In the last video, we learned all about the different financial institutions and the services they provide.

But one big question was left unanswered.

What is interest?

And why is it such a big deal for savings accounts and loans?

Well, in this lesson, you're gonna learn the answers to those burning questions.

By the end of this lesson, you'll be able to compare interest rates, identify preferable rates and calculate accrued interest.

To achieve that objective, we're gonna first discuss the basis of what interest is.

Then we'll look at how the two main types of interest, simple interest and compound interest work and how they're calculated.

We'll also learn about the rule of 72, a valuable tool for estimating how quickly compound interest grows.

Let's get into it.

In finances, when we say interest, we're referring to an extra charge paid for the privilege of borrowing money.

Essentially, interest is what you pay to get a loan.

Imagine Marco's got plenty of money, but Jimmy over here is flat broke.

Jimmy needs some cash bad, so he asks Marco for some money.

Marco agrees to loan Jimmy the money, but is going to charge him interest.

Jimmy will pay back Marco in small amounts until he's paid back all the money he borrowed plus a little extra as thanks for letting him borrow the money.

That extra amount is the interest.

When it comes to interest, there are two main types.

The first type is simple interest.

With simple interest, you pay interest only on what you borrowed initially.

This amount is called the principal, and your goal is to pay that off.

Simple interest is most commonly used for auto loans and personal loans.

How simple interest works isn't the only thing that makes it simple.

The formula for calculating it is pretty simple too.

To calculate how much interest accrues, you only need to multiply three things together.

The principal amount, the annual interest rate, and how many years you'll take to pay it off.

To make the equation a little more condensed, we can remove the multiplication dots since it's assumed to be multiplication anyway.

Add the principal to that, and you get the total amount that will be owed.

Although, usually, you'll see it written in this form, which factors out the P from both terms so that you only have to plug in the principal once.

Let's check out some examples of that.

Let's say you borrow $1,000 from me.

If you need to, just let me know.

I'll charge you 4% annual interest and give you two years to pay me back.

To figure out how much you'll owe me, we can use the total amount formula.

Replace the variables with their corresponding values, and evaluate.

The total amount you'll owe me is $1,080.

You can afford that, right?

This is just a basic example of simple interest, but we'll discuss it more in depth in the unit on loans.

In the last video, we mentioned savings and checking accounts, which utilize compound interest instead.

Compound interest is, well, it's not simple.

See, compound interest accrues interest not just on the principal, but also on the interest that has already accrued.

In other words, you pay interest on the interest.

The more interest you allow to accrue, the more interest will accrue the next time, and the next time, and the next.

This is known as compounding, and compounding can happen on any schedule, yearly, monthly, even daily.

It can get really out of hand really quickly, which is why it's good to have compounding interest on a savings account, and not so great to have it on a student loan.

Whereas the formula for simple interest is simple, the formula for compound interest is anything but simple.

When we say compound interest grows exponentially, we mean it.

There's an exponent right there in the formula, and that exponent is why compound interest grows faster and faster.

But let's take it one step at a time, because there are a lot of variables in this formula.

The first variable you should already recognize.

It's the principal, or the amount that you initially borrowed.

R should look familiar too.

Just like before, it's the yearly interest rate.

Oh, and T is once again the amount of years.

Okay, so most of the variables are the same.

What about this N that appears twice?

That's a major part of compound interest.

It's how often the interest is compounded each year.

By putting all of this together, we can calculate the total amount owed on the loan.

If we wanted to know only how much interest is accrued, we would then just subtract the principal from the total.

Let's do a quick example.

Let's say that, after you borrowed those $1,000 from me before, you realized you didn't wanna have to do that again.

So you deposit $1,000 into a savings account.

Remember, when you deposit money into a savings account, you're actually loaning your money to the financial institution, which means they're gonna owe you interest.

Oddly enough, your savings account has the same interest rate that I gave you, 4%.

You deposit this money, and then leave it alone for two whole years.

Basically, the terms of loaning your money to the bank is exactly the same as my loan to you, except it compounds quarterly, meaning four times a year.

With this information, do you think you'd be able to calculate the total amount?

Remember, since this is compound interest, we need the formula for the total amount from compound interest, not simple interest.

Pause the video here and see if you can calculate how much you'll end up with.

When we plug in all of our variables, this is what we get.

The easiest way to evaluate it is to type it into a calculator, just like this.

