Sharafat Shaman

The zip function returns a tuple iterator, which is used to find the values at the same position of two or more iterable items.

The name of the function is zip, which is a visual word. Think of the two parts of a zipper that have their teeth interlocked as it closes.

We see it with an example when we return to our field. Imagine we have a list with the values and another with the values.

We will get an iterator with the values when we pass these two lists as arguments.

The first position of each of the lists has a tuple that combines the values of the first position.

The second position of the lists has another tuple with the values. You know, in the third.

We can use the iterator to access the values of both lists.

I present two different versions, one in which we directly access the iterator and the other in which we directly access the values.

If we execute the previous code, either of the two loops will generate the same result on the screen.

It is very comfortable.

If you need to save the list of tuples, you can call the list function in this way. If the combined list is displayed on the screen, we will get the following:

The enumerate function can be used if we need more control over the iteration.

The enumerate function returns a tuple iterator with a counter and a piece of data from the collection we are traversing. In the same loop, the list is used to get the index and its data.

The truth is that this function is very convenient and doesn't have to be defined or controlled. We show an example so that you understand it better.

We get the following result when we run the above code

In this example, you will say that there is only one list and that it is about traversing two lists at the same time. There's a trick. We have an index variable that tells us the position of the current element in the loop. We can use that index to find the value of the other list.

And we will get as a result.

This option gives us more flexibility because we can use the index for whatever we need to. We need the index since the values we get through the zip or enumerate are copies of the values of the lists.

If we want to walk the walk in a more classical way, we can do that. I have two alternatives for you.

The first option is to use a for loop that loops through the numbers between 0 and the length of the lists. The len function gives us the length of the lists and the range function, so we will use this to do this.

In each loop of the loop, we have each of the indexes of the lists between 0 and their length. We can use that index to access the data.

The most flexible option is the one that uses a while loop and controls the index variable to make sure it takes the position values of the lists.

We do it in a certain way.

The two forms are more flexible than the previous ones because the index allows us to make the traversals not be parallel, that is, element by element and in the same order, if we include the option with enumerate.

For example, we might want to go back and forth between a list element by element and another two elements by two, or we might want to go back and forth between a list element by element and another two elements by two.

This type of tours are more comfortable if we have the value of the indices.

There are many times when we need to go through multiple lists at the same time.

The truth is that it gets more complicated because I have told you that everything is applicable to multiple lists.

The zip function can take more than two lists as parameters and return a tuple with the values of one position from all the lists. The example is:

If we need the values of the indices in addition to the route, we can access multiple lists within the body of the loop, the same way we can access multiple lists if we want to modify the value of the lists.

Combining the use of enumerate and zip is a possibility.

But first, let's define our terms. The easiest way to think of CAGR is to recognize that over a number of years, the value of something may change—hopefully for the better—but often at an uneven rate. The CAGR provides the one rate that defines the return for the entire measurement period. For example, if we were presented with year-end prices for a stock like:

From year-end 2015 to year-end 2016, the price appreciated by 20% (from $100 to 120). From year-end 2016 to year-end 2017, the price appreciated by 4.17% (from $120 to $125). On a year-over-year basis, these growth rates are different, but we can use the formula below to find a single growth rate for the whole time period.

CAGR requires three inputs: an investment’s beginning value, its ending value and the time period (expressed in years). Online tools, including Investopedia’s CAGR calculator, will give the CAGR when entering these three values. The formula is:

Plugging in the above values we get [(125 / 100)^(1/2) - 1] for a CAGR of 11.8%. Despite the fact that the stock's price increased at different rates each year, its overall growth rate can be defined as 11.8%.

One mistake that's easy to make in figuring CAGR is to incorrectly count the time period. For instance, in the above example, there are three calendar years. But since the data is presented as year-end prices, we really only have two completed years. That's why the equation reads 1/2, not 1/3.

Now, let's say we had a stock whose annual price data was presented in percentage, instead of dollar, terms:

In this case, the data is being shown from the beginning of the year, as in, the entire yearly return in 2015 (10%), the entirely yearly return in 2016 (15%), and the entire yearly return in 2017 (-4%). So when calculating CAGR, we would actually be working with a time period of three years.

We would need to convert these percentages into actual beginning and ending values. This is a good opportunity to use a spreadsheet, since it's easy to add a helper column to convert the percentages into values.

The math formula is the same as above: You need ending values, beginning values and a length measured in years. Although Excel has a built-in formula, it is far from ideal, so we will explain that last.

Financial modeling best practices require calculations to be transparent and auditable. The trouble with piling all of the calculations into a formula is that you can't easily see what numbers go where, or what numbers are user inputs or hard-coded.

The way to set this up in Excel is to have all the data in one table, then break out the calculations line by line. For example, let's derive the compound annual growth rate of a company's sales over 10 years:

The CAGR of sales for the decade is 5.43%.

