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.
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,
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.
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,
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
Concepts covered:
Concept of Time value of Money
What is Time Line
Concept of Future Value
What is Simple interest and Compound Interest
Using Financial Calculator or Excel functions
What is Present value and Discounting
Finding the discount rate
Finding number of period
Rule of 72
This is the third presentation for the University of New England Graduate School of Business unit GSB711 - Managerial Finance. It explores the time value of money, using examples to help students clarify this concept.
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
Concepts covered:
Concept of Time value of Money
What is Time Line
Concept of Future Value
What is Simple interest and Compound Interest
Using Financial Calculator or Excel functions
What is Present value and Discounting
Finding the discount rate
Finding number of period
Rule of 72
This is the third presentation for the University of New England Graduate School of Business unit GSB711 - Managerial Finance. It explores the time value of money, using examples to help students clarify this concept.
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.
Time lines
Future value / Present value of lump sum
FV / PV of annuity
Perpetuities
Uneven CF stream
Compounding periods
Nominal / Effective / Periodic rates
Amortization
CHAPTER 9Time Value of MoneyFuture valuePresent valueAnn.docxtiffanyd4
CHAPTER 9
Time Value of Money
Future value
Present value
Annuities
Rates of return
Amortization
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1
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
CF3
CF2
0
1
2
3
I%
9-‹#›
2
Drawing time lines
100
100
100
0
1
2
3
I%
3 year $100 ordinary annuity
100
0
1
2
I%
$100 lump sum due in 2 years
9-‹#›
3
Future Value of Money
If you deposit $1,000 today at 10%, how much will you have after 15 years?
Interest($) = Principal ∙ Interest Rate(%)
Simple Interest
The original principal stays the same.
There is no interest on interest. The interest is only on the original principal.
Compound Interest
The principal changes through time.
There is “interest on interest”. The interest is on the new principal.
9-‹#›
9-‹#›
9-‹#›
Simple Interest
Interest($) = Principal($) ∙ Interest Rate(%) = V0 ∙ I
V1 = V0 + Interest = V0 + V0 ∙ I = V0(1 + I)
V2 = V1 + Interest = V1 + V0 ∙ I = V0(1 + I) + V0 ∙ I
= V0(1 + I + I) = V0(1 + 2I)
V3 = V2 + Interest = V2 + V0 ∙ I = V0(1 + 2I) + V0 ∙ I
= V0(1 + 2I + I) = V0(1 + 3I)
.
.
Vn = V0(1 + nI)
FVn = PV(1 + nI)
9-‹#›
Compound Interest
Interest ($) = Principal ($) ∙ Interest Rate (%) = V ∙ I
V1 = V0 + Interest = V0 + V0 ∙ I = V0(1 + I)
V2 = V1 + Interest = V1 + V1 ∙ I = V1(1 + I)
V3 = V2 + Interest = V2 + V2 ∙ I = V2(1 + I)
V2 = V1(1 + I) = V0(1 + I)(1 + I) = V0(1 + I)2
V3 = V2(1 + I) = V0(1 + I)2(1 + I) = V0(1 + I)3
Vn = V0 (1 + I)n
FVn = PV(1 + I)n = PV∙FVIF
V2 = V1 + Interest = V1 + (V0 + Interest) ∙ I
9-‹#›
Example
What is the future value of $20 invested for 2 years at 10%?
Simple: FV = PV(1+nI)
= 20(1+2I) = 20(1+0.2) = $24
Compound: FV = PV(1+I)n
= 20(1+I)2 = 20(1+0.1)2 = $24.2
What is the future value of $20 invested for 100 years at 10%?
Simple: FV = 20(1+ ) =
Compound : FV = 20(1.1)100 = 275,612.25
9-‹#›
The Power of Compounding
The Value of Manhattan
In 1626, the land was bought from American Indians at $24.
In 2018, value = $24(1+I)392
9-‹#›
Solving for FV:
The formula method
Solve the general FV equation:
FVN = PV∙(1 + I)N = PV ∙ FVIF
FV15 = PV∙(1 + I)15 = $1,000∙(1.10)15 = $4,177.25
= $1,000∙4.177 = $4,177
(Table A)
9-‹#›
Present Value of Money
If you want to have $4,177.25 after 15 years, how much do you have to deposit today at 10%?
9-‹#›
PV = ?
4,177.25
Present Value of Money
Finding the PV of a cash flow or series of cash flows is called discounting (the reverse of compounding).
0
1
2 …
15
10%
9-‹#›
13
Solving for PV:
The formula method
Solve the general FV equat.
What price will pi network be listed on exchangesDOT TECH
The rate at which pi will be listed is practically unknown. But due to speculations surrounding it the predicted rate is tends to be from 30$ — 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
how to sell pi coins at high rate quickly.DOT TECH
Where can I sell my pi coins at a high rate.
Pi is not launched yet on any exchange. But one can easily sell his or her pi coins to investors who want to hold pi till mainnet launch.
This means crypto whales want to hold pi. And you can get a good rate for selling pi to them. I will leave the telegram contact of my personal pi vendor below.
A vendor is someone who buys from a miner and resell it to a holder or crypto whale.
Here is the telegram contact of my vendor:
@Pi_vendor_247
how to sell pi coins effectively (from 50 - 100k pi)DOT TECH
Anywhere in the world, including Africa, America, and Europe, you can sell Pi Network Coins online and receive cash through online payment options.
