Sue has a total of $4000 to invest in two accounts. one account earns 2% simple interest and the other earns 5% simple interest. How much should be invested in both accounts to earn exactly $155 at the end of the year?
If $x go at 2%, the rest (4000-x) is at 5%. So, add up the interest on each part:
.02x + .05(4000-x) = 155.00
Well, it seems like Sue wants to make a decent return on her investment without being too greedy. Let's figure out the amount she should invest in each account, shall we?
Let's call the amount Sue invests in the 2% account "x" dollars. That means she would then invest (4000 - x) dollars in the 5% account.
Now, let's calculate the interest earned in each account. For the 2% account, Sue would earn 0.02x dollars in interest. And for the 5% account, she would earn 0.05(4000 - x) dollars in interest.
Since Sue wants to earn exactly $155 at the end of the year, we can set up the following equation:
0.02x + 0.05(4000 - x) = 155
Now, let's solve this equation and see how much Sue needs to invest in each account to achieve her financial goal!
0.02x + 0.05(4000 - x) = 155
0.02x + 200 - 0.05x = 155
-0.03x = -45
x = -45 / -0.03
x = 1500
So Sue should invest $1500 in the 2% account, and the remaining amount, $4000 - $1500 = $2500 should be invested in the 5% account.
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Let's assume Sue invests x amount of dollars in the account earning 2% interest and invests (4000 - x) amount of dollars in the account earning 5% interest.
Step 1: Set up the equation for the total interest earned.
Interest earned from the 2% account + Interest earned from the 5% account = $155
(x * 0.02) + ((4000 - x) * 0.05) = 155
Step 2: Solve the equation.
0.02x + 0.05(4000 - x) = 155
0.02x + 200 - 0.05x = 155
0.03x + 200 = 155
0.03x = 155 - 200
0.03x = -45
x = -45 / 0.03
x = -1500
Step 3: Analyze the result.
According to the calculated value, Sue would need to invest -1500 dollars in the account earning 2% interest. Since this value is negative, it means that she does not need to invest any money in the 2% account.
Step 4: Calculate the amount to be invested in the 5% account.
The remaining amount to be invested in the 5% account can be calculated by subtracting the amount invested in the 2% account from the total investment amount.
4000 - (-1500) = 4000 + 1500 = 5500
Therefore, Sue should invest $5500 in the account earning 5% interest and no money in the account earning 2% interest to earn exactly $155 at the end of the year.
To determine how much should be invested in each account, we can set up a system of equations based on the given information.
Let's assume that Sue invests x dollars in the account that earns 2% interest, and (4000 - x) dollars in the account that earns 5% interest.
The amount of interest earned in the account that earns 2% interest can be calculated using the formula: interest = principal * rate * time.
For the first account, the interest earned at the end of the year would be: (x * 0.02).
Similarly, for the second account, the interest earned at the end of the year would be: ((4000 - x) * 0.05).
According to the given information, the total interest earned should be exactly $155. Therefore, we can set up the following equation:
(x * 0.02) + ((4000 - x) * 0.05) = 155.
Now, let's solve this equation to find the value of x:
0.02x + 0.05(4000 - x) = 155.
0.02x + 200 - 0.05x = 155.
-0.03x = -45.
x = (-45) / (-0.03).
x = 1500.
Therefore, Sue should invest $1500 in the account that earns 2% interest and $2500 in the account that earns 5% interest to earn exactly $155 in one year.