Question 122771: I figured out the answer but I am clueless as to the equation. Can you please help???? thanks
Simple interest word problems refer to applications in which money is invested in an account paying simple interest rather than compounded. The relationship between principle (P), interest rate (r), length of time the money is invested (t), and earned interest (I) is given by the following formula:
I = Prt
An approach to solving a simple interest problem runs pretty close to how one would set up a table and from that table, formulate a single variable equation to solve the problem. As an example, consider the following simple interest problem.
Mr. Jones deposits $8000 in one simple interest account and $2000 in a second simple interest account. The interest rate on the $8000 account is 2% more than the rate on the $2000 account. If the total yearly amount of interest on the two accounts is $578, find the interest rate on each account.
Steps to solve this problem:
Step 1: Identify which column you can complete from the information given in the problem (without having to use a variable) and fill it out. In this case you can set up a table since you know the amount invested in each account.
Principle T (Time) R ( rate) = Interest
$8000 account $8000
$2000 account $2000
Step 2: Identify what you are looking for and define your variable. Here we are looking for the interest rate on each account. But since they are not the same interest rate we cannot let x represent them both. Arbitrarily I will choose the following:
Let x represent the interest rate for the $2000 account.
• Place x in the appropriate cell (interest rate of the $2000 account)
• Fill out the rest of the column using the fact that the interest rate of the $8000 account is 2% more than the interest rate (x) of the $2000 account.
Principle T (Time) R ( rate) = Interest
$8000 account $8000 x + .02
$2000 account $2000 x
Note: We want to express the interest rate as a decimal rather than a percentage. Therefore, instead of using 2% (the percent form) we use .02 (the decimal form).
Step 3: Since the money is only deposited for one year, Time = 1. Fill out the last column by using the first two columns and following the equation at the top of the chart
Prt = I
Principle T (Time) R ( rate) = Interest
$8000 account $8000 (1) x + .02 $8000 (x+.02)
$2000 account $2000 (1) x $2000 (x)
Step 4: The equation that will model this problem will now be drawn from the last column
Interest earned on the $8000 account + Interest earned on the $2000 account
= $578
8000 (x+.02) + 2000 (x) = 578
Step 5: Now solve the equation and answer the original question.
Solving, we get: x = .0418 and x + .02 = .0618
Answer to the original question: The interest rate on the $2000 account is 4.18% and the interest rate in the $8000 account is $6.18%.
Now using this example as a template, formulate the following problem in a table format and solve the following problem. Keep in mind that full credit for this project will only be awarded if your solution is correct.
Ms. Parker deposits $8000 in one simple interest account and $2000 in a second simple interest account. The interest rate on the $8000 account is 2% more than the rate on the $2000 account. If the total yearly amount of interest earned on the $8000 account is $459 more than the interest earned on the $2000 account, find the interest rate on each account. Clearly state your solution in relation to the interest rate on each account.
The interest on the $8000 account is .069834 = 6.9834%
The interest on the $2000 account is .049834 = 4.9834%
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! solve the following problem. Keep in mind that full credit for this project will only be awarded if your solution is correct.
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Ms. Parker deposits $8000 in one simple interest account and $2000 in a second simple interest account.
The interest rate on the $8000 account is 2% more than the rate on the $2000 account.
If the total yearly amount of interest earned on the $8000 account is $459 more than the interest earned on the $2000 account, find the interest rate on each account.
Clearly state your solution in relation to the interest rate on each account.
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1st Investment:
Principal = $8000
Let rate = "x"
Interest = 8000x
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2nd Investment:
Principal = #2000
Rate = "x-.02"
Interest = 2000(x-.02)
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EQUATION:
Interest in 1st - Interest in 2nd = 459
8000x - 2000(x-0.02) = 459
6000x+40 = 459
6000x = 419
x = 0.0698 (interest on the $8000)
x-0.02 = 0.0498 (interest on $2000)
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Cheers,
Stan H.
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