|
Question 1079941: Question: Cathy won $10,000 in the lottery. She wants to put some in an accessible savings account, and the rest to a long-term investment. She has been considering a savings account which has been paying an annual percentage rate of 2.64%, and a mutual fund which has been paying an APR of 8.9%. At the end of 1 year, Cathy hopes to earn $750. How much money must she invest in each type of acct.?
a. Model situation algebraically.
b. Determine solution algebraically and graphically.
c. Is there any way Cathy can invest the money to earn $1,000 in interest in one year? Explain how you arrived at your conclusion.
I started by defining my variables, s=Savings account, m=Mutual fund. Then, I tried modeling it algebraically like so: $750=2.64s+8.9m. I tried different numbers for each variable to get to $750, but it's not seeming to work, and I am stumped on how to solve this any further on a, b, or c. Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you need to solve 2 equations simultaneously.
s + m = 10,000
.0264s + .089m = 750
decimal equivalent = percent / 100.
2.64% = .0264
8.9% = .089
we'll solve by elimination.
you could also solve by substitution or by graphing.
i'll do elimination and then show you the graphical solution.
your 2 equations are:
s + m = 10,000
.0264s + .089m = 750
multiply both sides of the first equation by .0264 to get:
.0264s + .0264m = 264
.0264s + .089m = 750
subtract the first equation from the second to get:
.0626m = 486
solve form to get m = 486 / .0626 = 7763.578275
s is equal to 10,000 - 7763.578275 = 2236.421725
s + m = 10,000
.0264s + .089m = 750
solution looks good.
the graphical solution is shown below:
you let x = amount invested in savings and y = amount invested in mutual funds.
your equations to graph are:
.0264 * x + .089y = 750
x + y = 10,000
solve for y in both equations to get:
y = (750 - .0264x) / .089
y = 10000 - x
the intersection of the lines of these 2 equations should be your solution.
the solution is shown in (x,y) format where x represents the investment in the savings account and y represents the investment in the mutual fund account.
it does not appear that she can earn 1000 interest in one year with .0264 interest on the savings and .089 interest on the mutual fund.
the problem is that, even if she invested all the money in the mutual fund account, the best she could get was 890 in interest.
|
|
|
| |
