Final answer:
To achieve a total annual income of $999 with two different simple interest rates, $6300 invested at 3% and $2700 invested at 9%, the correct answer is option A, which describes the amount that needs to be invested at 9%.
Step-by-step explanation:
The correct answer is option A, $1700 should be invested at 9%.
First, calculate the annual simple interest from the $6300 investment at 3%:
Interest = Principal × Rate × Time
Interest = $6300 × 0.03 × 1
Interest = $189
The total yearly income from both investments must be $999, and you already have $189 from the first investment. So, the income needed from the second investment at 9% simple interest is:
$999 - $189 = $810
Let 'P' be the principal amount needed at 9%. Then, use the simple interest formula again:
$810 = P × 0.09 × 1
P = $810 / 0.09
P = $9000
Therefore, $9000 must be the total money invested at both 3% and 9%. Because you already have $6300 at 3%, subtract this from $9000 to find the amount needed at 9%:
$9000 - $6300 = $2700
So, $2700 should be invested at 9% to get a total annual income of $999.