Final answer:
To maximize growth for Tina's investment, investing the full amount at 7% interest immediately is the optimal choice because it combines the highest rate with the longest time for compound interest to work.
Step-by-step explanation:
To achieve the highest growth for Tina's investment, she should select the option of investing the whole amount this year at 7% interest. Here's an explanation that uses the concept of compound interest, which refers to the addition of interest to the principal sum of a loan or deposit, or in other words, interest on interest.
When comparing the given options, a higher interest rate results in a greater accumulation of wealth over time due to compound interest. Starting with the entire amount as early as possible allows more time for the investment to grow. If Tina invests the whole amount at 5% interest, it will grow, but not as much as it would at a 7% interest rate. If she starts investing only half of the amount at either rate, even in two years, that would significantly reduce the potential growth due to less principal to grow and less time for compounding.
Referencing the power of compounding, as shown in the illustrative example provided, where an investment of $3,000 at a 7% annual rate grows to $44,923 after 40 years, it's clear that the higher rate and starting with the full amount provides the best advantage.