Time Value of Money - Present Value vs Future Value
Summary
TLDRThis video explains the concepts of future value and present value, illustrating the time value of money. It demonstrates how $10,000 today will grow to $32,071.35 in 20 years at a 6% annual interest rate, and conversely, how $100,000 ten years in the future has a present value of $55,839.48. The script emphasizes the diminishing purchasing power of money over time, highlighting why the same amount of money today has more value than in the future.
Takeaways
- 💡 The present value (PV) is the value of money today, while the future value (FV) is the value of that money in the future.
- 🔢 The formula to calculate FV is FV = PV * (1 + r)^n, where r is the annual interest rate and n is the number of years.
- 🌐 If you invest $10,000 today at a 6% annual interest rate, it will be worth $32,071.35 in 20 years.
- 💸 The time value of money concept shows that money today has a higher purchasing power than the same amount in the future.
- 🛒 An example of purchasing power is that $1 today can buy more goods than it could 20 years ago.
- 📉 The formula to calculate the present value is PV = FV / (1 + r)^n, which is used to find the current value of a future sum.
- 💲 The present value of $100,000 ten years from now, at a 6% interest rate, is $55,839.48.
- 📈 Inflation affects the time value of money; a 6% inflation rate means that $55,839.48 today has the same purchasing power as $100,000 in the future.
- 🏦 The script illustrates that the same amount of money is worth more in the present than it will be in the future due to the time value of money.
- 🤔 If given a choice between receiving $1,000 now or in ten years, the $1,000 now has more purchasing power.
- 📚 Understanding the time value of money is crucial for making informed financial decisions and understanding the impact of interest and inflation on savings and investments.
Q & A
What is the concept of present value in finance?
-The present value of money represents the value of money today, as opposed to its value in the future. It's the amount of money that, if invested now at a given interest rate, would grow to a specified future value.
What is the formula used to calculate the future value of an investment?
-The formula to calculate the future value (FV) is FV = PV * (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years the money is invested or will be invested for.
What is the future value of $10,000 after 20 years with an annual interest rate of 6%?
-Using the future value formula, the future value of $10,000 after 20 years with an annual interest rate of 6% is $32,071.35.
What does the time value of money illustrate?
-The time value of money illustrates that a dollar today is worth more than a dollar in the future due to its potential earning capacity, which is affected by factors like inflation and interest rates.
How does the purchasing power of money change over time?
-The purchasing power of money decreases over time due to inflation and other economic factors, meaning that the same amount of money can buy less in the future than it can today.
What is the concept of future value in finance?
-The future value of money represents the value of an amount of money at a future date, considering a specific interest rate. It's the amount that money will grow to if it is invested now.
What is the formula used to calculate the present value of a future sum of money?
-The formula to calculate the present value (PV) is PV = FV / (1 + r)^n, where FV is the future value, r is the annual interest rate, and n is the number of years until the future value is received.
What is the present value of $100,000 ten years from now with an annual interest rate of 6%?
-Using the present value formula, the present value of $100,000 ten years from now with an annual interest rate of 6% is $55,839.48.
Why is the present value of a future sum of money less than the future sum itself?
-The present value is less than the future sum because it takes into account the time value of money, meaning that money available now can be invested to earn interest, and thus is worth more than the same amount in the future.
How does inflation affect the value of money?
-Inflation erodes the purchasing power of money over time, meaning that the same amount of money will buy fewer goods and services in the future as it does today.
What is the implication of the time value of money for financial decision-making?
-The time value of money implies that when making financial decisions, one should consider the present value of future cash flows and the potential earnings or savings that can be made by investing money now rather than in the future.
Outlines
💰 Future Value Calculation
This paragraph introduces the concept of future value and present value in the context of money. It explains that present value is the current worth of money, while future value is its worth at a later time. The paragraph uses an example to illustrate the calculation of future value: if you have $10,000 today with an annual interest rate of 6%, the future value after 20 years would be $32,071.35. This demonstrates the time value of money, showing that money today has a greater purchasing power than the same amount in the future.
📉 Present Value and Time Value of Money
The second paragraph delves into the concept of present value and its relation to the time value of money. It discusses how to calculate the present value of a future sum of money, using the example of $100,000 ten years in the future with the same 6% interest rate. The calculation results in a present value of $55,839.48. The paragraph emphasizes that the same amount of money has more purchasing power now than it will in the future, highlighting the importance of understanding the time value of money in financial decisions.
