The Organic Chemistry Tutor · YouTube · 5:14
This introductory lesson explains the core concepts of present value and future value within the time value of money framework. Using a whiteboard format, the instructor defines these terms and presents a practical example: calculating the future value of $10,000 over 20 years at a 6% annual interest rate. The video derives the solution using the standard compound interest formula, FV = PV()^n, arriving at approximately $32,071.35. It concludes by illustrating why money today is worth more than the same amount in the future through a relatable example of changing purchasing power. This 150-second whiteboard segment teaches present value through a worked finance example. It first uses a chips analogy to show that purchasing power falls over time, then introduces the rearranged formula PV = FV/()^n. The speaker applies it to find the present value of $100,000 received 10 years from now at 6% annual interest, obtaining $55,839.48. The clip closes by interpreting that result as the amount with the same purchasing power as $100,000 ten years later under 6% inflation, summarizing the time value of money. This short whiteboard segment introduces the time value of money through present value and future value examples. The board already shows two numerical cases at 6% annual interest: $10,000 growing to $32,071.35 in 20 years, and $100,000 received in 10 years having present value $55,839.48. A third row compares $1000 now with $1000 in the future, and the speaker emphasizes that the present amount has more purchasing power. The formula PV = FV / ()^n is written on the board and applied to the $100,000 example.
Use the learning inspector for key ideas and moments, or open the reading tabs for the complete notes.
Generated from the video's visuals and explanation; not verbatim speech.
The video opens by defining the fundamental concepts of finance: present value (the worth of money today) and future value (its worth at a later date). This establishes the framework for understanding how money grows over time.
To demonstrate these concepts, a specific problem is introduced: finding the future value of $10,000 invested for 20 years at a 6% annual interest rate. A simple timeline diagram is drawn to visually organize the given information—present value, time, and interest rate—and identify the unknown future value.
The mathematical tool for solving this is the compound interest formula, FV = PV()^n. The instructor substitutes the problem's values into the equation: FV = 10,. After simplifying the base to 1.06, the calculation yields a future value of approximately $32,071.35.
Finally, the lesson connects the numerical result back to economic reality. It explains that receiving $10,000 today is preferable to receiving it in 20 years because of its higher purchasing power. A relatable example compares the cost of a bag of chips today versus twenty years ago, illustrating how inflation erodes the real value of money over time.
The clip opens on a black digital whiteboard with the earlier future-value problem still visible: $10,000 grows to $32,071.35 over 20 years at 6%, and the formula FV = PV()^n is already written below. Over this, the instructor adds a simple purchasing-power comparison, writing $ bags and $ bag. The spoken example is slightly inconsistent in its time wording, but the mathematical point is clear: the same nominal dollar buys fewer goods later, so real purchasing power declines as time moves forward.
The instructor then turns to the second part of the problem, asking for the present value of $100,000 ten years from now at the same 6% annual interest rate. On the board, $100,000 is placed under the FV label, and the horizon is marked as 10 years with the same 6% rate. This reframes the situation: instead of compounding a present amount forward, the task is to discount a known future amount backward to today.
To do that, the video explicitly rearranges the compound-interest relationship. The general formula shown is , where is the future amount, is the annual rate as a decimal, and is the number of years. The instructor substitutes the given values step by step: , then simplifies the base to get , and finally evaluates the quotient to obtain .
With the numerical answer on screen, the clip shifts from calculation to interpretation. The instructor says that if inflation is also 6%, then $55,839.48 today has the same purchasing power as $100,000 ten years later. This is the key conceptual bridge: the discounted present value is not just a formula output, but the amount that makes a present sum and a future sum economically comparable. The segment closes by stating the general principle of the time value of money: the same amount of money is worth more now than it will be worth in the future.
The clip opens on a completed whiteboard problem about present value and future value. At the top, the written prompts ask for the future value of $10,000 twenty years from now at 6% annual interest and the present value of $100,000 ten years from now at the same rate. The left column is labeled PV and the right column is labeled FV, with arrows running left to right to show movement through time.
