The document discusses time value of money concepts including present value and future value. It explains that money received today is worth more than the same amount in the future due to factors like risk, inflation, and investment opportunities. It provides formulas for simple and compound interest as well as future and present value calculations. Examples are given to demonstrate compound interest, rule of 72, annuities, and amortizing a loan over time.
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.
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
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.
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
this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
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
this is a lecture on time value of money which explains the topic time value of money in a very easy and simple way... it also explains some examples on the topic... plus definition of rate of return, real rate of return, inflation premium, nominal interest rate,market risk, maturity risk,liquidity risk,and default risk,
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
CFA LEVEL 1- Time Value of Money_compressed (1).pdfAlison Tutors
This document focuses on End of Chapter questions and commonly asked questions under Quantitative methods (Time Value of Money ) . The mainly asked questions include :
-calculation and interpretation of Future Value and Present Value of a single sum of money , an ordinary annuity, annuity due, a perpetuity (PV only) and a series of unequal cash flows.
-demonstration of the use of timelines in modeling and solving time value of money
This is a very interesting topic!
Present value: The current worth of a future sum of money or stream of cash flows, given a specified rate of return. Future cash flows are "discounted" at the discount rate; the higher the discount rate, the lower the present value of the future cash flows. Determining the appropriate discount rate is the key to valuing future cash flows properly, whether they be earnings or obligations.[2]
Present value of an annuity: An annuity is a series of equal payments or receipts that occur at evenly spaced intervals. Leases and rental payments are examples. The payments or receipts occur at the end of each period for an ordinary annuity while they occur at the beginning of each period for an annuity due.[3]
Present value of a perpetuity is an infinite and constant stream of identical cash flows.[4]
Compound interest (or compounding interest) is interest calculated on the initial principal and also on the accumulated interest of previous periods of a deposit or loan. Thought to have originated in 17th-century Italy, compound interest can be thought of as “interest on interest,” and will make a sum grow at a faster rate than simple interest, which is calculated only on the principal amount. The rate at which compound interest accrues depends on the frequency of compounding; the higher the number of compounding periods, the greater the compound interest. Thus, the amount of compound interest accrued on $100 compounded at 10% annually will be lower than that on $100 compounded at 5% semi-annually over the same time period.
Basic Time Value of Money Formula and Example
Depending on the exact situation in question, the TVM formula may change slightly. For example, in the case of annuity or perpetuity payments, the generalized formula has additional or less factors. But in general, the most fundamental TVM formula takes into account the following variables:
FV = Future value of money
PV = Present value of money
i = interest rate
n = number of compounding periods per year
t = number of years
Based on these variables, the formula for TVM is:
FV = PV x (1 + (i / n)) ^ (n x t)
For example, assume a sum of $10,000 is invested for one year at 10% interest. The future value of that money is:
FV = $10,000 x (1 + (10% / 1) ^ (1 x 1) = $11,000
The formula can also be rearranged to find the value of the future sum in present day dollars. For example, the value of $5,000 one year from today, compounded at 7% interest, is:
PV = $5,000 / (1 + (7% / 1) ^ (1 x 1) = $4,673
What website can I sell pi coins securely.DOT TECH
Currently there are no website or exchange that allow buying or selling of pi coins..
But you can still easily sell pi coins, by reselling it to exchanges/crypto whales interested in holding thousands of pi coins before the mainnet launch.
Who is a pi merchant?
A pi merchant is someone who buys pi coins from miners and resell to these crypto whales and holders of pi..
This is because pi network is not doing any pre-sale. The only way exchanges can get pi is by buying from miners and pi merchants stands in between the miners and the exchanges.
How can I sell my pi coins?
Selling pi coins is really easy, but first you need to migrate to mainnet wallet before you can do that. I will leave the telegram contact of my personal pi merchant to trade with.
Tele-gram.
@Pi_vendor_247
The secret way to sell pi coins effortlessly.DOT TECH
Well as we all know pi isn't launched yet. But you can still sell your pi coins effortlessly because some whales in China are interested in holding massive pi coins. And they are willing to pay good money for it. If you are interested in selling I will leave a contact for you. Just telegram this number below. I sold about 3000 pi coins to him and he paid me immediately.
