Final answer:
Comparing Tina's investment options, investing the whole amount immediately at a higher interest rate allows for maximum growth. The power of compound interest significantly benefits investments over a long time, especially when starting early with a high rate.
Step-by-step explanation:
The question involves comparing investment options to determine which would allow the highest growth for Tina's investment, considering different rates of return and starting times. The principle of compound interest is crucial here, since it enables invested money to grow over time at a rate that accrues interest on the initial principal and accumulated interest from previous periods.
Starting early with investments generally leads to more significant growth due to the power of compound interest, as seen in the provided scenario where a $3,000 investment grows nearly fifteen fold over 40 years with a 7% rate of return. Given Tina's options, starting immediately with a higher interest rate will likely yield the best results. For example, if Tina invests $1,000 at a 7% interest rate, using the compound interest formula A = P(1 + r/n)^(nt), where A is the amount of money accumulated after n years, including interest, P is the principal amount, r is the annual interest rate, n is the number of times that interest is compounded per year, and t is the number of years the money is invested, she will maximize the potential growth of the initial investment compared to the other options.