CF, hit RCL CFj –
To see subseqent CF, hit RCL CFj +
To see CF 0-9, hit RCL CFj 1 (to see CF
1). To see CF 10-14, hit RCL CFj .
(period) 1 (to see CF 11).
43. 2-43
Input in “CFLO” register:
CF0 = 0
CF1 = 100
CF2 = 300
CF3 = 300
CF4 = -50
Enter I = 10%, then press NPV button
to get NPV = 530.09. (Here NPV = PV.)
45. 2-45
Nominal rate (iNom)
Stated in contracts, and quoted by banks
and brokers.
Not used in calculations or shown on time
lines
Periods per year (m) must be given.
Examples:
8%; Quarterly
8%, Daily interest (365 days)
46. 2-46
Periodic rate (iPer )
iPer = iNom/m, where m is number of
compounding periods per year. m = 4 for
quarterly, 12 for monthly, and 360 or 365
for daily compounding.
Used in calculations, shown on time lines.
Examples:
8% quarterly: iPer = 8%/4 = 2%.
8% daily (365): iPer = 8%/365 =
0.021918%.
47. 2-47
Will the FV of a lump sum be larger or
smaller if we compound more often,
holding the stated I% constant? Why?
LARGER! If compounding is more
frequent than once a year--for
example, semiannually, quarterly,
or daily--interest is earned on interest
more often.
48. 2-48
FV Formula with Different Compounding
Periods (e.g., $100 at a 12% nominal rate with
semiannual compounding for 5 years)
= $100(1.06)10
= $179.08.
FV = PV 1 .+
i
m
n
Nom
mn
FV = $100 1 +
0.12
2
5S
2x5
49. 2-49
FV of $100 at a 12% nominal rate for 5
years with different compounding
FV(Annual)= $100(1.12)5
= $176.23.
FV(Semiannual)= $100(1.06)10
=$179.08.
FV(Quarterly)= $100(1.03)20
= $180.61.
FV(Monthly)= $100(1.01)60
= $181.67.
FV(Daily) = $100(1+(0.12/365))(5x365)
= $182.19.
50. 2-50
Effective Annual Rate (EAR = EFF%)
The EAR is the annual rate which causes PV
to grow to the same FV as under multi-period
compounding Example: Invest $1 for one
year at 12%, semiannual:
FV = PV(1 + iNom/m)m
FV = $1 (1.06)2
= 1.1236.
EFF% = 12.36%, because $1 invested for one
year at 12% semiannual compounding would
grow to the same value as $1 invested for one
year at 12.36% annual compounding.
51. 2-51
An investment with monthly
payments is different from one
with quarterly payments. Must
put on EFF% basis to compare
rates of return. Use EFF% only
for comparisons.
Banks say “interest paid daily.”
Same as compounded daily.
52. 2-52
How do we find EFF% for a nominal
rate of 12%, compounded
semiannually?
EFF% = - 1(1 + )iNom
m
m
= - 1.0(1 + )0.12
2
2
= (1.06)2
- 1.0
= 0.1236 = 12.36%.
53. 2-53
Finding EFF with HP10BII
Type in nominal rate, then Orange Shift
key, then NOM% key (in orange).
Type in number of periods, then Orange
Shift key, then P/YR key (in orange).
To find effective rate, hit Orange Shift
key, then EFF% key (in orange).
55. 2-55
Can the effective rate ever be equal to
the nominal rate?
Yes, but only if annual compounding
is used, i.e., if m = 1.
If m > 1, EFF% will always be greater
than the nominal rate.
56. 2-56
When is each rate used?
iNom: Written into contracts, quoted
by banks and brokers. Not
used in calculations or shown
on time lines.
57. 2-57
iPer: Used in calculations, shown on
time lines.
If iNom has annual compounding,
then iPer = iNom/1 = iNom.
58. 2-58
(Used for calculations if and only if
dealing with annuities where
payments don’t match interest
compounding periods.)
EAR = EFF%: Used to compare
returns on investments
with different payments
per year.
61. 2-61
Step 2: Find interest charge for Year 1.
INTt = Beg balt (i)
INT1 = $1,000(0.10) = $100.