While the speaker says that the thousand dollars in the present has more purchasing power than the thousand dollars in the future, a red box is drawn around the left $1000 in the third row. That visual emphasis marks the present-dollar amount as the economically stronger one, even though the right side also shows $1000.
The speaker then states the general principle behind the whole board: money is worth more now than it is in the future. This verbal summary matches the structure of the examples above, where equal nominal amounts are not treated as equal in value across time.
The bottom of the board supplies the quantitative rule for that idea: . The symbols are used consistently across the examples: is present value, is future value, is the annual rate, and is the number of years.
The worked examples show how the formula is applied. In the first case, at for years becomes in the future. In the second case, the board substitutes into the formula as , and the displayed present-value result is . The clip ends with the conceptual point still foregrounded: discounting and compounding are the arithmetic expressions of the time value of money.
Present value (PV) is the current worth of a sum of money, while future value (FV) is what that sum will be worth at a later date after earning interest. Understanding this distinction is crucial because money available now can be invested to grow, making it more valuable than the same nominal amount in the future.
The future value of a lump sum is calculated using the compound interest formula: FV = PV()^n. In this equation, PV is the initial principal balance, r is the interest rate per period, and n is the number of compounding periods. This formula shows how an investment grows exponentially over time.
To find the future value of $10,000 after 20 years at a 6% annual interest rate, substitute the values into the formula: FV = 10,. Simplifying gives FV = 10,. Evaluating this expression results in a future value of approximately $32,071.35.
The time value of money is closely tied to purchasing power. Due to inflation, a dollar today generally buys more goods and services than a dollar will in the future. For example, if a bag of chips costs $1.00 now but cost $0.25 twenty years ago, the real value of the dollar has decreased, highlighting why future sums must be discounted to compare fairly with present sums.
The opening example compares what one dollar can buy at different times, using bags of chips as a concrete good. The board writes $ bags and $ bag, showing that the same nominal dollar purchases less later. This motivates discounting future cash flows because a future dollar is not equivalent in real value to a present dollar.
Before solving the second part, the earlier relation remains visible from the first example. It serves as the starting point for the next step: if you know the future amount and want today’s equivalent, you must solve the same relationship for .
The video rearranges the compound-interest equation to isolate present value: . Here is the known future amount, is the annual interest rate expressed as a decimal, and is the number of years. This formula converts a future sum into its equivalent amount today under the given rate.
The instructor applies the formula to the specific data , , and . The substitution is , which evaluates to . Thus, $100,000 received ten years from now is worth $55,839.48 today at a 6% annual rate.
After computing the present value, the speaker interprets the result economically: if inflation averages 6% per year, then $55,839.48 today has the same purchasing power as $100,000 ten years later. This links the algebraic discount factor to the real-world idea that rising prices reduce the future buying power of money.
The closing takeaway is that the same nominal amount of money is worth more now than in the future. The worked PV calculation illustrates why: positive rates imply that future cash must be discounted to compare fairly with cash available today.
The video states the central principle directly: money available today is worth more than the same nominal amount in the future. This is illustrated by comparing $1000 now with $1000 later, where the speaker says the present amount has more purchasing power.
The board gives the discounting relation . Here is the future amount, is the periodic interest or discount rate, and is the number of periods. The example on the board applies it with , , and .
The first worked example shows $10,000 on the PV side growing over 20 years at 6% to $32,071.35 on the FV side. The clip presents the result visually rather than deriving it step by step.
The second example asks for the present value of 55,839.48$ on the PV side.
A common mistake is to treat $1000 today and $1000 in the future as equivalent just because the numbers match. The video explicitly rejects that by highlighting the present $1000 and saying it has more purchasing power than the future $1000.
Explore conditions, steps and evidence. Supplementary explanations are labeled separately from content shown in the video.
The speaker says, "So right now in the present we have ten thousand dollars. So that's the present value."
The handwritten label "PV" is written above "$10,000".
The formula "FV = PV()^n" is written on the screen.
PV
Present value, representing the value of money today.
Monetary amount (dollars).
The speaker says, "So we're looking for the future value."
The handwritten label "FV" is written at the end of the arrow.
The formula "FV = PV()^n" is written on the screen.
