Final answer:
The question involves calculating the future value and total interest earned from monthly savings over 36 years with an annual compound interest rate of 4.19%. The computation requires the annuity due formula for compound interest, which illustrates how the investment grows over time as interest accumulates on both the principal and the accrued interest.
Step-by-step explanation:
The question pertains to compound interest and requires finding the future value of a series of monthly savings at an annual interest rate, as well as calculating the total interest earned over a given period. Since the investments are made at the beginning of each month, we must use the formula for the future value of an annuity due:
- Convert the annual interest rate to a monthly rate by dividing by 12.
- Calculate the future value using the annuity due formula.
- To find the total interest earned, subtract the total amount deposited from the future value of the fund.
However, for the sake of brevity and without the entire future value formula provided, it is not possible to compute the exact balance and interest earned in this format. In general, to illustrate the power of compound interest, a higher balance is achieved over time compared to simple interest, as the interest itself earns interest.
As with the example of a $3,000 initial investment growing fifteen fold over 40 years with a 7% annual rate of return, Janet's regular savings over 36 years at a rate of 4.19% would have grown significantly, showcasing the long-term benefits of regular investments and compound interest in wealth accumulation.