Final answer:
Ellen would have $856.50 after 12 years if she invested $385 at an 8.3% annual interest rate with annual compounding. The formula for compound interest demonstrates the advantages of long-term investing and the substantial growth that can be achieved over time with this method.
Step-by-step explanation:
To calculate the future value of an investment with compound interest, we use the 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 (the initial amount of money), r is the annual interest rate (decimal), n is the number of times that interest is compounded per year, and t is the time the money is invested for in years. In Ellen's case, she has a principal of $385, an annual interest rate of 8.3%, compounded annually (n = 1), for 12 years (t = 12).
Using these values, the formula becomes A = 385(1 + 0.083/1)^(1*12). Calculating this results in A = $856.50 (rounded to two decimals).
The direct answer in two line is that after 12 years, Ellen would have $856.50 if she invests $385 at an 8.3% annual interest rate with annual compounding.
Compound interest can significantly increase the value of an investment over a long period. This process illustrates the benefit of starting to save and invest early, as the power of compound interest has more time to work, and larger sums can accrue over extended periods.