FV
Future value, representing the value of money at a specified time in the future.
Monetary amount (dollars).
The speaker says, "The interest rate is six percent or point zero six."
The variable "r" is used in the formula "FV = PV()^n" and substituted with "0.06".
r
Annual interest rate.
Decimal fraction (e.g., 0.06 for 6%).
The speaker says, "n is the number of time periods... which is twenty years."
The variable "n" is used as the exponent in the formula "FV = PV()^n" and substituted with "20".
n
Number of compounding periods (years in this context).
Positive integer.
PV is written in the problem statement and used as the left-hand side of the present-value formula.
The speaker refers to “present value” while setting up the second part of the problem.
PV
Present value, the current worth of a future amount discounted at rate r over n periods.
Monetary amount; in this example dollars.
FV is written in the problem statement and used as the numerator in the rearranged formula.
The speaker says “we’re given the future value, which is $100,000.”
FV
Future value, the amount at a later date that is being discounted back to the present.
Monetary amount; in this example dollars.
r appears in FV = PV()^n and in PV = FV/()^n.
The speaker states that r is still 0.06 for the 6% annual interest rate.
r
Annual interest rate expressed as a decimal.
Rate per period; here .
n appears as the exponent in both formulas.
The speaker says “and n is 10” when substituting into the present-value formula.
n
Number of compounding periods (years).
Positive integer count of years; here for the second part.
$100,000 is written under the FV label and substituted into the numerator of the PV formula.
The speaker identifies $100,000 as the future value in the second part of the problem.
$100,000
Given future amount to be discounted back 10 years.
Dollar amount.
$55,839.48 is written as the result of the present-value calculation.
The speaker reads the answer as fifty-five thousand eight hundred thirty-nine dollars and forty-eight cents.
$55,839.48
Computed present value of $100,000 received 10 years from now at 6% annual interest.
Dollar amount.
The board shows the label PV and the formula PV = FV / ()^n.
The speaker discusses present value in words while the PV label is visible.
PV
Present value; the current worth of a future amount discounted at rate r over n periods.
Monetary value, typically dollars.
The board shows the label FV and the numerator FV in PV = FV / ()^n.
The speaker contrasts present value with future value.
FV
Future value; the amount an investment grows to after n periods at rate r.
Monetary value, typically dollars.
The speaker states, "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."
Present value (PV) is the current worth of a sum of money, while future value (FV) is the worth of that same sum at a later date, assuming it earns interest over time.
Applies to monetary amounts subject to interest rates over time.
The speaker says, "The formula that we could use to calculate the future value from the present value is this formula: FV is equal to PV times one plus r raised to the n."
The equation "FV = PV()^n" is written on the screen.
This formula calculates the future value of a present sum using compound interest. It multiplies the present value by the growth factor raised to the power of the number of periods .
Assumes annual compounding when is an annual rate and is in years.
Interest rate remains constant over the period.
The board shows PV = FV / ()^n.
The speaker says the formula needs to be rearranged and states: “The present value is equal to the future value divided by one plus r raised to the n.”
The video uses the rearranged compound-interest relation to compute today’s equivalent of a future amount. The denominator discounts the future value back over periods at rate .
FV is known.
r is the periodic interest rate expressed as a decimal.
n is the number of periods.
The earlier worked setup on the board includes FV = PV()^n and the substitution 10,,.
The speaker transitions from the first part of the problem to the second part, indicating the same interest-rate framework continues.
Before solving for present value, the board retains the standard future-value relation , which is then algebraically rearranged to isolate .
PV is known.
r is the periodic interest rate expressed as a decimal.
n is the number of periods.
The speaker concludes: “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.”
The board contrasts $55,839.48 today with $100,000 ten years later.
The clip defines the practical meaning of the calculation: a dollar today has greater purchasing power than the same nominal dollar in the future, so a future sum is worth less in present terms.
Comparison is made across different points in time using the same discount/interest rate.
The speaker says, “So twenty 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.”
The board writes $ bags and $ bag.
The spoken phrase “twenty years in the past” conflicts with the surrounding explanation about future purchasing power; the intended contrast is between an earlier time and the present/future direction of declining buying power.