Telegram: @Pi_vendor_247
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 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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how can I sell my pi coins for cash in a pi APPDOT TECH
You can't sell your pi coins in the pi network app. because it is not listed yet on any exchange.
The only way you can sell is by trading your pi coins with an investor (a person looking forward to hold massive amounts of pi coins before mainnet launch) .
You don't need to meet the investor directly all the trades are done with a pi vendor/merchant (a person that buys the pi coins from miners and resell it to investors)
I Will leave The telegram contact of my personal pi vendor, if you are finding a legitimate one.
@Pi_vendor_247
#pi network
#pi coins
#money
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
USDA Loans in California: A Comprehensive Overview.pptxmarketing367770
USDA Loans in California: A Comprehensive Overview
If you're dreaming of owning a home in California's rural or suburban areas, a USDA loan might be the perfect solution. The U.S. Department of Agriculture (USDA) offers these loans to help low-to-moderate-income individuals and families achieve homeownership.
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USDA loans are an excellent option for those looking to buy a home in California's rural and suburban areas. With no down payment and flexible requirements, these loans make homeownership more attainable for many families. Explore your eligibility today and take the first step toward owning your dream home.
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Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
Turin Startup Ecosystem 2024 - Ricerca sulle Startup e il Sistema dell'Innov...Quotidiano Piemontese
Turin Startup Ecosystem 2024
Una ricerca de il Club degli Investitori, in collaborazione con ToTeM Torino Tech Map e con il supporto della ESCP Business School e di Growth Capital
If you are looking for a pi coin investor. Then look no further because I have the right one he is a pi vendor (he buy and resell to whales in China). I met him on a crypto conference and ever since I and my friends have sold more than 10k pi coins to him And he bought all and still want more. I will drop his telegram handle below just send him a message.
@Pi_vendor_247
how can I sell pi coins after successfully completing KYCDOT TECH
Pi coins is not launched yet in any exchange 💱 this means it's not swappable, the current pi displaying on coin market cap is the iou version of pi. And you can learn all about that on my previous post.
RIGHT NOW THE ONLY WAY you can sell pi coins is through verified pi merchants. A pi merchant is someone who buys pi coins and resell them to exchanges and crypto whales. Looking forward to hold massive quantities of pi coins before the mainnet launch.
This is because pi network is not doing any pre-sale or ico offerings, the only way to get my coins is from buying from miners. So a merchant facilitates the transactions between the miners and these exchanges holding pi.
I and my friends has sold more than 6000 pi coins successfully with this method. I will be happy to share the contact of my personal pi merchant. The one i trade with, if you have your own merchant you can trade with them. For those who are new.
Message: @Pi_vendor_247 on telegram.
I wouldn't advise you selling all percentage of the pi coins. Leave at least a before so its a win win during open mainnet. Have a nice day pioneers ♥️
#kyc #mainnet #picoins #pi #sellpi #piwallet
#pinetwork
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
Falcon stands out as a top-tier P2P Invoice Discounting platform in India, bridging esteemed blue-chip companies and eager investors. Our goal is to transform the investment landscape in India by establishing a comprehensive destination for borrowers and investors with diverse profiles and needs, all while minimizing risk. What sets Falcon apart is the elimination of intermediaries such as commercial banks and depository institutions, allowing investors to enjoy higher yields.
3. The Core Question of
Finance
Congratulations!!!
You have won a cash prize!
There are two optional payment
schedules:
A - receive $100,000 now
B - receive $100,000 in five years.
Which option would you choose?
3
4. Time Value of Money
Concept
In simple terms
the concept
implies that money today
is always better than
money tomorrow.
4
5. Why Time Value of Money
Exists?
