A total of $5000 is invested: part at 5% and the remainder at 15%. How much is invested at each rate if the annual interest is $720
Let's represent the amount invested at 5% as x and the amount invested at 15% as 5000 - x.
The interest earned from the amount invested at 5% is the principal multiplied by the rate, so it is x * 5% = 0.05x.
The interest earned from the amount invested at 15% is (5000 - x) * 15% = 0.15(5000 - x) = 750 - 0.15x.
The total interest earned from both amounts is $720, so:
0.05x + 750 - 0.15x = 720.
Combining like terms, we have:
0.1x + 750 = 720.
Subtracting 750 from both sides gives:
0.1x = 720 - 750 = -30.
Dividing both sides by 0.1 gives:
x = -30 / 0.1 = -300.
Since the amount cannot be negative, we made an error somewhere. Additionally, it is important to note that the amounts invested must add up to $5000.
Let's try a different approach:
Let the amount invested at 5% be represented by x.
Therefore, the amount invested at 15% is $5000 - x.
The interest earned from investing x dollars at 5% is 0.05x.
The interest earned from investing $5000 - x dollars at 15% is 0.15(5000 - x) = 750 - 0.15x.
The total interest earned from both amounts is $720, so:
0.05x + 750 - 0.15x = 720.
Combining like terms, we get:
-0.1x + 750 = 720.
Subtracting 750 from both sides, we have:
-0.1x = 720 - 750 = -30.
Dividing both sides by -0.1 (which is equivalent to multiplying by -10), we get:
x = (-30) / (-0.1) = 300.
Therefore, $300 is invested at 5% and $5000 - $300 = $4700 is invested at 15%.