Question

Kyle plans to invest $5000, part at 6% simple interest and the rest at 7% simple interest. What is the most that he can invest at 6% and still be guaranteed at least $330 in interest per year?

Answer 1

To guarantee at least $330 in annual interest, Kyle can invest a maximum of $2,000 at 6%, with the remainder invested at 7%.

Step-by-step explanation:

Kyle is considering how to divide his $5,000 investment between two different simple interest rates to guarantee at least $330 in annual interest. Let's represent the amount invested at 6% as x and the amount invested at 7% as y. The total amount Kyle is investing is $5,000, so we can write the equation x + y = 5,000.

The interest earned from the portion invested at 6% would be 0.06x, and the interest earned from the portion invested at 7% would be 0.07y. Kyle wants to guarantee at least $330 in interest per year, which gives us the inequality 0.06x + 0.07y ≥ 330. We already know that x + y = 5,000, so we can substitute y in the inequality with 5,000 - x. This gives us 0.06x + 0.07(5,000 - x) ≥ 330, which simplifies to 0.06x + 350 - 0.07x ≥ 330, and further simplifies to -0.01x ≥ -20. Dividing by -0.01 (and remembering to flip the inequality since we're dividing by a negative number) gives us x ≤ 2,000.

Therefore, the most Kyle can invest at 6% while still being guaranteed at least $330 in interest per year is $2,000.

Answer 2

Kyle can invest a maximum of $2000 at a 6% simple interest rate to ensure he earns at least $330 in interest per year. By setting up an inequality and solving for the amount at 6%, the calculations show that investing more than $2000 would yield less than the desired interest.

Step-by-step explanation:

Kyle plans to divide his $5000 investment between two simple interest rates: 6% and 7%. He wants to earn at least $330 in interest per year. To determine the most he can invest at 6%, we'll let x represent the amount invested at 6%, and the remaining (5000 - x) will be the amount invested at 7%. The interest from the amount at 6% is 0.06x, and from the 7% is 0.07(5000 - x). The total interest should be at least $330:

0.06x + 0.07(5000 - x) ≥ 330

By solving this inequality, we'll find the maximum x.

0.06x + 350 - 0.07x ≥ 330

-0.01x ≥ -20

x ≤ 2000

Therefore, the most Kyle can invest at 6% simple interest and still be guaranteed at least $330 in interest per year is $2000.