Risk and Uncertainty-future always involves some risk, especially in
respect to cash inflows of company as they are highly uncontrollable;
Inflation-in an inflationary economy a dollar today has always more
purchasing power in compared to a dollar some point in future;
Consumption Preference- individuals generally prefer current
consumption to a future one;
Investment Opportunities-an investor can profitably use money received
today by investing it immediately;
5
6. Allows investors to adjust cash
flows for the passage of time;
It’s an integral part of Capital
Budgeting Processes;
Applied in present and future
value calculations;
6
10. SI = P0(i)(n)
= $1,000(.07)(2)
= $140$140
Simple Interest Example
Assume that you deposit $1,000 in an
account earning 7% simple interest for 2
years. What is the accumulated interest at
the end of the 2nd year?
10
11. Compound Interest
Yields higher return for
investors or deposit
holders;
Cumbersome for
borrowers;
Makes borrowers to be
more adhere to their
payment schedule,for
example.credit cards;
11
12. Assume that you deposit $1,000$1,000 at a
compound interest rate of 7% for 22
yearsyears.
Compound Interest
Example
0 1 22
$1,000$1,000
FVFV22
7%
12
13. At the end of first year
PP00 (1+i)1
= $1,000x$1,000x (1.07)
= $1,070$1,070
Compound Interest
You earned $70 interest on your $1,000
deposit over the first year.
This is the same amount of interest you
would earn under simple interest.
Compound Interest
Example
13
14. At the end of first yearAt the end of first year = $1,000$1,000 (1.07)
= $1,070$1,070
At the end of second yearAt the end of second year = 1070 (1+i)1
1070x(1.07)
$1,144.90$1,144.90
You earned an EXTRA $4.90$4.90 in Year 2 with
compound over simple interest.
Compound Interest
Example(cont.)
14
17. Future Value
The value at some future time of a present
amount of money, or a series of payments
evaluated at a given interest rate;
The interest earned on the initial principal
amount becomes a part of the principal at
the end of the compounding period;
17
18. Future Value Example
Problem
Suppose you invest $1000 for three years in a saving account that pays 10 %
interest per year. If you let your interest income be reinvested, your investment
will grow as follows:
First year : Principal at the beginning $1000
Interest for the year ($1,000 × 0.10) $100
Principal at the end $1,100
Second year : Principal at the beginning $1,100
Interest for the year ($1,100 × 0.10) $110
Principal at the end $1,210
Third year : Principal at the beginning $1,210
Interest for the year ($1210 × 0.10) $121
Principal at the end $1,331
18
19. FormulaFormula
FV = P0(1+i)n
FV: Future Value
P0: Deposit today (t=0)
i: Interest Rate per Period
n: Number of Time Periods
In the previous example
FV=1000(1+0.1)3
=1,331
19
20. Double Your Money!
We will use
the““Rule-of-72Rule-of-72””
Quick! How long
does it take to
double $5,000 at a
compound rate of
12% per year
(approx.)?
20
21. Approx. Years to Double = 7272 / i%
7272 / 12% = 6 Years6 Years
[Actual Time is 6.12 Years]
The “Rule-of-72”
Quick! How long does it take to
double $5,000 at a compound rate
of 12% per year (approx.)?
21
22. Present Value
Which one would you prefer assuming that
the rate is 8%?
a)$1000 today or,
b)$2000 10 years later?
22
To answer this question we have to
express $2000 in today’s money.
PV=FV/(1+i)n
$926=2000/(1+0.8)10
23. Types of Annuities
• Ordinary AnnuityOrdinary Annuity: Payments or receipts
occur at the end of each period(coupon);
• Annuity DueAnnuity Due: Payments or receipts occur at
the beginning of each period(rent);
An AnnuityAn Annuity represents a series of equal
payments (or receipts) occurring over a
specified number of equidistant periods.