Pi has not yet been launched on any exchange because we are currently using the confined Mainnet. The planned launch date for Pi is June 28, 2026.
Reselling to investors who want to hold until the mainnet launch in 2026 is currently the sole way to sell.
Consequently, right now. All you need to do is select the right pi network provider.
Who is a pi merchant?
An individual who buys coins from miners on the pi network and resells them to investors hoping to hang onto them until the mainnet is launched is known as a pi merchant.
debuts.
I'll provide you the Telegram username
@Pi_vendor_247
US Economic Outlook - Being Decided - M Capital Group August 2021.pdfpchutichetpong
The U.S. economy is continuing its impressive recovery from the COVID-19 pandemic and not slowing down despite re-occurring bumps. The U.S. savings rate reached its highest ever recorded level at 34% in April 2020 and Americans seem ready to spend. The sectors that had been hurt the most by the pandemic specifically reduced consumer spending, like retail, leisure, hospitality, and travel, are now experiencing massive growth in revenue and job openings.
Could this growth lead to a “Roaring Twenties”? As quickly as the U.S. economy contracted, experiencing a 9.1% drop in economic output relative to the business cycle in Q2 2020, the largest in recorded history, it has rebounded beyond expectations. This surprising growth seems to be fueled by the U.S. government’s aggressive fiscal and monetary policies, and an increase in consumer spending as mobility restrictions are lifted. Unemployment rates between June 2020 and June 2021 decreased by 5.2%, while the demand for labor is increasing, coupled with increasing wages to incentivize Americans to rejoin the labor force. Schools and businesses are expected to fully reopen soon. In parallel, vaccination rates across the country and the world continue to rise, with full vaccination rates of 50% and 14.8% respectively.
However, it is not completely smooth sailing from here. According to M Capital Group, the main risks that threaten the continued growth of the U.S. economy are inflation, unsettled trade relations, and another wave of Covid-19 mutations that could shut down the world again. Have we learned from the past year of COVID-19 and adapted our economy accordingly?
“In order for the U.S. economy to continue growing, whether there is another wave or not, the U.S. needs to focus on diversifying supply chains, supporting business investment, and maintaining consumer spending,” says Grace Feeley, a research analyst at M Capital Group.
While the economic indicators are positive, the risks are coming closer to manifesting and threatening such growth. The new variants spreading throughout the world, Delta, Lambda, and Gamma, are vaccine-resistant and muddy the predictions made about the economy and health of the country. These variants bring back the feeling of uncertainty that has wreaked havoc not only on the stock market but the mindset of people around the world. MCG provides unique insight on how to mitigate these risks to possibly ensure a bright economic future.
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
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
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.
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
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
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.
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.
Empowering the Unbanked: The Vital Role of NBFCs in Promoting Financial Inclu...
Time value of money
1.
2.
3. Time line for a $100 lump sum due at the end of Year 2. 100 0 1 2 Year i%
4. Time line for an ordinary annuity of $100 for 3 years. 100 100 100 0 1 2 3 i%
5. Time line for uneven CFs: -$50 at t = 0 and $100, $75, and $50 at the end of Years 1 through 3. 100 50 75 0 1 2 3 i% -50
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. After 3 years: FV 3 = PV(1 + i) 3 = $100(1.10) 3 = $133.10. In general, FV n = PV(1 + i) n .
9. What’s the PV of $100 due in 3 years if i = 10%? 10% Finding PVs is discounting, and it’s the reverse of compounding. 100 0 1 2 3 PV = ?
10. Solve FV n = PV(1 + i ) n for PV: PV = $100 1 1.10 = $100 0.7513 = $75.13. 3
11. Ordinary Annuity PMT PMT PMT 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
12. What’s the FV of a 3-year ordinary annuity of $100 at 10%? 100 100 100 0 1 2 3 10% 110 121 FV = 331
13. What’s the PV of this ordinary annuity? 100 100 100 0 1 2 3 10% 90.91 82.64 75.13 248.69 = PV
14. Find the FV and PV if the annuity were an annuity due. 100 100 0 1 2 3 10% 100
15. What is the PV of this uneven cash flow stream? 0 100 1 300 2 300 3 10% -50 4 90.91 247.93 225.39 -34.15 530.08 = PV
17. We will deal with 3 different rates: i Nom = nominal, or stated, or quoted, rate per year. i Per = periodic rate. EAR = EFF% = . effective annual rate
18.
19.
20.
21. How do we find EFF% for a nominal rate of 10%, compounded semiannually? Or use a financial calculator. = - 1.0 ( 1 + ) 0.10 2 2 = (1.05) 2 - 1.0 = 0.1025 = 10.25%. EFF% = - 1 ( 1 + ) i Nom m m
23. FV of $100 after 3 years under 10% semiannual compounding? Quarterly? = $100(1.05) 6 = $134.01. FV 3Q = $100(1.025) 12 = $134.49. FV = PV 1 . + i m n Nom mn FV = $100 1 + 0.10 2 3S 2x3
24. 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
25. 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
26. What’s the PV of this stream? 0 100 1 5% 2 3 100 100 90.70 82.27 74.62 247.59
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![[object Object],CF 0 CF 1 CF 3 CF 2 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.](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)