Final answer:
The student's question pertains to calculating the necessary monthly rate of return to accumulate $1 million by saving $1,101.4 monthly over 32 years, which involves understanding compound interest. Starting to save early can considerably increase wealth due to the effects of compound interest. The future value of an annuity formula or a financial calculator would be used to determine the required rate of return.
Step-by-step explanation:
The student's question deals with the goal of accumulating $1 million for retirement by saving $1,101.4 every month for 32 years. To achieve this goal, the student is questioned about the necessary monthly rate of return. This is a financial scenario where understanding and using compound interest is essential. The power of compound interest allows savings to grow at a faster rate as the interest earned is reinvested into the principal balance, causing an exponential increase in the account's value over time.
For example, saving $3,000 at a 7% annual rate of return for 40 years, without additional contributions, would result in approximately $44,923 due to compound interest. This demonstrates how starting to save early and allowing compound interest to work over a long period can significantly increase wealth.
However, to answer the student's question specifically, one would need to calculate the future value of an annuity with a series of monthly payments using the future value formula or a financial calculator. The formula incorporates the monthly contribution amount, the length of time for investing, and the expected monthly rate of return to determine if the goal is achievable and what the rate of return would need to be.