Time value of money | Interest and debt | Finance & Capital Markets | Khan Academy (2023)


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Why when you get your money matters as much as how much money. Present and future value also discussed. Created by Sal Khan.

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Narrator: Whenever, we talk about money.

The amount of money is not the only thing that matters.

What also matters is when you have to get or when you have to give the money.

So, to think about this or to make it a little bit more concrete, let's assume that we live in a world that if you put money in a bank, you are guaranteed, 10%, interest, 10% risk, free interest in a bank.

This is high by historical standards.

But it will make our math easy.

So, let's, just assume that you can always get 10% risk, free interest in the bank.

Now, given that.

Let me throw out scenarios and have you think about which of these that you would most want.

So, I could give you $100 right? Now., That's option, 1., I, could, in one year.

Instead of giving you the $100 immediately, in one year, I could give you $109.

And then in 2 years, this is kind of option, 3, I'd, be willing to give you $120.

So your choice, is, someone walks up to you off the street.

I could give you $100 bill now, $109, bill ..., (laughing), $109, bill, $109 in a year, $120, 2 years from now.

And you know in the back of your mind, you could get 10% risk, free interest.

So, given that you don't have an immediate need for money.


Assuming that this money, you will save.


You don't have a bill to pay immediately, which of these things are the most desirable? Which of these would you most want to have? Well,? If you just cared about the absolute value, or the absolute amount of the money you would say, "Hey, look., $120, that's, the biggest amount of money." "I'm going to take that one because that's just the biggest number." But.

You probably have in the back of your mind, "Well, I'm, getting that later, so there's, maybe something I'm losing out there?" And.

You'd be right.

You'd be losing out on the opportunity to get the 10% risk, free interest.

If you were to get the money, earlier.


If you wanted to compare them directly, the thought process would be, "Well, let's, see., If I took option.


If, I got the $100." And.

If you were to put it in the bank, what would that grow to based on that 10% risk free interest? Well,? After 1 year, 10% of $100 is $10.


You would get $10 in interest.

So, after one year, you're entire savings in the bank will now be $110.

So, just doing that little exercise.

We actually see that $100 given now, put it in the bank at 10% risk.

Free, will actually turn into $110 in a year from now, which is better than the $109 one year from now.

So, given this scenario, or given this kind of situation or this option, you would rather do this than do this.

A year from now you're better off by $1.

What about 2 years from now? Well.

If you take that $100 after 1 year, it becomes $110.

Then 10% of $110 is $11.

You want to add $11 to it.

So it becomes $121.


Once again, you're better off taking the $100, investing it in the bank risk.

Free, 10% per year.

It turns into $121.

That is a better situation than just someone guaranteeing you to give the $120 in 2, years.

Once again.

You are better off by $1.


This idea that not just the amount matters.

But when you get it, this idea is called the time value of money., Time value of money.


Another way to think about it is, think about what the value of this money is over time.


Some expected interest rate.

And when you do that, you can compare this money to equal amounts of money at some future.



Another way of thinking about the time value, or, I guess.

Another related concept to the time value of money is the idea of present value, present value., Maybe, I'll, talk about present and future, value.

So, present and future.

Value, future.


So, given this assumption.

This 10% assumption, if someone were to ask you, "What is the present value of $121 2 years in the future?" They're, essentially asking you.

So what is the present value? PV stands for present value.

So,? What is the present value of $121 2 years in the future? That's equivalent to asking what type of money or what amount of money would you have to put into the bank risk free for the next 2 years to get $121?, We know, that.

If, you put $100 in the bank for 2 years at 10% risk.


You would get $121.


The present value here.

The present value of $121 is the $100.

Or another way to think about present and future value.

If someone were to ask, what is the future? Value? So,? What is the future value of this $100 in 1 year? So, in 1 year.


If you get 10% in the bank, that's guaranteed, it's future value is $110.

After 2, years, it's 2 year.

Future value is $121.

So, with that in mind.

Let me give you one slightly more interesting, problem., So, let's say that I have ..

let's, say, we're going to assume this the whole time that makes our math easy at 10% risk, free interest.

And let's say that someone says they're willing to give us $65 in 1 year.

And we were to ask ourselves, "What is the present value of this?" So.

What is the present value of this.


The present value is just asking you.

What amount of money, that if you were to put it.

In the bank at this risk free interest, would be equivalent to.

This $65? Which of.

These 2 are equivalent to you? You would say, "Well, look.

Whatever amount of money that is?" Let's call that X.

Whatever amount of money that is, times.

If I grow it by 10%, that's, literally, I'm, taking X+10%X+ ...

Let me write it.

This way.

+10%xX, ..

Let me write it.


Let me make it clear this.

Way., X+10%X should be equal to our $65.


I, take the amount I, get 10% of that amount over the year, that should be equal to $65.

This, is the same thing as 1X or we can say that 1X+10% is the same thing as 0.10X is equal to 65, or you.

Add these 2.

1.10X = 65, and if you want to solve for the actual amount of the present value.