23
24. Parts of an Annuity
0 1 2 3
$100 $100 $100
(Ordinary Annuity)
EndEnd of
Period 1
EndEnd of
Period 2
Today
EqualEqual Cash Flows
Each 1 Period Apart
EndEnd of
Period 3
24
25. Parts of an Annuity
0 1 2 3
$100 $100 $100
(Annuity Due)
BeginningBeginning of
Period 1
BeginningBeginning of
Period 2
Today
EqualEqual Cash Flows
Each 1 Period Apart
BeginningBeginning of
Period 3
25
26. FVAFVA33 = $1,000(1.07)2
+
$1,000(1.07)1
+ $1,000(1.07)0
= $1,145 + $1,070 + $1,000
= $3,215 or R(FVIFA$3,215 or R(FVIFAi,ni,n))
Example of an
Ordinary Annuity -- FVA
$1,000 $1,000 $1,000
0 1 2 33 4
$3,215 = FVA$3,215 = FVA33
7%
$1,070
$1,145
Cash flows occur at the end of the period
26
27. PVAPVA33 = $1,000/(1.07)1
+
$1,000/(1.07)2
+
$1,000/(1.07)3
= $934.58 + $873.44 + $816.30
= $2,624.32 or R(PVIFA$2,624.32 or R(PVIFAi,ni,n))
Example of an
Ordinary Annuity -- PVA
$1,000 $1,000 $1,000
0 1 2 33 4
$2,624.32 = PVA$2,624.32 = PVA33
7%
$934.58
$873.44
$816.30
Cash flows occur at the end of the period
27
28. FVADFVAD33 = $1,000(1.07)3
+
$1,000(1.07)2
+ $1,000(1.07)1
= $1,225 + $1,145 + $1,070
= $3,440 or R(FVIFA$3,440 or R(FVIFAi,ni,n)(1+i))(1+i)
Example of an
Annuity Due -- FVAD
$1,000 $1,000 $1,000 $1,070
0 1 2 33 4
$3,440 = FVAD$3,440 = FVAD33
7%
$1,225
$1,145
Cash flows occur at the beginning of the period
28
29. PVADPVADnn = $1,000/(1.07)0
+ $1,000/(1.07)1
+
$1,000/(1.07)2
= $2,808.02$2,808.02
oror R(PVIFAR(PVIFA’,n-1’,n-1+1)+1)
Example of an
Annuity Due -- PVAD
$1,000.00 $1,000 $1,000
0 1 2 33 4
$2,808.02$2,808.02 = PVADPVADnn
7%
$ 934.58
$ 873.44
Cash flows occur at the beginning of the period
29
30. Julie Miller will receive the set of cash
flows below. What is the Present ValuePresent Value at
a discount rate of 10%10%.
Mixed Flows Example
0 1 2 3 4 55
$600 $600 $400 $400 $100$600 $600 $400 $400 $100
PVPV00
10%10%
30
31. How To Solve
1 2 3 4 55
$600 $600 $400 $400 $100$600 $600 $400 $400 $100
10%
$545.45$545.45
$495.87$495.87
$300.53$300.53
$273.21$273.21
$ 62.09$ 62.09
$1677.15$1677.15 == PVPV00 of the Mixed Flowof the Mixed Flow 31
32. The actual rate of interest earned (paid)
after adjusting the nominal rate for
factors such as the number of
compounding periods per year.
(1 + [ i / m ] )m
- 1
Effective Annual
Interest Rate
32
33. Basket Wonders (BW) has a $1,000 CD at
the bank. The interest rate is 6%
compounded quarterly for 1 year. What
is the Effective Annual Interest Rate
(EAREAR)?
EAREAR = ( 1 + 6% / 4 )4
- 1
= 1.0614 - 1 = .0614 or 6.14%!6.14%!
BW’s Effective
Annual Interest Rate
33
34. Julie Miller is borrowing $10,000$10,000 at a
compound annual interest rate of 12%.
Amortize the loan if annual payments are
made for 5 years.
Step 1: Payment
PVPV00 = R (PVIFA i%,n)
$10,000$10,000 = R (PVIFA 12%,5)
$10,000$10,000 = R (3.605)
RR = $10,000$10,000 / 3.605 = $2,774$2,774
Amortizing a Loan Example
34
35. Amortizing a Loan Example
End of
Year
Payment Interest Principal Ending
Balance
0 --- --- --- $10,000
1 $2,774 $1,200 $1,574 8,426
2 2,774 1,011 1,763 6,663
3 2,774 800 1,974 4,689
4 2,774 563 2,211 2,478
5 2,775 297 2,478 0
$13,871 $3,871 $10,000