Final answer:
Larry Mitchell invested $5,000 at 6% simple interest and $14,000 at 3% simple interest to achieve a total yearly interest of $720 from his $19,000 total investment.
Step-by-step explanation:
Larry Mitchell needs to determine the amount invested at both 6% and 3% annual simple interest rates when his total investment is $19,000, and his total yearly interest from both accounts is $720.
Let's assume Larry invested $x at 6% simple interest. Therefore, he invested $(19,000 - x) at 3% simple interest. The total interest from both investments is $720 per year. To find the amounts invested at each rate, we can set up the following equations:
Interest from 6% investment: 0.06x
Interest from 3% investment: 0.03(19,000 - x)
Total interest: 0.06x + 0.03(19,000 - x) = $720
Solving this equation:
- 0.06x + 0.03(19,000) - 0.03x = 720
- 0.06x - 0.03x + 570 = 720
- 0.03x = 720 - 570
- 0.03x = 150
- x = 150 / 0.03
- x = $5,000
Therefore, Larry invested $5,000 at 6% and $19,000 - $5,000 = $14,000 at 3% interest.