12. You has investments totaling $8000 in two accounts: a savings account paying
5% interest, and the other a bond paying 8% interest. If the amount of interest after
one year from both investments was $600, how much did you invest in both accounts
initially?
let x = amount in savings
8000-x = amount invested
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0.05x + 0.08(8000-x) = 600
Solve for x and 8000-x
Well, well, well, someone's got a knack for making money! Let's do some math and get to the bottom of this.
Let's assume the amount invested in the savings account is x dollars. That means the amount invested in the bond is 8000 - x dollars.
Now let's calculate the interest earned from each account. The interest from the savings account is 0.05x dollars, and the interest from the bond is 0.08(8000 - x) dollars.
Since the total interest earned is $600, we can set up an equation:
0.05x + 0.08(8000 - x) = 600.
Solving this equation will give us the initial investment amounts. But hey, solving equations can be quite boring. Want me to tell you a joke while we wait for the answer?
Let's assume you invested x dollars in the savings account and (8000 - x) dollars in the bond account.
The interest earned from the savings account is given by the formula:
Interest = Principal * Rate
So, the interest earned from the savings account after one year would be:
0.05x
Similarly, the interest earned from the bond account after one year would be:
0.08(8000 - x)
The total interest earned from both accounts is given as $600. Therefore, we can write the equation:
0.05x + 0.08(8000 - x) = 600
Simplifying the equation:
0.05x + 640 - 0.08x = 600
-0.03x = 600 - 640
-0.03x = -40
Dividing both sides by -0.03, we get:
x = -40 / -0.03
x = 1333.33 (rounded to two decimal places)
Therefore, you initially invested $1333.33 in the savings account, and the remaining amount of $6666.67 (8000 - 1333.33) in the bond account.
To find the amount that was invested in each account initially, you can set up a system of equations:
Let x be the amount invested in the savings account and y be the amount invested in the bond account.
From the given information, we are given the following equations:
Equation 1: x + y = 8000 (the total amount invested in both accounts is $8000)
Equation 2: 0.05x + 0.08y = 600 (the total interest earned from both accounts is $600)
To solve this system of equations, you can use the substitution method or the elimination method. Let's use substitution:
From Equation 1, we solve for x:
x = 8000 - y
Substitute this value of x into Equation 2:
0.05(8000 - y) + 0.08y = 600
Now, simplify the equation:
400 - 0.05y + 0.08y = 600
-0.03y = 200
y = 200 / -0.03
y = -200 / 0.03
y = 6666.67 (rounded to two decimal places)
Now, substitute this value of y back into Equation 1 to find x:
x + 6666.67 = 8000
x = 8000 - 6666.67
x = 1333.33 (rounded to two decimal places)
Therefore, you originally invested $1333.33 in the savings account and $6666.67 in the bond account.