user: Q: 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=200000∗2.718(0.042)(30){\displaystyle A=200000*2.718^{(0.042)(30)}} A=200000∗2.7181.26{\displaystyle A=200000*2.718^{1.26}} A=200000∗3.525{\displaystyle A=200000*3.525} A=705000{\displaystyle A=705000} Notice the enormous value of compounding interest continuously.
A: Understand continuously compounding interest. Know the variables for calculating the interest. Know the details of your loan. Use the formula to calculate the interest.

Q: Use 6 ounces/180ml if you are certain of the freshness of the starter. When in doubt, use a full cup of buttermilk as starter.  Shake thoroughly to mix. Label it with the date. If you find it takes longer than 36 hours, the starter was no longer active (the bacteria had died).  The buttermilk may or may not be tasty if it takes longer than 36 hours but it can still be used for baking. This happens because the bacteria have fermented the milk, and the lactic acid is causing the milk proteins to thicken. Refrigerate immediately
A: Add a bacterial starter of 6 to 8 ounces/180-235ml of active fresh cultured buttermilk to a clean quart jar. Fill the rest of the jar with fresh milk. Screw the lid on securely. Let it sit out in a warm part of the room until thickened, which should take about 24 hours. Check to make sure the thickened buttermilk coats the glass.

Q: Own up to your mistakes and apologize to your parents right away. Take full responsibility for your actions without blaming someone else. Share your regret and tell them how it will be different next time. For example, say, “I promised I’d be home at 10 and I wasn’t. I prioritized my own fun over your rules. I’m sorry I stayed out and it won’t happen again.” Your parents might feel disappointed, upset, or angry, so let them be upset. They won’t get over broken trust right away. Give them some time to cool down and recover. In the meantime, be on your best behavior. Don’t breach their trust any more. If you’ve made a mistake, ask how you can regain their trust back. Being proactive by asking might show them that you’re mature and want to make things right. However, be prepared. They might ask you to do more chores or show more responsibility with something else. For example, say, “I know I let you down when I lied about going out with that friend. How can I get your trust back?”
A:

assistant: Give a sincere apology. Give it some time. Ask how you can regain their trust.