Final answer:
Compound interest is a financial concept used to calculate the future value of an investment. The formula A = P(1 + r/n)^(nt) is instrumental for such calculations, underlining the growth potential of early and sustained investment strategies with examples showing substantial growth over time.
Step-by-step explanation:
The topic we're discussing is compound interest, which is a key concept in financial mathematics. 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. For our example, if a student invests $700 at a 15% annual interest rate, compounded yearly over six years, the formula would be 700(1 + 0.15/1)^(1*6). This calculation allows investors to see how their investments can grow over time and helps illustrate the power of starting to save early due to the effects of compounding.