Final answer:
To earn at least $1720 in yearly interest, with $10,000 earning 13% from a CD, the remaining $6,000 needs to be invested at a rate of 7%.
Step-by-step explanation:
To solve how much the remainder of the money needs to be invested at to yield at least $1720 in yearly interest, we must first calculate the interest earned from the $10,000 certificate of deposit (CD). The CD pays 13% annual simple interest, so it would earn $10,000 × 0.13 = $1,300 in interest per year.
Since the total interest required is $1,720, we subtract the interest earned from the CD from this amount to find out how much more interest is needed. That amount is $1,720 - $1,300 = $420.
The remainder of the money to be invested is $16,000 - $10,000 = $6,000. If we let r represent the unknown interest rate (expressed as a decimal), the equation for the interest earned by the remaining amount would be $6,000 × r = $420. To find r, we divide both sides by $6,000 to get r = $420 / $6,000, which simplifies to r = 0.07, or 7%.
Therefore, to achieve the desired total interest of at least $1,720 per year, the remaining $6,000 must be invested at a rate of 7%.