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Altrecite5 6 W Explanations

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Subject
Mathematics
School
Homewood Flossmoor High School
Type
Homework
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Solutions for Week 5 of Recitation/Week 6 of classes
Question 1: Why did you choose to do the alternate assignment instead of attending recitation?
(It’s not required to attend, and you can get full points by completing this assignment, I’m just
curious.)
(Opinion based)
Question 2: Define each of these terms in your own words: Principal, Simple Interest,
Compound interest, annual percentage yield (APY), and continuous compounding interest.
Principal is the initial amount of money or any other numeric value that is being
prepared to become compound.
Simple interest is a formula of calculating an amount with interest that only factors in
the interest rate, the principal amount, and the amount of time passed.
Compound interest is a formula that is more complex than the simple interest, which
includes all the variables of the simple interest, along with the amount of times that the
interest is applied per time period.
Annual Percentage Yield (APY) is the actual rate of return that factors in the effects of
compound interest instead of simple interest.
Continuous compounding interest is the highest point that the compound interest can
reach over a long period of time.
Question 3: Here are three formulas for calculating interest:
A = P + ((APR x P) x Y)
A = P x (1 + APR/n)nY
A = P x e(APR x Y)
Identify what kind of interest each one helps you calculate and what each of the variables
represent. (“x” indicates multiplication)
This formula helps to calculate for the interest paid, using simple interest:
A represents the total balance after time
P represents the principal/initial amount
APR represents the interest rate
Y represents the number of years
This formula helps to calculate for the interest paid a number of times per year, using compound
interest:

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A represents the total balance after time
P represents the principal/initial amount
APR represents the interest rate
N represents the amount of times the interest is compound per year
Y represents the number of years
This formula is used to calculate the interest paid using continuous compounding:
A represents the total balance after time
P represents the principal/initial amount
APR represents the interest rate
Y represents the number of years
e represents Euler’s number
Question 4: Convert the following expressions into a form that is equivalent but no longer
contains a fractional exponent: 161/4, (-4)1/2, -41/2, 26/3, and 82/3. (if you’re typing, you may
just say for example, “square root (#)” and you can hold “ctrl” “shift” “=” to make an exponent or
just use the ^)
Question 5: From Q4, are there any that do not yield a real number? Which one(s) and why?
(-4)^½ did not yield a real number because in order to obtain the square root of a negative
number, the imaginary number i, which is equal to the square root of -1, had to be inserted in
order to obtain -4.
Question 6: Suppose you invest $1000 into a savings account that offers 7% annual interest
rate. After 9 years, calculate how much you’d have if the 7% is simple interest. (show work,
round to nearest cent if necessary)

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Solutions for Week 5 of Recitation/Week 6 of classes Question 1: Why did you choose to do the alternate assignment instead of attending recitation? (It’s not required to attend, and you can get full points by completing this assignment, I’m just curious.) (Opinion based) Question 2: Define each of these terms in your own words: Principal, Simple Interest, Compound interest, annual percentage yield (APY), and continuous compounding interest. ● ● ● ● ● Principal is the initial amount of money or any other numeric value that is being prepared to become compound. Simple interest is a formula of calculating an amount with interest that only factors in the interest rate, the principal amount, and the amount of time passed. Compound interest is a formula that is more complex than the simple interest, which includes all the variables of the simple interest, along with the amount of times that the interest is applied per time period. Annual Percentage Yield (APY) is the actual rate of return that factors in the effects of compound interest instead of simple interest. Continuous compounding interest is the highest point that the compound interest can reach over a long period ...
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Anonymous
Very useful material for studying!

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