Step 3: Find repayment of principal in
Year 1.
Repmt = PMT - INT
= $402.11 - $100
= $302.11.
62. 2-62
Step 4: Find ending balance after
Year 1.
End bal = Beg bal - Repmt
= $1,000 - $302.11 = $697.89.
Repeat these steps for Years 2 and 3
to complete the amortization table.
63. 2-63
Interest declines. Tax implications.
BEG PRIN END
YR BAL PMT INT PMT BAL
1 $1,000 $402 $100 $302 $698
2 698 402 70 332 366
3 366 402 37 366 0
TOT 1,206.34 206.34 1,000
64. 2-64
$
0 1 2 3
402.11
Interest
302.11
Level payments. Interest declines because
outstanding balance declines. Lender earns
10% on loan outstanding, which is falling.
Principal Payments
65. 2-65
Amortization tables are widely
used--for home mortgages, auto
loans, business loans, retirement
plans, and so on. They are very
important!
Financial calculators (and
spreadsheets) are great for
setting up amortization tables.
66. 2-66
On January 1 you deposit $100 in an
account that pays a nominal interest
rate of 11.33463%, with daily
compounding (365 days).
How much will you have on October
1, or after 9 months (273 days)?
(Days given.)
69. 2-69
What’s the value at the end of Year 3 of
the following CF stream if the quoted
interest rate is 10%, compounded
semiannually?
0 1
100
2 3
5%
4 5 6 6-mos.
periods
100 100
70. 2-70
Payments occur annually, but
compounding occurs each 6
months.
So we can’t use normal annuity
valuation techniques.
72. 2-72
Could you find the FV with a
financial calculator?
Yes, by following these steps:
a. Find the EAR for the quoted rate:
2nd Method: Treat as an Annuity
EAR = (1 + )- 1 = 10.25%.
0.10
2
2
73. 2-73
3 10.25 0 -100INPUTS
OUTPUT
N I/YR PV FVPMT
331.80
b. Use EAR = 10.25% as the annual rate
in your calculator:
74. 2-74
What’s the PV of this stream?
0
100
1
5%
2 3
100 100
90.70
82.27
74.62
247.59
75. 2-75
You are offered a note which pays
$1,000 in 15 months (or 456 days)
for $850. You have $850 in a bank
which pays a 6.76649% nominal
rate, with 365 daily compounding,
which is a daily rate of 0.018538%
and an EAR of 7.0%. You plan to
leave the money in the bank if you
don’t buy the note. The note is
riskless.
Should you buy it?
76. 2-76
3 Ways to Solve:
1. Greatest future wealth: FV
2. Greatest wealth today: PV
3. Highest rate of return: Highest EFF%
iPer = 0.018538% per day.
1,000
0 365 456 days
-850
77. 2-77
1. Greatest Future Wealth
Find FV of $850 left in bank for
15 months and compare with
note’s FV = $1,000.
FVBank = $850(1.00018538)456
= $924.97 in bank.
Buy the note: $1,000 > $924.97.
78. 2-78
456 -850 0
924.97
INPUTS
OUTPUT
N I/YR PV FVPMT
Calculator Solution to FV:
iPer = iNom/m
= 6.76649%/365
= 0.018538% per day.
Enter iPer in one step.
79. 2-79
2. Greatest Present Wealth
Find PV of note, and compare
with its $850 cost:
PV = $1,000/(1.00018538)456
= $918.95.
80. 2-80
456 .018538 0 1000
-918.95
INPUTS
OUTPUT
N I/YR PV FVPMT
6.76649/365 =
PV of note is greater than its $850
cost, so buy the note. Raises your
wealth.
81. 2-81
Find the EFF% on note and
compare with 7.0% bank pays,
which is your opportunity cost of
capital:
FVn = PV(1 + i)n
$1,000 = $850(1 + i)456
Now we must solve for i.
3. Rate of Return
82. 2-82
456 -850 0 1000
0.035646%
per day
INPUTS
OUTPUT
N I/YR PV FVPMT
Convert % to decimal:
Decimal = 0.035646/100 = 0.00035646.
EAR = EFF% = (1.00035646)365
- 1
= 13.89%.