The chips example illustrates that the same nominal amount buys fewer goods later, motivating why future cash flows must be discounted to compare them with present cash.
Assumes prices rise over time or real purchasing power falls.
Speaker says: 'So the basic idea behind the time value of money is that money is worth more now than it is in the future.'
The video states the core principle of the time value of money: a given amount of money is worth more today than the same nominal amount in the future. This is presented verbally while the board already contains PV/FV examples and the discounting formula.
Applies when comparing monetary amounts at different points in time under positive interest or discount rates.
Bottom-left board text reads: PV = FV / ()^n = $100,.
The board gives the present-value relation PV = FV / ()^n and applies it to a future amount of $100,000 with % and years. The formula expresses how a future sum is discounted back to the present by dividing by the growth factor ()^n.
PV is the present value.
FV is the future value.
r is the periodic interest or discount rate.
n is the number of periods.
The displayed application uses annual compounding with and .
The speaker says that if inflation is 6%, then $55,839.48 has the same purchasing power as $100,000 ten years later.
This follows from the computed PV relation implied by the displayed calculation.
The video verbally equates the interest rate with inflation for interpretation; it does not separately derive an inflation model.
At a 6% annual inflation rate, $55,839.48 today has the same purchasing power as $100,000 ten years from now.
Inflation is 6% per year.
The comparison spans 10 years.
Discounting uses the same annual rate as inflation.
For the specific amounts and horizon stated in the example.
The speaker explicitly states: “the same amount of money is worth more now than it will be worth in the future.”
The same nominal amount of money is worth more now than it will be worth in the future.
There is positive time value of money, represented here by a positive annual rate.
General conclusion drawn from the worked example.
The speaker verbally substitutes the values: "So the present value is ten thousand... interest rate is six percent or point zero six... n is... twenty years. So it's going to be ten thousand times one point zero six raised to the twentieth power."
The step-by-step calculation is written: "= 10,", then "= 10,", and finally the result "$32,071.35" is written next to the FV label.
Substitute the given values into the future value formula: PV = 10,000, , .
Direct application of the formula FV = PV()^n with the problem's specific parameters.
Simplify the term inside the parentheses by adding 1 and 0.06.
Basic arithmetic simplification.
Calculate the final value using a calculator.
Numerical evaluation of the expression 10,.
The future value of $10,000 after 20 years at a 6% annual interest rate is approximately $32,071.35.
The board shows PV = FV/()^n, then substitutes $100,000, 1.06, and exponent 10, yielding $55,839.48.
The speaker narrates each substitution: future value is 100,000; r is 0.06 so is 1.06; n is 10.
Start from the rearranged compound-interest formula shown on the board.
Algebraic rearrangement of FV = PV()^n.
Insert the given future value, annual rate, and number of years.
Problem data: FV = $100,000, , .
Simplify the base of the denominator.
Arithmetic: .
Evaluate the quotient to obtain the present value.
Numerical computation of .
The present value of $100,000 received 10 years from now at 6% annual interest is $55,839.48.
The speaker compares what one dollar buys in the past versus the present/future using bags of chips.
The board writes $ bags and $ bag.
The exact temporal wording in the audio is inconsistent, but the mathematical point is the decline of purchasing power over time.
Earlier, one dollar could buy four bags of chips.
Illustrative purchasing-power comparison stated in the audio and written on the board.
Later, the same dollar buys only one bag.
Illustrative purchasing-power comparison stated in the audio and written on the board.
Therefore a future dollar is worth less in real terms than a present dollar.
Direct interpretation of the two comparisons.
The chips example motivates why future cash amounts must be discounted to compare them with present cash.
The board writes PV = FV / ()^n and then the substituted expression $100,.
The final numerical value of $100, is not written on the board in this clip.
Start from the general present-value formula shown on the board.
Directly observed formula on the whiteboard.
Substitute FV = 100,000, , and into the formula.
Matches the second worked example on the board, which asks for the present value of $100,000 ten years from now at 6%.
The clip shows the setup for computing the present value of $100,000 received 10 years from now at 6% annual interest, but does not display the final evaluated number.
