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Tutor profile: Matthew A.

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Matthew A.
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Questions

Subject: World Geography

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Question:

What are the names of the Great Lakes?

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Matthew A.
Answer:

The lakes in North America referred to as the Great Lakes are Lake Superior, Lake Michigan, Lake Huron, Lake Erie, and Lake Ontario.

Subject: Basic Math

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Question:

Solve (12 x 5(4-3))/2 - 6 + 3² using the order of operations.

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Matthew A.
Answer:

The order of operations tell us to follow the acronym PEMDAS. This means to address parentheses, exponents, multiplication, division, addition, and subtraction as they come from left to right. We first notice there are two parentheses. By addressing the inner parenthesis first we can work on the bigger one after. So, we subtract 4-3 and end up 1. Now, we have (12 x 5(1))/2 - 6 + 3². Within the larger parenthesis we now have 12 x 5(1). We multiply across and get 60. We can now simplify the expression to 60/2 - 6 + 3². Our next step is to see if there any numbers with exponents. There certainly is with 3² so we can calculate that by 3 x 3 which equals 9. We are now left with 60/2 - 6 + 9. With no more exponents, we look for multiplication and division as it comes from left to right. We find 60/2 which results in 30. We are now down to 30 - 6 + 9. With only addition and subtraction left in the problem, we can simply subtract or add as it comes from left to right. 30 minus 6 is 24 and then 24 plus 9 results in 33. As a result, (12 x 5(4-3))/2 - 6 + 3² = 33

Subject: Personal Finance

TutorMe
Question:

What is the difference between APR (Annual Percentage Rate) and APY (Annual Percentage Yield)?

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Matthew A.
Answer:

APR (Annual Percentage Rate) refers to the simple interest rate applied to a balance while APY (Annual Percentage Yield) takes into account the effect of compounding on the balance. In simpler terms, with APR, the "rate" at which interest accrues on a balance remains the same each year. With APY, as the amount of the balance increases, so does the interest that is added to that balance. This results in a much higher accrual rate over time. When you owe money, APY is your worst enemy, but when you're earning interest, APY is your best friend. For example, imagine you invest $1,000 in a high yield savings account with an interest rate of 3%. Taking the APR into account, you would earn $30 per year in interest or a total of $90 over three years. This would give you a balance of $1,090.00. However, with that same $1,000 starting balance and that 3% interest rate compounded each year, at the end of year 3 you would have $1,092.73. Higher balances with higher interest rates over a longer period of time drastically diverge the ending balances between APR and APY.

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