Marilee takes all the money from her piggy bank and puts it into a savings account at her local bank. The bank promises an annual interest rate of 2.5% on the balance, compounded semiannually. How much will she have after one year if her initial deposit was $400?
A) $390.06
B) $420.25
C) $410.06
D) $420.50

Which situation would be represented by a discrete probability distribution?
A) the thickness of an item
B) the lifespan of a fruit fly
C) the temperature of a solution
D) number of complaints a company receives in a day

The amount of money in a bank account that is compounded yearly can be represented by the function A(y) = P(1 + r)y, where P is the amount initially deposited, r is the annual interest rate expressed as a decimal, and y is the number of years that have passed since the initial deposit. $2,700 was deposited 14 years ago into a bank account that is compounded yearly, and no additional deposits or withdrawals have been made. If the amount of money now in the bank account is $7,930.42, what is the annual interest rate?
A) about 5%
B) about 6%
C) about 7%
D) about 8%

Which type of data is BEST described by a continuous model?
A) points scored
B) pages in a book
C) children in a family
D) temperature of an engine

2 Answer

  • A=400×(1+0.025÷2)^(2)

  • Answer:

    C) $410.06;  D) number of complaints a company receives in a day ; D) about 8% ; D) temperature of an engine

    Step-by-step explanation:

    The equation for compound interest is

    [tex]y=p(1+\frac{r}{n})^{nt}[/tex], where p is the amount of principal, r is the interest rate, n is the number of times the interest is compounded yearly, and t is the number of years.

    Our principal is 400; r is 2.5%, which is 0.025 (2.5% = 2.5/100 = 0.025); n is 2 since it is compounded semiannually; and t is 1:

    [tex]y=400(1+\frac{0.025}{2})^{2\times 1}\\\\=400(1+0.0125)^2\\\\=400(1.0125)^2=410.0625 \approx 410.06[/tex]

    A discrete probability distribution will be of something that has distinct values, with no values inbetween.  The thickness of an item has fractions and decimals, not distinct values.  The lifespan of a fruitfly can be in hours, which can be broken down to minutes and seconds; these are not distinct values.  The temperature of a solution can be expressed in decimal form; these are not distinct values.  However, the number of complaints a company receives in a day has to be distinct values.  You can have 1 complaint or 2, but not 1.5.  This means the answer is D.

    Plugging our numbers into our equation, we have


    Dividing both sides by 2700,


    Next we take the 14th root of each side, to cancel the exponent of 14.  To do this we can raise it to the 1/14 power:


    Subtract 1 from each side:

    1.079999984-1 = 1+r-r

    0.079999984 = r

    0.08 ≈ r

    This is about 8%.

    A continuous model includes not only distinct values but values between them.  The number of points scored would only be distinct values, no values between; you will not score 2.5 points, only 2 or 3.  The pages in a book are distinct; you cannot have 2.5 pages, either 2 or 3.  The number of children in a family is distinct; you cannot have 2.5 children, either 2 or 3.  However the temperature of an engine can be different fractions or decimals between distinct temperatures; this makes it continuous.