Final answer:
To find the balance in Janet's fund after 28 years, we use the future value of an annuity formula considering monthly deposits and annual compound interest. The total interest earned is the difference between the fund's future value and the total amount Janet deposited over the period.
Step-by-step explanation:
The student's question involves calculating the future value of a series of monthly deposits over a specific timeframe, using the formula for compound interest. This exercise demonstrates the impact of regular savings and the growth of an investment over time at a given interest rate.
Calculating the Future Value
To determine the balance in Janet's fund at the end of the 28-year period, we need to use the formula for the future value of an annuity when interest is compounded annually. In this case, Janet makes a monthly deposit of $350 at an annual interest rate of 4.58%. However, since the compounding is annual but the deposits are monthly, we must calculate the equivalent annual deposit and then apply the annuity formula.
After computing the future value, we subtract the total amount deposited from this value to find the total amount of interest earned over the period. The total amount deposited is simply the monthly deposit amount multiplied by the total number of months.
To solve this, we use specialized financial calculators or formulas, as the calculations can become quite complex due to the nature of compound interest spanning over monthly deposits and annual compounding.