Final answer:
The best investment option is B) an investment earning 10 percent for 20 years, as it will yield the highest future value compared to the other options when using the compound interest formula.
Step-by-step explanation:
The preferred investment would be B) an investment earning 10 percent for 20 years. To understand why, we calculate the future value of each investment over the given periods using the compound interest formula, which is 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 lump sum of money).
- r is the annual interest rate (decimal).
- n is the number of times that interest is compounded per year.
- t is the time the money is invested for in years.
Assuming a single compound per year, we can compare the investments without the need to specify P, since it will be the same for all calculations and will not affect which option has the higher return.
- For option A: A = P(1 + 0.085)^20
- For option B: A = P(1 + 0.10)^20
- For option C: A = P(1 + 0.03)^40
- For option D: A = P(1 + 0.05)^40
The highest return comes from option B because 10% compounded annually over 20 years yields the highest future value compared to the other options.