As you saw in the previous example, compound interest grows faster than simple interest by adding the interest back to the principal at certain times. Compounding quarterly is more valuable than compounding annually. Compounding monthly is even more valuable than compounding quarterly. The most valuable situation would have the interest compounding continuously - that is, every instant. As quickly as interest can be calculated, it is returned to the account and adds to the principal. This is obviously only theoretical. Using some calculus, mathematicians have developed a formula that simulates interest that is compounded and added back to the account in a continuous stream. This formula, which is used to calculate continuously compounding interest, is: A=Pert{\displaystyle A=Pe^{rt}} The formula for the continuously compounding interest looks similar to the early situations, with some slight differences. The variables for the formula are: A{\displaystyle A} is the future value (or Amount) of money that the loan will be worth after compounding the interest. P{\displaystyle P} is the principal. e{\displaystyle e}. Although this looks like a variable, it is actually a constant number. The letter e{\displaystyle e} is a special number called "Euler's constant," named for the mathematician Leonard Euler who discovered its properties. Most advanced graphing calculators have a button for ex{\displaystyle e^{x}}. If you press this button, with the number 1, to represent e1{\displaystyle e^{1}}, you will learn that the value of e{\displaystyle e} is approximately 2.718. r{\displaystyle r} is the interest rate per year. t{\displaystyle t} is the term of the loan, measured in years. Banks typically use continuously compounding interest on home mortgage loans. Suppose you want to borrow $200,000 at a rate of 4.2% for a 30 year mortgage. The variables that you will use for the calculation are, therefore: P=200,000{\displaystyle P=200,000} e{\displaystyle e}, again, is not a variable but is the constant 2.718. r=0.042{\displaystyle r=0.042} t=30{\displaystyle t=30} Apply the values to the formula to calculate the amount of interest that you will owe on the 30 year loan. A=Pert{\displaystyle A=Pe^{rt}} A=2000002.718(0.042)(30){\displaystyle A=200000*2.718^{(0.042)(30)}} A=2000002.7181.26{\displaystyle A=200000*2.718^{1.26}} A=2000003.525{\displaystyle A=200000*3.525} A=705000{\displaystyle A=705000} Notice the enormous value of compounding interest continuously.
++++++++++
One-sentence summary -- Understand continuously compounding interest. Know the variables for calculating the interest. Know the details of your loan. Use the formula to calculate the interest.

Add the ingredients and stir them thoroughly until the mixture appears to be all one color. Pour the sauce into another bowl through a fine sieve to strain out any large chunks. Use a wooden spoon to gently force the liquid through. If any chunks remain in the sieve, throw them out. This will give the ingredients a chance to meld and create a single flavor. Pour the sauce into an airtight container and leave it in the fridge for at least 2 hours before serving. If you are using the sauce for a glaze or marinade, there's no need to bring it to room temperature, since it will be heated in the process of cooking or grilling. However, if you're using it for a dipping sauce, take it out of the fridge at least 30 minutes before serving to bring it to room temperature. Since this sauce is made with preserved fruit instead of fresh, it will last at least 1 month if refrigerated. Store it in an airtight container in your fridge.
++++++++++
One-sentence summary -- Put all the ingredients in a large mixing bowl and stir them with a whisk. Strain the mixture through a sieve. Refrigerate the sauce for at least 2 hours to let the flavors combine. Bring the sauce to room temperature 30 minutes before serving it. Store any unused sauce in the fridge for up to 1 month.

If you aren't already logged in, do so with your phone number (or email address) and password. To text or call your driver from within the app, you'll first have to order a ride. You'll see this at the bottom of your screen. Your choices include: Call - Call your driver from within the Uber app. Text - Send your driver a message in the Uber app. If you decide to text, type in your message and tap Send. If your Uber driver is currently driving, they likely won't get back to you immediately.
++++++++++
One-sentence summary -- Open the Uber app. Order an Uber. Tap your driver's name. Tap Contact. Decide on a contact method. Tap Call or Text. Wait for a response.

Put cup (60 mL) of chicken broth (you may choose a reduced-sodium variety, if desired), teaspoon (0.5 mL) of onion powder, teaspoon (0.5 mL) of garlic powder, and a dash of pepper into a frying pan. Stir to combine, and heat the mixture until it boils. Mix in 5 ounces (150 g) of washed and trimmed fresh arugula. Make sure the arugula is evenly coated in the broth and spice mixture by using tongs to toss the greens in the liquid. Keep the pan on the burner for another minute or two to allow the arugula leaves to wilt. If needed, add another splash of chicken broth to keep the arugula wet. Stir the mixture occasionally. All you need to do now is turn off your burner, remove the pan from heat, and serve the arugula. You can have it as a side dish with a meal, put it on mashed potatoes, or use it as a salad topping.
++++++++++
One-sentence summary --
Heat chicken broth and spices on the stovetop. Add arugula to the pan. Stir occasionally and let it wilt. Remove the pan from heat and serve the dish.