Final answer:
The student's question deals with comparing two different investment options with annual interest rates of 6% and 10% over a period of five years. To determine which is a better option, the future value of each investment must be calculated using compound interest formulas, taking into account the frequency of compounding and the time frame considered.
Step-by-step explanation:
This student question is related to the concept of interest rates and their impact on investments. In the scenario presented, there are two investments with different annual interest rates: one offering 6% and another offering 10%. It is important to understand how these rates affect the return on investment over a specific period, in this case, five years. When choosing between different investments, the interest rate is a critical factor as it dictates the rate of compound interest, which demonstrates the exponential growth of money over time.
Compound interest can be calculated using 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, 'r' is the annual interest rate (decimal), 'n' is the number of times that interest is compounded per year, and 't' is the number of years the money is invested for.
To make an informed decision between these two investments, one would compare the respective futures values they would yield after the specified time frame. The investment with the higher return over the five-year period would generally be considered the better option, though risk and other factors should also be considered.