Time Value of Money - Present Value vs Future Value

Summary

This 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

00:00

💰 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.

05:00

📉 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.

Keywords

💡Present Value

Present Value refers to the value of a sum of money at the current point in time, considering its potential to grow or shrink due to factors like inflation or interest rates. In the video's theme, it is the starting point for understanding the time value of money. For instance, the script discusses how ten thousand dollars today has a Present Value and will have a different Future Value in 20 years.

💡Future Value

Future Value is the value of money at a future date, taking into account the effects of interest or investment growth. It is a critical concept in the video, as it helps illustrate the potential increase in the value of an initial sum. The script uses the example of ten thousand dollars growing to thirty-two thousand, seventy-one dollars and thirty-five cents over twenty years at an annual interest rate of six percent.

💡Annual Interest Rate

The Annual Interest Rate is the percentage of an investment's interest earned each year. It is a key component in calculating both Present and Future Value. The script consistently uses an annual interest rate of six percent to demonstrate how money can grow over time, impacting both the Future Value of an initial investment and the Present Value of a future sum.

💡Time Value of Money

The Time Value of Money is the concept that a sum of money is worth more now than the same sum in the future due to its potential earning capacity. The video's main message revolves around this principle, explaining how the purchasing power of money decreases over time. The script gives a practical example comparing the purchasing power of a dollar now versus what it will be able to buy in the future.

💡Purchasing Power

Purchasing Power is the value of a currency in terms of the goods and services it can buy. The script uses this term to emphasize the Time Value of Money, noting how the same amount of money can buy more now than it will in the future. The example of a bag of chips costing a quarter 20 years ago versus a dollar now illustrates this concept.

💡Inflation

Inflation is the rate at which the general level of prices for goods and services is rising, and subsequently, the purchasing power of currency is falling. In the script, inflation is used to explain how the value of money decreases over time, and it is given as six percent, the same as the interest rate, to show how it affects the Present Value of a future sum of money.

💡Formula

In the context of the video, a formula is a mathematical equation used to calculate the Present and Future Value of money. The script provides the formulae for both calculations, showing how to apply them with given values to find out how much money will be worth in the future or what it is worth now.

💡Credited

In the financial context used in the script, credited refers to the process of adding interest to the principal sum of an account or investment. The term is important as it explains how the Future Value is calculated, with interest being 'credited' annually, affecting the total amount over time.

💡Principal

The Principal is the initial amount of money that is invested or borrowed. In the script, the Principal is the starting point for calculating the Future Value, with ten thousand dollars being the Principal in the first example, and the growth of this amount over time is demonstrated.

💡Interest

Interest is the cost of borrowing money or the return on investment. In the script, interest is the mechanism by which the Principal grows to become the Future Value. The annual interest rate of six percent is applied to calculate the increase in the Principal over a period of time.

💡Compound Interest

Compound Interest is the interest on a loan or deposit calculated based on both the initial principal and the accumulated interest from previous periods. The script implicitly discusses compound interest when explaining how the Future Value increases over the 20 years due to the interest being added to the Principal annually.

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