Gina plans to invest $12,000, part at 4% simple interest and the rest at 6% simple interest. What is the most she can invest at 4% and still be guaranteed at least $650 in interest per year?
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To find out the maximum amount Gina can invest at 4%, we need to determine the amount that will generate $650 in interest per year.
Let's assume that Gina invests x dollars at 4% interest. The interest earned from this investment would be (x * 4%) or 0.04x dollars.
Gina also plans to invest the rest of her money, which we can calculate as (12,000 - x) dollars, at 6% interest. The interest earned from this investment would be ((12,000 - x) * 6%) or 0.06(12,000 - x) dollars.
To ensure she makes at least $650 in interest per year, we can set up the following equation:
0.04x + 0.06(12,000 - x) ≥ $650
Now we can solve for x:
0.04x + 0.06(12,000 - x) ≥ 650
0.04x + 720 - 0.06x ≥ 650
-0.02x + 720 ≥ 650
-0.02x ≥ -70
x ≤ -70 / -0.02
x ≤ 3,500
Therefore, Gina can invest a maximum of $3,500 at 4% to guarantee at least $650 in interest per year.