Final answer:
To calculate the total amount invested and the interest rate for the first 8 years in the investment account that earns 10.6% compounded semiannually, use the compound interest formula. To find the interest rate for the next 2 years when compounded monthly, use the compound interest formula.
Step-by-step explanation:
To calculate the total amount invested and the interest rate for the first 8 years in the investment account that earns 10.6% compounded semiannually, we need to use the compound interest formula: A = P(1 + r/n)^(nt). In this case, the initial investment (P) is unknown, the interest rate (r) is 10.6%, the number of compounding periods per year (n) is 2 (semiannually), and the time (t) is 8 years. Plugging in these values, we can solve for A to find the total amount invested. Similarly, to find the interest rate for the next 2 years when compounded monthly, we can use the compound interest formula A = P(1 + r/n)^(nt), where the interest rate (r) is unknown, the number of compounding periods per year (n) is 12 (monthly), and the time (t) is 2 years. We can solve for r to find the interest rate.