Final answer:
Brian has a total of $6000 invested, with equal parts in stocks paying an 8% dividend and 14% interest to yield a total annual income of $660.
Step-by-step explanation:
Brian has half his investments in stock paying an 8% dividend and the other half in a stock paying 14% interest. If his total annual interest is $660, we can find out how much he has invested by setting up a system of equations. Let the total investment be $x, so each half is $x/2. The total interest from both stocks is:
($x/2) × 0.08 + ($x/2) × 0.14 = $660
Now, solving for $x gives:
0.04$x + 0.07$x = $660
0.11$x = $660
$x = $660 ÷ 0.11
$x = $6000
So, Brian has a total of $6000 invested.
To solve this problem, we can use the formula for calculating interest. Let's assume that Brian has $x invested in total. Since he has half of his investments in a stock paying an 8% dividend, this means he has $x/2 invested in that stock. Similarly, he has $x/2 invested in a stock paying a 14% interest.
So, the total annual interest he receives from these investments can be calculated as (x/2)*(0.08) + (x/2)*(0.14) = 0.08x + 0.14x = 0.22x. Given that his total annual interest is $660, we can set up the equation 0.22x = 660 and solve for x. Dividing both sides of the equation by 0.22 gives us x = 660/0.22 = $3000.