Find the interest rate needed for an Investment of $4,000 to grow to an amount of $5,000 in 4 yr If interest is compounded continuously. Please round the answer to the nearest hundredth of percent. A)...

Solution: The formula to calculate the compound interest is
(


)
P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year
Given P=$4000, A=$5000, t=4 years, n=1(since the interest is compounded annually).
Therefore,
(


)
( )
( )



( )
Therefore the interest rate needed is 5.7%
Answer: B)
Solution: Given equations are and
Using the method of substitution,
( )
Substituting back, we get ( )
Therefore the solution to the system of equations is (3, 2) and this is the only solution.
Answer: A)
Solution: In set-builder representation of a set, all the elements of the set have a single
common property that is exclusive to the elements of the set i.e., no other element outside the
set has that property.
In set-builder form, we describe an element of a set by a symbol x (though we may use any
other small letter), which is followed by a colon (:). After the colon, we describe the
characteristic property possessed by all the elements of that set.
The given set is * +, which can be rewritten as
* ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )
( ) +
Therefore the set builder form of the given set can be written as
* | +
Answer: B)
Solution: The formula to calculate the compound interest is
(


)
P = principal amount (the initial amount you borrow or deposit)
r = annual rate of interest (as a decimal)
t = number of years the amount is deposited or borrowed for.
A = amount of money accumulated after n years, including interest.
n = number of times the interest is compounded per year
Given A=$40,000, t=4 years, r=8%, n=12(since the interest is compounded monthly).
Therefore,
(


)
( )
( )
( )
Therefore the present value is $29076.82.
Answer: C)
Solution: Given F = {2, 4, 6} and G = {2, 3}
Subsets F and G have 1 element in common. If the die shows 2, both events F and G will
have occurred at the same time and therefore F and G are not mutually exclusive
Answer: B)
Solution: A matrix is in row-reduced form if:
 The first non-zero entry ("leading entry") in each row is a 1;
 The column of every leading entry is clear; that is, the other entries in the column are
all zero;
 The rows are arranged so that the leading entries go from left to right as you go down
the rows. Further, rows of zeros (if any) must be placed at the bottom.
Since the given matrix satisfies the above conditions, the matrix is in row reduced form.
Answer: B)
Solution: The plot of annual sales versus the year is shown below.
A straight line is drawn joining the points corresponding the first and fifth year which are
(1, 5.8) and (5, 9).
The equation for the line joining these two points can be written as
( ) (


) ( )
( ) ( )
( )
Answer:
5.8 6.1
7.2
8.3
9
0
1
2
3
4
5
6
7
8
9
10
0 1 2 3 4 5 6
y

x
Annual Sales every Year
Solution: The formula to calculate the simple interest is




P = principal amount (the initial amount you borrow or deposit)
R = annual rate of interest (as a decimal)
T = number of years the amount is deposited or...