The text on screen reads: "1. What is the future value of $10,000 twenty years from now given an annual interest rate of 6%?"
The speaker reads the first part of the problem and proceeds to solve it.
What is the future value of $10,000 twenty years from now given an annual interest rate of 6%?
Present Value (PV) = $10,000
Time period (n) = 20 years
Annual interest rate (r) = 6% or 0.06
Calculate the Future Value (FV).
Identify and write down the appropriate formula for calculating future value with compound interest.
Standard financial mathematics formula for single-sum future value.
Substitute the known values into the formula.
Direct substitution based on the problem statement.
Perform the addition inside the parentheses.
Arithmetic simplification.
Compute the final numerical result.
Calculator evaluation of the exponential expression.
$32,071.35
The speaker uses an off-screen calculator to verify the result, stating the final amount aloud and writing it on the board.
The speaker introduces the second part: “What is the present value of $100,000 ten years from now given the same annual interest rate of 6%?”
The board writes PV = FV/()^,,839.48.
Find the present value of $100,000 received ten years from now at an annual interest rate of 6%.
FV = $100,000
years
% = 0.06
Compute PV.
Use the present-value form of the compound-interest equation.
Rearrange FV = PV()^n to solve for PV.
Substitute the given values into the formula.
Direct substitution from the problem statement.
Simplify the denominator base.
Arithmetic simplification: .
Evaluate the expression numerically.
Calculator evaluation shown and read aloud in the video.
$55,839.48
The result is consistent with the displayed formula and the spoken interpretation that this amount today is equivalent in purchasing power to $100,000 ten years later at 6%.
Top prompt reads: 'What is the future value of $10,000 twenty years from now given an annual interest rate of 6%?'
Left side shows $10,000 under PV with an arrow labeled 20 yrs and 6% pointing right to $32,071.35 under FV.
Find the future value of $10,000 twenty years from now at an annual interest rate of 6%.
PV = $10,000
years
% annually
Compute FV.
Identify the present amount, annual rate, and time horizon from the board.
These values are explicitly written beside the first arrow.
Read the resulting future value written on the right side of the first example.
The board directly displays $32,071.35 as the FV outcome.
$32,071.35
The displayed result is consistent with compound growth at 6% for 20 years, though the intermediate calculation is not shown in this clip.
Top prompt reads: 'What is the present value of $100,000 ten years from now given the same annual interest rate of 6%?'
Second row shows $55,839.48 on the left under PV, an arrow labeled 10 yrs and 6%, and $100,000 on the right under FV.
Bottom-right substitution reads $100,.
The clip shows the formula setup but not the arithmetic evaluation step from $100, to $55,839.48.
Find the present value of $100,000 ten years from now at an annual interest rate of 6%.
FV = $100,000
years
% annually
Compute PV.
Identify the future amount, annual rate, and time horizon from the second example.
These values are explicitly written on the board and in the top prompt.
Apply the present-value formula with the given numbers.
This exact substitution is written on the bottom-right of the board.
Read the present-value result shown on the left side of the second example.
The board directly displays $55,839.48 as the PV outcome.
$55,839.48
The displayed result matches the standard discounting computation for 10 years at 6%, although the clip does not show the intermediate arithmetic.
Third row shows $1000 on the left and $1000 on the right with no interest-rate arrow between them.
Speaker says: 'The thousand dollars in the present has more purchasing power than the thousand dollars in the future.'
A red box is drawn around the left $1000 during the spoken comparison.
The board does not write a numerical discount rate or time length for this $1000 comparison; the interpretation relies on the spoken explanation.
Interpret the meaning of placing $1000 on both the present-value side and the future-value side.
Left amount: $1000
Right amount: $1000
No explicit rate or period shown between these two $1000 amounts
Explain why the two equal nominal amounts are not economically equivalent.
Although the nominal dollar amounts are equal, the speaker distinguishes the present $1000 from the future $1000.
Audio explicitly states that the present $1000 has more purchasing power than the future $1000.
The visual emphasis marks the present amount as the more valuable one in the comparison.
