Sure, let's compare the two investments!
For the investment compounded annually with a principal of $3,000, an annual interest rate of 9%, and a number of years of 16, we can calculate the future value using the formula:
Future Value = Principal * (1 + (Interest Rate / Number of Compounding Periods))^(Number of Compounding Periods * Number of Years)
Let's calculate the future value for the investment compounded annually:
Future Value = $3,000 * (1 + (0.09 / 1))^(1 * 16)
Future Value = $3,000 * (1 + 0.09)^16
Future Value ≈ $8,235.05
Now, for the investment compounded periodically, we know that after 16 years, it will be worth $1,230.23 more than the investment compounded annually. So, we can calculate the future value for the investment compounded periodically:
Future Value = $8,235.05 + $1,230.23
Future Value ≈ $9,465.28
Therefore, the investment compounded periodically will be worth approximately $9,465.28 after 16 years, which is $1,230.23 more than the investment compounded annually.