You invested a total of $15,000 at 4 1/2% and 5% simple interest. During one year, the two accounts earned $715. How much did you invest in each account
IDK
Let's assume you invested $x in the account with a 4 1/2% interest rate.
Therefore, the amount invested in the account with a 5% interest rate would be $15,000 - $x (as the total investment is $15,000).
The interest earned from the 4 1/2% account can be calculated as: (x * 4.5%) = 0.045x
Similarly, the interest earned from the 5% account is: ((15000 - x) * 5%) = 0.05(15000 - x)
According to the given information, the total interest earned from both accounts is $715.
So, we can set up the equation: 0.045x + 0.05(15000 - x) = 715
Simplifying this equation, we get: 0.045x + 750 - 0.05x = 715
Combining like terms, we have: -0.005x + 750 = 715
Now, let's isolate the x-variable by subtracting 750 from both sides of the equation: -0.005x = 715 - 750
Simplifying further, we have: -0.005x = -35
Dividing both sides of the equation by -0.005, we get: x = -35 / -0.005
Therefore, x ≈ 7000.
This means you invested approximately $7,000 in the account with a 4 1/2% interest rate.
Substituting this value back into the equation, the amount invested in the account with a 5% interest rate would be: 15000 - 7000 = $8000.
Hence, you invested $7,000 in the 4 1/2% account and $8,000 in the 5% account.
To find out how much you invested in each account, let's set up a system of equations.
Let's denote the amount invested at 4 1/2% as "x" and the amount invested at 5% as "y".
The interest earned from the account invested at 4 1/2% can be calculated using the formula: Interest = (Principal * Rate * Time) / 100. In this case, the rate is 4 1/2% or 0.045.
So, the interest earned from the account invested at 4 1/2% is: (x * 0.045 * 1) = 0.045x.
Similarly, the interest earned from the account invested at 5% is: (y * 0.05 * 1) = 0.05y.
According to the given information, the interest earned from both accounts is $715.
So, we have the equation: 0.045x + 0.05y = 715.
We also know that the total investment amount is $15,000, so we have another equation: x + y = 15000.
Now, we can solve the system of equations to find the values of x and y.
1. Multiply the first equation by 100 to eliminate the decimal points: 4.5x + 5y = 71500.
2. Rewrite the equations:
4.5x + 5y = 71500
x + y = 15000
3. Multiply the second equation by 4.5 to match the coefficient of x:
4.5x + 4.5y = 67500
4. Subtract the second equation from the first equation to eliminate x:
4.5x + 5y - (4.5x + 4.5y) = 71500 - 67500
0.5y = 4000
5. Solve for y:
y = 4000 / 0.5
y = 8000
6. Substitute the value of y back into the second equation to find x:
x + 8000 = 15000
x = 15000 - 8000
x = 7000
Therefore, you invested $7,000 at 4 1/2% and $8,000 at 5%.
amount at 4.5% ---- x
amount at 5% = 15000-x
solve for x:
.045x + .05(15000-x) = 715