A more complex situation arises when the measurement period is not in even years. This is a near-certainty when talking about investment returns, compared to annual sales figures. The solution is to figure out the total completed years and add them to the partial year (called the stub year).

Let's take the same figures, but have them be stock prices:

The CAGR is superior to other calculations, such as average returns, because it takes into account the fact that values compound over time.

On the downside, CAGR dampens the perception of volatility. For instance, let's say you have an investment that's posted these changes over three years:

That's actually a 5% CAGR, but the year-over-year volatility in those returns is huge. The reality is many investments experience significant short-term ups and downs, and by smoothing them out, so to speak, the CAGR might give a numerically accurate, but emotionally misleading impression of performance. It's like a map that correctly informs you your destination is only five miles away, without indicating the bumpy condition of the road.

CAGR is also subject to manipulation depending on the measurement period, which is ultimately (and often arbitrarily) selected. A CAGR can be shifted to avoid a negative year in the stock market (such as 2008), or to include a year of strong performance (such as 2013).

Suppose you subscribe to a service that monitors your credit. In that case, you already have enough help to get the answers to the questions above. But, if you are buying a car on your own, you’ve got your work cut out, as there is a lot of seemingly conflicting data out there.

For example, there are multiple credit scores on one side and the FICO score on the other. FICO scores themselves have several versions. Then, there are the three credit bureaus. Each one uses its score system, which makes an auto loan credit check sound like rocket science. Not to mention that car dealers might be in contact with all three credit agencies or perhaps just one of them when assessing your creditworthiness.

Worry not. We’ve gathered all the tips and tricks you’ll need to turn those credit checks to your advantage. By the time you’re done reading, your expertise will rival that of the auto loan companies.

Let’s answer first the question of which credit score is used to buy a car.

When buying a car (unless you already have the whole sum you’ll need) you’ll have to work with lenders. More than 90% of car lenders use the FICO credit score. An individual FICO score results from an algorithm that factors in many aspects of your credit history, such as unpaid debts, the number and types of open loan accounts, and how long you have kept these accounts open. Then, there is the percentage of the total credit you’ve used, new credit requests, potential bankruptcy reports, foreclosure, and debt collections.

We’ve mentioned the credit score first because every time you apply for an auto loan, a FICO score check will be performed to determine your creditworthiness. Credit bureaus are intrinsically important to the overall story. Still, as a potential car buyer, you should know your credit score beforehand.

The most straightforward way is to go to myfico.com and ask for the 1B report. The service isn’t free, but the good thing is that this report is very exhaustive: It includes 28 industry-specific scores, and one of them is the auto credit score you need.

Another way to obtain your credit score is to check your monthly billing statements from the company that issued your credit card. Bank of America, Citibank, and American Express offer free FICO score status for their clients. You can also get your FICO score via the Discover Credit Scorecard program that is free for all users. You only need to leave your Social Security number along with a few other personal details.

FICO scores go from 300 to 850. The higher your score, the better your chances of getting favorable loan terms. Good score ratings go from 670 upward, with most credit holders having a score between 600 and 750.

It’s important to know which credit bureau is most used for auto loans, so we’ll cover that in a later section of this article, but your FICO credit score will affect you more. Buying a car with a bad credit score means you’ll have fewer options to choose from when looking for an auto loan to finance your new car purchase.

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You've got a bag full of brand new equipment and you're ready to get out on the ice to show everyone what you're made of. Just one problem: your new skates are so stiff you can barely feel your ankles.

You think about returning them to the store, assuming you can find the jaws of life to get them off your feet. But there are a few simple steps to help you break in those skates.

Buy the right skates

If you buy your skates in a specialty hockey shop, don't hesitate to ask questions and see if it's possible to get any adjustments made. Some skate shops may even throw in free sharpenings and adjustments over the life your skates.

Heat and Bake

One of the most popular in-store adjustments involves using heat. If they prefer not to do it at the store, some people use a hair dryer, which can be applied to the boot of the skate for 2-3 minutes before trying the skate on to mold it to their foot. Some specialty shops even offer to help you "bake" your skate before you leave the store, so feel free to ask about that.

Bear in mind that too much heat can potentially result in a premature breakdown of the boot of your skate. Some players also just prefer to break in skates the more natural way.

The Hard Way

As with most tasks, there is no substitute for hard work when it comes to breaking in new skates. There are a few short cuts, but there's nothing quite like molding a skate to your foot by simply lacing up and taking the ice, which is ideally what you want to do anyways.

The first skate will definitely be arduous and your feet will likely feel sore both during and after. But by your third skate you should notice greater ease when putting on and using your skates. By the time you've enjoying about a half-dozen skates, you should notice a clear difference when it comes time to finding a snug fit when you lace up.

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