Mindmap
Keywords
💡Present Value
💡Future Value
💡Annual Interest Rate
💡Time Value of Money
💡Purchasing Power
💡Inflation
💡Formula
💡Credited
💡Principal
💡Interest
💡Compound Interest
Highlights
The present value of money represents its value today, while the future value represents its value in the future.
The future value of $10,000 in 20 years at a 6% annual interest rate is calculated using the formula fv = pv * (1 + r)^n.
The future value of $10,000 after 20 years at a 6% interest rate is $32,071.35.
The time value of money concept is illustrated by comparing the purchasing power of $1 today versus in the future.
In the past, $1 could buy four bags of chips, whereas today it can only buy one, showing the decrease in purchasing power over time.
The present value of $100,000 ten years from now at a 6% annual interest rate is calculated using the rearranged formula pv = fv / (1 + r)^n.
The present value of $100,000 ten years in the future is $55,839.48, given a 6% interest rate.
Inflation at 6% means that $55,839.48 today has the same purchasing power as $100,000 would have in ten years.
The time value of money principle states that money is worth more now than it will be in the future.
The choice between receiving $1,000 now or in ten years should favor the present due to its higher purchasing power.
The video explains the importance of understanding the time value of money for financial planning.
The formula for calculating future value helps in understanding how money grows over time with interest.
The formula for calculating present value is essential for determining the current worth of a future sum of money.
The video uses a clear example to demonstrate the concept of future value with a 6% interest rate over 20 years.
The video provides a practical example of present value calculation for a sum of money ten years in the future.
The video emphasizes the impact of inflation on the purchasing power of money over time.
The video concludes by reinforcing the concept that money available today has greater value than the same amount in the future.
Transcripts
in this video we're going to talk about
how to solve a few basic
future value and present value problems
the present value of money represents
the value of money today right now in
the present
whereas the future value represents
the value of that money in the future
so let's start with the first part of
this problem
what is the future value of ten thousand
dollars
twenty years from now
given an annual interest rate of six
percent
so right now
in the present we have ten thousand
dollars
so that's the present value how much
will this amount of money be worth
20 years from now
at an interest rate of six percent
so we're looking for the future value
the formula that we could use to
calculate the future value
from the present value
is this formula
fv is equal to pv
times 1 plus r
raised to the n
so the present value is 10 000.
the interest rate
is six percent or point zero six
n is the number of time periods in this
case
since the interest
is credited on an annual basis and it's
going to be the number of years
which is 20 years
so it's going to be 10 000
times 1.06
raised to the 20th power
now let me go ahead and plug this in
so the future value
of ten thousand dollars twenty years
from now i'm gonna write it here
is
it's worth thirty two thousand
seventy one dollars and thirty five
cents
and so this really helps to illustrate
the time value of money
ten thousand dollars today is a it's
worth a lot more than 10 000 in the
future
for instance
you can buy more of a dollar now than
what you could buy 20 years you know
later
for example
now you can buy a small bag of chips for
about a dollar
20 years ago you can buy
a bag of chips for 25 cents
so 20 years in the past one dollar can
buy you four bags of chips
in the present a dollar can buy you one
bag of chips
so the purchasing power of money
goes down as time moves forward
you can buy a lot more stuff with a
dollar today
than what you will be able to buy with a
dollar in the future
so now let's move on to the second part
of the problem
what is the present value of a hundred
thousand dollars
ten years from now
given the same annual interest rate of
six percent
so in the second part of the problem
we're given the future value
which is a hundred thousand dollars and
we want to calculate how much that is
worth
ten years
in the past or rather in the present so
to speak
and the interest rate is the same
so the formula that we need to use
we need to rearrange it a little the
present value is equal to the future
value divided by one plus r raised to
the n
so the future value is a hundred
thousand
r is still point zero six so one plus
point 0.06 that's
1.06
and n is 10.
so 100 000 divided by 1.06 raised to the
10th power
gives us
a present value
of 55
839 dollars and 48 cents
so let's say that inflation is six
percent the value of all goods
increases by an average of six percent
fifty five thousand dollars eight
hundred
fifty five thousand eight hundred thirty
nine dollars and forty eight cents has
the same purchasing power as a hundred
thousand dollars ten years later
so as you can see this really
illustrates the time value of money
and that is
the same amount of money is worth more
now than it will be worth in the future
so if you have a choice of selecting
a thousand dollars now versus a thousand
dollars ten years from now
the thousand dollars in the present
has more purchasing power than
the thousand dollars in the future
so the basic idea behind the time value
of money is that money is worth more now
than it is in the future
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