Here, you would just divide both sides by the 1.10.

You get X is equal to ...

Let me do it.

This way.

It will be a little bit more clear about it., So, let's, divide, both sides by 1.0 and really that trailing.

Zero doesn't, matter., We're, not really too worried about the precision here because this actually exactly 10%.


This is going to be ...

These cancel out and X is going to be equal to.

Let me get the calculator.

Out, X is going to be equal to 65 divided by 1.1, $59.09, rounding it., So, X=59.09, which was the present value of $65 in one year, or another way to think about it is if you wanted to know what the future value of $59.09 is in 1 year.

Assuming the 10% interest, you would get the $65.


How does Sal Khan earn money? ›

Khan Lab School & World School

Sal Khan hopes to eventually share his learnings with educators around the world. Khan Academy generates revenue via tuition fees that it charges for attending the school. Enrolled students (or rather their parents) currently pay $29,000 in annual tuition.

How do you calculate time value of money? ›

For instance, if the present value (PV) of an investment is $10 million, and the amount is invested at a rate of return of 10% for one year, the future value (FV) is equal to: FV = $10 million * [1 + (10% / 1] ^ (1 × 1) = $11 million.

Is the amount a future cash flow is worth today? ›

Present value (PV) is the current value 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, and the higher the discount rate, the lower the present value of the future cash flows.

What is the time value of money for dummies? ›

The time value of money is the concept that money is worth more in the present than in the future due to its potential earning capacity, or alternatively, to inflation. If you invest $100 today, that money can start earning interest or dividends.

Does Khan Academy have enough money? ›

Khan Academy Expenses

In 2018 and 2019, Khan Academy was losing money on an annual basis due to an increase in expenses and decrease in Contributions and Grants. But it did have tens of millions in assets and could have sustained this situation for a few years.

How much is Khan Academy per month? ›

Learning at Khan Academy is always free! All of Khan Academy's library of trusted, standards-aligned videos, articles, practice questions, and lessons are completely free for anyone who wants to use them. We do not require contracts, have no spam, and no ads.

How much interest does $10000 earn in a year? ›

If you put $10,000 into a high-yield savings account, you can earn from $300 to $420 in a year — assuming your variable high-yield savings rate remains above 3.00%. Several banks are offering rates between 3.40% and 4.20% APY.

What is an example of time value of money? ›

Now that you understand what the time value of money is, let's look at a concrete example. Let's say someone would like to buy your car and they can offer you $15,000 for it today or $15,500 if they can pay you two years from now. TVM teaches us that $15,000 today is worth more than $15,500 in two years.

What is time value of money in Excel? ›

Excel's FV function can be used to determine the future payment for a loan based on the periodic constant payment and a constant interest rate. The syntax of the FV Function is. =FV(rate, nper, pmt, [pv],[type])

What are the disadvantages of time value of money? ›

  • Unconventional cash flows may result multiple answers.
  • If projects are mutually exclusive may lead to incorrect decisions.
  • Not always easy to calculate.
  • Difficult to interpret (particularly if the project has multiple r's)
  • IRR may have unrealistic reinvestment rate.

How is the future value of $500 invested for one year at 6 annual interest computed? ›

The future value of $500 one year from today if the interest rate is 6 percent is $530.

Why money today is worth more than tomorrow? ›

The core principle of finance assumes, given that money can earn interest, any amount of money received sooner is worth more than the same amount of money received later. In other words, a dollar today is worth more than a dollar tomorrow because you can invest the money the sooner you get it.

What are factors that affect the time value? ›

They are:
  • Number of time periods involved (months, years)
  • Annual interest rate (or discount rate, depending on the calculation)
  • Present value (what you currently have in your pocket)
  • Payments (If any exist; if not, payments equal zero.)
  • Future value (The dollar amount you will receive in the future.

What is the basic concept of the time value of money a dollar today is worth more than a dollar at any future point in time? ›

The time value of money is a concept that states a dollar today is always worth more than a dollar tomorrow (or a year from now). One reason for this is the opportunity costs of holding cash instead of investing in higher-return projects. It also arises due to inflation.

What are the four time value of money? ›

What are the four basic parts (variables) of the time-value of money equation? The four variables are present value (PV), time as stated as the number of periods (n), interest rate (r), and future value (FV).

How does Khan Academy make a profit? ›

Khan Academy makes money through advertisements, donations, tuition fees from Khan Lab School, and compensation from its SAT prep courses. Khan Academy is a nonprofit organization and relies partly on donations given through sponsors. The bulk of Khan Academy's funding is through donor support.

Who pays for Khan Academy? ›

Funding. Khan Academy is a 501(c)(3) nonprofit organization, mostly funded by donations coming from philanthropic organizations.

What is the monthly income of cute beauty Khan? ›

Beauty Khan's salary is Two lakhs per month and His lead source of income is Brand Endorsements, acting, and modeling. Khan has an approx total Networth of 7 Crores (1 million US Doller) in 2022.

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