# What is Interest?

Interest is the price of borrowing money — What you pay to use someone else’s or what you charge others you lend to.

## 🤔 Understanding interest

When you borrow money, there are several reasons the lender may not want to give it to you for free. For one thing, the same amount today will probably be worth less in the future, since prices are likely to rise due to inflation. The lender could be earning a return on the money by investing it if he weren’t giving it to you. And he faces the risk that you won’t pay it back. To make up for these downsides, lenders usually charge interest — It’s the cost of borrowing money. You can earn interest by putting your money in things like savings accounts or certificates of deposit (CDs), or you may pay interest on a student loan, mortgage, or credit card balance. There are several ways to calculate interest, so make sure you read the fine print.

Imagine you borrow $200 for one year at an interest rate of 3%. That means you will pay back the $200 you originally borrowed (known as the principal) and also $6 in interest at the end of the term. Say your friend applies for the same loan from the same institution but gets an interest rate of 10%. At the end of one year, she would pay $200 plus $20 in interest. The same loans can come with different interest rates depending on market rates and how risky the lender perceives the borrower to be. These are small numbers, but with bigger loans and a longer time period, interest can make a big difference!

## Takeaway

Just like in preschool, people don’t always like to share...

Especially, when there are no guarantees they’ll get their stuff back. Interest gives the lender the confidence they need to part with their money for a while and take on all the risks that entails.

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## What is interest?

Interest is the cost of borrowing money, usually expressed as a percentage. Interest rates fluctuate over time, and the specific rate you might earn or pay is determined by many factors. One important consideration is the going rates of the day, which are influenced by the rate the Federal Reserve, the country’s central bank, charges other banks to borrow money. The Federal Reserve is typically reactive to the economy and interest rate environment — It often lowers rates to spur economic growth and fight unemployment, and raises them when the economy is doing well. In determining your individual rate, your lender will also consider how risky you are as a borrower. That involves things like your credit history, your level of debt compared to your income, and negative financial events in your past, like bankruptcies. Interest can be calculated in different ways, but the purpose is always the same — To make the lender comfortable with giving you money in light of the opportunity cost and risks involved.

## How does interest work?

The amount of interest you pay (or earn, if you’re the lender) depends on four factors:

- The amount of money being borrowed
- How long it’s being borrowed for (the length of the loan)
- How often interest is calculated (daily, monthly, annually, etc.)
- The interest rate

All things being equal, the more you borrow, the more you’ll pay in interest, since interest is calculated as a percentage of the loan amount. Generally speaking, borrowing will also cost more the longer you hold the loan, since there is more time for interest to pile up.

The frequency of the interest calculation also impacts the total amount you owe. We’ll get into the specifics below, but basically, the more often interest is calculated, the higher the final amount will be. So 3% calculated monthly will result in more interest than 3% calculated annually, even if the original loan amount and term of the loan are the same.

The higher the interest rate, the more interest you’ll pay — a 10% interest rate will result in more interest than a 5% rate, if other factors are equal. The catch is that when you’re comparing interest rates you need to make sure you’re comparing apples to apples. As we just covered, 3% interest monthly is different than 3% annually.

APR (Annual Percentage Rate) is the most common interest formula used in consumer finance. Expressed as a percentage, this is likely the number you’ll see when taking out a credit card, car loan, or mortgage. APR includes not only interest, but typically also other fees associated with the loan, per year. So, if a payday lender adds a $10 arrangement fee, that will probably be included in APR.

APY (Annual Percentage Yield) is also expressed annually, but unlike APR, it also factors in how often interest is calculated. So if your interest rate is 3% annually, with no additional fees, your APY is 3%. If your interest rate is 3% calculated monthly, then your APY is actually 3.04%. (The formula for APY is (1 + r/n)n – 1 where r is the interest rate and n is how often interest is calculated.)

## What is the difference between simple and compound interest?

You can generally figure out how much interest you owe in a given period by multiplying the interest rate by the amount you borrowed. But is the amount borrowed the original principal or what you owe today, now that interest has been piling up? That’s the difference between simple and compound interest.

Calculating simple interest means just multiplying the interest rate by the principal (or the original amount borrowed). Compound interest involves multiplying the interest rate by the principal plus any interest that hasn’t been paid yet. That’s why the more frequently interest is calculated, or compounded, the more interest will be paid or earned overall.

Imagine borrowing $100 for 12 months at an interest rate of 12% per year. If you’re dealing with simple interest, the interest you owe at the end of the year would be 0.12 * $100 = $12. So in all you would pay $100 + 12 = $112.

Now assume the 12% is compound interest, and it’s compounding monthly. This means at the end of each month interest will be calculated based on the amount outstanding at that time ($100 plus any interest). After one month you’d owe roughly $101 ($100 x (12% per year divided by 12 months)). After the second month you’d owe interest on $101, not $100. After the third month you’d owe interest on $102, and so on. (These numbers are rounded to the nearest dollar for clarity.)

## How is interest calculated?

To figure out how much interest you’ll pay, you need to know four things, as we discussed earlier:

- The principal or amount of money being borrowed (P)
- The length of the loan (t)
- How often interest is calculated (n)
- The interest rate (i)

To help us walk through the most common interest calculations, let’s imagine the following scenario:

You take out a $1,000 loan (P) for two years (t) at a rate of 5% (i). If there is no compounding, you can use the simple interest formula, which is:

P(1 +rt)

$1,000(1+ (.05)(2)) = $1,100

So, at the end of two years you would owe $1,100 — That’s the $1,000 principal plus $100 of interest.

Now imagine the 5% compounds monthly.

The formula for compound interest is:

P(1 + i/n)^nt

$1000(1 + .05/12)^(12*2) = $1,104.94

Note: You can also use this calculation if there is no compounding — just put ‘1’ as n.

## What is a good interest rate?

There is no firm definition of a "good" interest rate. In general, lenders want the highest possible rate, while borrowers want the lowest. The rate you can get will depend on a number of factors, including your creditworthiness and market rates.

If you’re offered an interest rate, how do you know whether it’s good? A great place to start is to check out average market rates. For instance, using Bankrate.com, you can find the current rates on a variety of products. As of October 2019, here are some average rates:

- 30-year fixed mortgage rate: 3.96%
- 15-year fixed mortgage rate: 3.26%
- 60-month new car loan rate: 4.61%
- 48-month new car loan rate: 4.57%
- Variable credit card rate: 17.56%
- Student loans: 2.14% – 5.74%

If you’re offered a rate above the current market average, you can be fairly confident that it’s a good rate.

One of the worst interest rates you can get, as a borrower, is on short-term emergency products, such as payday loans and cash advance loans. The Federal Trade Commission warns that it’s not uncommon for these to have APRs as high as 391%!

The free stock offer is available to new users only, subject to the terms and conditions at rbnhd.co/freestock. Free stock chosen randomly from the program’s inventory. Securities trading is offered through Robinhood Financial LLC.