Animation shows a red rectangle drawn around the left $1000 while the speaker makes the point.
The present $1000 is treated as more valuable than the future $1000 because money available now has greater purchasing power.
This example functions as a conceptual illustration rather than a numerical calculation; it aligns with the stated time-value-of-money principle.
A horizontal timeline is drawn. "$10,000" is written on the left with "PV" above it. An arrow points right, labeled "20 yrs" above and "6%" below. "FV" is written at the tip of the arrow.
Horizontal arrow representing time
Text labels: PV, $10,000, 20 yrs, 6%, FV
Drawing of the timeline arrow
Addition of present value and its label
Addition of time and interest rate parameters
Addition of the future value target label
The direction of the arrow always points from present to future.
Visually maps the components of the time value of money problem, showing the starting amount, the duration, the growth rate, and the unknown ending amount.
The board shows $ bags and $ bag beneath the earlier future-value work.
The speaker explains that one dollar buys four bags earlier and one bag later.
The spoken time reference is internally inconsistent, but the visual contrast itself is clear.
$1
4 bags
1 bag
arrow notation
The board adds a two-line comparison showing what one dollar buys at different times.
The nominal amount remains $1 in both lines.
Holding the dollar amount fixed, the quantity of goods purchasable falls from 4 bags to 1 bag, illustrating loss of purchasing power over time.
$100,000 is written under FV, then the formula PV = FV/()^n is written and filled in with 100,000, 1.06, and 10.
Writing proceeds stepwise from the general formula to the substituted expression and finally the numerical answer.
PV
FV
()^n
$100,000
(1.06)^{10}
$55,839.48
The board first labels the known future amount, then writes the general PV formula, then substitutes values, then simplifies the base, then writes the final dollar result.
The interest rate remains 6% throughout the second-part calculation.
The horizon remains 10 years throughout the second-part calculation.
The visual sequence shows the algebraic path from a future amount to its discounted present equivalent.
The completed PV calculation remains visible while the speaker interprets the result.
The speaker states that $55,839.48 has the same purchasing power as $100,000 ten years later and summarizes the time value of money.
$55,839.48
$100,000
time value of money statement
No new formula is introduced; the emphasis shifts from calculation to economic interpretation.
The computed numerical result stays on screen as the basis for the conclusion.
The finished arithmetic is used to explain that present and future sums can be equivalent in purchasing power once discounted at the given rate.
Static whiteboard layout with PV on the left, FV on the right, arrows showing time and 6% interest, and the formula PV = FV / ()^n at the bottom.
PV column
FV column
two horizontal arrows labeled with years and 6%
bottom formula PV = FV / ()^n
substitution $100,
PV is consistently placed on the left.
FV is consistently placed on the right.
The arrows run from left to right to indicate movement through time.
The layout visually separates present amounts from future amounts and uses arrows to encode the direction of compounding or discounting over time.
A red rectangular outline is drawn around the left $1000 in the third row.
During this interval the speaker says the present $1000 has more purchasing power than the future $1000.
left $1000
red rectangle
A red box appears around the left $1000.
The right $1000 remains unboxed.
The rest of the board content stays unchanged.
The animation singles out the present-dollar amount to reinforce the verbal claim that the same nominal sum is more valuable now than later.
The speaker explains, "this really helps to illustrate the time value of money. Ten thousand dollars today is worth a lot more than ten thousand in the future... you can buy more of a dollar now than what you could buy twenty years later... now you can buy a small bag of chips for about a dollar. Twenty years ago, you can buy a bag of chips for twenty-five cents."
Believing that a fixed nominal amount of money (e.g., $10,000) holds the same purchasing power regardless of when it is received.
Due to inflation and the potential to earn interest, money available today has greater purchasing power than the same amount in the future. The example of chip prices illustrates how the real value of a dollar changes over time.
The speaker says, “So let’s say that inflation is six percent,” and uses the same 6% rate to interpret purchasing power.
This is an analyst clarification, not a separate warning stated by the video author.
One may think the 6% annual interest rate in the formula is inherently an inflation rate.