That symbol before the exponent is called a caret, and the button usually looks something like this.

You can use it anytime you need to type an exponent into your calculator.

Once we type it in, we just hit Enter, and we get this answer.

We started with $1,000 and gained $82.86 in interest.

But what happened in between?

To understand that, we have to understand the pieces of the formula.

This fraction is the interest rate per compounding period.

For a yearly interest rate of 4%, that compounds four times a year, the interest rate per compounding period is 1%.

And the exponent represents the number of times the interest has compounded.

If it compounds four times per year and we leave it for two years, it'll compound a total of eight times.

We don't have to skip straight to the end, though.

We can actually track the total amount every time it compounds.

All we have to do is change the exponent to how many times it would have compounded at that point.

After three months, it will compound for the first time.

So we can just use an exponent of one to find that it will now have $1,010.

After another three months, it compounds a second time.

So the exponent is two.

And now the account is up to $1,020.10.

Why don't you pause the video now and try filling in the remaining amounts in your notes?

As the compounding periods continue, the value of the account continues to grow.

Did you notice anything about how quickly it grows?

Each time interest accrued, it was more than the last time.

This is why compound interest is so cool.

It grows faster the longer you let it accrue.

This is worth noting, however, that this is a pretty unrealistic example for a bank account.

A bank simply isn't going to give you that much free money.

A bank account would grow more like this.

Yeah, that's right.

The bank will give you a whopping two cents every month.

Remember, banks are there to make money, so their savings accounts have super low interest rates.

You're much more likely to find high interest rates on loans you borrow and have to pay back, like student loans or credit card loans.

In fact, let's do a little experiment with student loans.

Let's compare simple interest with compound interest.

Let's say you get a $5,000 loan your freshman year of college with a yearly interest rate of 5%, which you wait to start paying back until you graduate four years later.

Of course, compound interest has one extra variable to account for.

So let's make it easy and say it only compounds once a year.

With these terms, the simple interest loan will reach a total of $6,000 after four years, meaning it accrued $1,000 in interest.

The compound interest, though, will come out to $77 more, and that's just with it compounding once a year.

Most student loans actually compound daily.

That's 365 times every year.

So a more realistic estimate for this loan would be $6,106.93, over $100 more than if it were simple interest.

That's a lot of extra money you're paying on top of repaying the money you borrowed, and that's just for one semester of college.

Because of the speed at which compound interest grows, it's relatively easy to double the principal amount of an account that utilizes compound interest.

We can use the rule of 72 on any loan with compounding interest to estimate how long it will take to double in value.

The rule of 72 is pretty simple.

You take 72 and divide it by the annual interest rate.

Say the interest rate is 8%.

Then the value will double in approximately nine years.

The complicated part of the rule of 72 is that it's most accurate around 8%.

From there, every time the interest rate goes up by 3%, the number 72 should be increased by one.

If the interest rate increases another 3%, then the number on top grows by one again, and it's the same thing going the other way.

Every 3% down is one less than 72.

Let's use the rule of 72 for this example.

If an account has an interest rate of 3%, what number would we use on top?

3% is closer to 2% than to 5%, so we'll drop 72 twice down to 70.

70 divided by three, since the interest rate is 3%, tells us this amount will double in approximately 23 years.

What about an interest rate of 15%?

Pause the video now and try using the rule of 72 to find how long it will take to double.

15% is a little more than two jumps above 8%, so we'll bump the 72 up to 74, which means the value will double in about five years.

If you're offered a loan with a 15% compounding interest rate, run away, quickly.

Because compound interest is way better for accounts where you're getting money, like savings accounts or investment returns, but for accounts where you're paying money back, like loans or credit cards, you'll end up paying less if it's simple interest.

For a quick recap, simple interest is calculated using a simple formula.

Compound interest uses a less simple formula with an extra variable for how often it compounds per year.

Simple interest is designed to grow at a steady rate for its term, while compound interest grows exponentially over time.

For compound interest, you can use the rule of 72 to estimate how many years it will take to double the loan value.

But it's most accurate at around 8% interest, so you'll have to adjust it for higher or lower interest rates.

As we continue through this financial literacy course, interest is going to come up a lot.

Now that you understand financial institutions and interest,

I'd like to ask for your help.

Remember how my friend Caroline was having some money issues?

I need your help comparing financial institutions in her city to find the best place for her to open a savings account.

She's gonna owe us big time.

See you next time.

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