a. An employee invests $ 500 per month in an ordinary annuity. If the interest rate is 5 % , find the value of the annuity after 18 yr . b. If the employee invests $ 1000 per month in the annuity instead of $ 500 at 5 % interest, find the value of the annuity after 18 yr . Compare the result to part (a), c. If the employee invests $500 per month in the annuity at 5 % interest find the value of the annuity after 36 yr . Compare the result to part (a).
a. An employee invests $ 500 per month in an ordinary annuity. If the interest rate is 5 % , find the value of the annuity after 18 yr . b. If the employee invests $ 1000 per month in the annuity instead of $ 500 at 5 % interest, find the value of the annuity after 18 yr . Compare the result to part (a), c. If the employee invests $500 per month in the annuity at 5 % interest find the value of the annuity after 36 yr . Compare the result to part (a).
Solution Summary: The author calculates the future value of an ordinary annuity by comparing the values of P,n,r, and t.
a. An employee invests
$
500
per month in an ordinary annuity. If the interest rate is
5
%
, find the value of the annuity after
18
yr
.
b. If the employee invests
$
1000
per month in the annuity instead of
$
500
at
5
%
interest, find the value of the annuity after
18
yr
. Compare the result to part (a),
c. If the employee invests $500 per month in the annuity at
5
%
interest find the value of the annuity after
36
yr
. Compare the result to part (a).
1. Show that the vector field
F(x, y, z)
=
(2x sin ye³)ix² cos yj + (3xe³ +5)k
satisfies the necessary conditions for a conservative vector field, and find a potential function for
F.
1. Newton's Law of Gravitation (an example of an inverse square law) states that the magnitude
of the gravitational force between two objects with masses m and M is
|F|
mMG
|r|2
where r is the distance between the objects, and G is the gravitational constant. Assume that the
object with mass M is located at the origin in R³. Then, the gravitational force field acting on
the object at the point r = (x, y, z) is given by
F(x, y, z) =
mMG
r3
r.
mMG
mMG
Show that the scalar vector field f(x, y, z) =
=
is a potential function for
r
√√x² + y² .
Fi.e. show that F = Vf.
Remark: f is the negative of the physical potential energy, because F = -V(-ƒ).
2. Suppose f(x) = 3x² - 5x. Show all your work for the problems below.
College Algebra with Modeling & Visualization (5th Edition)
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