For Exercises 61-64, set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Sylvia invested a total of $ 40 , 000 . She invested part of the money in a certificate of deposit (CD) that earns 2 % simple interest per year. She invested in a stock that returns the equivalent of 8 % simple interest, and she invested in a bond fund that returns 5 % . She invested twice as much in the stock as she did in the CD, and earned a total of $ 2300 at the end of 1 yr . How much principal did she put in each investment?
For Exercises 61-64, set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination. Sylvia invested a total of $ 40 , 000 . She invested part of the money in a certificate of deposit (CD) that earns 2 % simple interest per year. She invested in a stock that returns the equivalent of 8 % simple interest, and she invested in a bond fund that returns 5 % . She invested twice as much in the stock as she did in the CD, and earned a total of $ 2300 at the end of 1 yr . How much principal did she put in each investment?
For Exercises 61-64, set up a system of linear equations to represent the scenario. Solve the system by using Gaussian elimination or Gauss-Jordan elimination.
Sylvia invested a total of
$
40
,
000
. She invested part of the money in a certificate of deposit (CD) that earns
2
%
simple interest per year. She invested in a stock that returns the equivalent of
8
%
simple interest, and she invested in a bond fund that returns
5
%
. She invested twice as much in the stock as she did in the CD, and earned a total of
$
2300
at the end of
1
yr
. How much principal did she put in each investment?
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
Can you answer this question and give step by step and why and how to get it. Can you write it (numerical method)
There are three options for investing $1150. The first earns 10% compounded annually, the second earns 10% compounded quarterly, and the third earns 10% compounded continuously. Find equations that model each investment growth and
use a graphing utility to graph each model in the same viewing window over a 20-year period. Use the graph to determine which investment yields the highest return after 20 years. What are the differences in earnings among the three
investment?
STEP 1: The formula for compound interest is
A =
nt
= P(1 + − − ) n²,
where n is the number of compoundings per year, t is the number of years, r is the interest rate, P is the principal, and A is the amount (balance) after t years. For continuous compounding, the formula reduces to
A = Pert
Find r and n for each model, and use these values to write A in terms of t for each case.
Annual Model
r=0.10
A = Y(t) = 1150 (1.10)*
n = 1
Quarterly Model
r = 0.10
n = 4
A = Q(t) = 1150(1.025) 4t
Continuous Model
r=0.10
A = C(t) =…
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