In the video, 6% is first used as the discount/interest rate in the PV formula; the speaker then adds an interpretive assumption that inflation is also 6% to connect the result to purchasing power. Those roles are conceptually distinct even though the same numerical rate is reused here.
The speaker says “twenty years in the past” while describing the chips example, then immediately talks about purchasing power going down as time moves forward.
The intended direction of the example is clear from context, but the exact spoken temporal wording is inconsistent.
The chips example can sound as if it compares the past to the present in a way that contradicts the later statement about future purchasing power.
The mathematical point of the example is that the same dollar buys fewer goods later in time; the clip’s wording around “past” is imprecise, but the intended lesson is the decline of purchasing power over time.
Speaker says: 'The thousand dollars in the present has more purchasing power than the thousand dollars in the future.'
The left $1000 is boxed in red while the right $1000 is not.
One might think that $1000 today and $1000 in the future are equivalent simply because the numbers are the same.
The video explicitly rejects that view by stating that the present $1000 has more purchasing power than the future $1000.
The speaker introduces the formula specifically to "calculate the future value from the present value".
The formula FV = PV()^n explicitly defines FV in terms of PV.
The future value formula is a mathematical tool used to apply the concept of time value of money, specifically to find the future equivalent of a present sum.
The board retains FV = PV()^n and then writes PV = FV/()^n.
The speaker says the formula needs to be rearranged a little before computing present value.
The present-value formula is obtained by algebraically rearranging the future-value formula to solve for PV.
The computed PV result is used directly in the concluding explanation.
The speaker says the example “really illustrates the time value of money.”
The numerical present-value calculation is the concrete application that demonstrates the broader principle of time value of money.
The chips comparison appears before the PV formula is introduced.
The speaker uses falling purchasing power to motivate why future money is worth less now.
The intuitive purchasing-power example provides the conceptual motivation for discounting future amounts with the PV formula.
The speaker states the general time-value-of-money principle.
The board simultaneously displays PV = FV / ()^n and worked PV/FV examples.
The present-value formula is the quantitative tool used to apply the qualitative time-value-of-money principle shown in the examples.
The bottom formula PV = FV / ()^n is written alongside the numeric examples above.
The second example substitutes $100,000 and 10 years into that formula.
The $100,000 example is a direct numerical application of the displayed present-value formula.
The on-screen text poses the exact question being solved.
The speaker provides definitions for present and future value at the beginning of the video.
PV = FV/()^n is written explicitly on the board.
The board shows both FV = PV()^n and PV = FV/()^n.
The speaker states the second-part problem: present value of $100,000 ten years from now at 6%.
The worked substitution yields $55,839.48.
The speaker concludes that the same amount of money is worth more now than in the future.
The speaker says that if inflation is 6%, then $55,839.48 has the same purchasing power as $100,000 ten years later.
Speaker defines the basic idea behind the time value of money.
Board shows PV = FV / ()^n.
Speaker compares $1000 in the present with $1000 in the future.
Red box highlights the present $1000.
Top prompt asks for the present value of $100,000 ten years from now at 6%.
Board shows $100, and result $55,839.48.
Top prompt asks for the future value of $10,000 twenty years from now at 6%.
Board shows $10,000 growing to $32,071.35.
Covered · Introduction to the concepts of present value and future value.
Covered · Presentation of the first example problem and creation of a visual timeline.
Covered · Introduction of the future value formula and step-by-step calculation of the example.
Covered · Conceptual explanation of the time value of money using a real-world purchasing power example.
Covered · Opening board state plus the chips-based purchasing-power explanation and the retained future-value formula.
Covered · Transition to the second part of the problem and setup of the known future value, horizon, and rate.
Covered · Explicit writing of PV = FV/()^n, substitution of values, and computation of $55,839.48.
Covered · Interpretation of the result as equivalent purchasing power and summary of the time value of money.
Covered · The board is already filled with PV/FV examples and the formula while the speaker explains that $1000 now has more purchasing power than $1000 in the future; the left $1000 is highlighted with a red box.
Covered · The speaker states the general time-value-of-money principle while the static whiteboard continues to show the PV/FV examples and the formula PV = FV / ()^n.
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