Final answer:
To find the future value of an investment with compound interest, use the formula Future Value = Principal × (1 + interest rate/n)^(n x time). For quarterly compounding, the future value is $536.69. For monthly compounding, the future value is $537.18.
Step-by-step explanation:
To find the future value of an investment with compound interest, you can use the formula: Future Value = Principal × (1 + interest rate/n)^(n x time), where n is the number of compounding periods per year and time is the number of years. In this case, we have an investment of $500 at 5% interest for two years and we need to find the future value if the interest is compounded quarterly and monthly.
If the interest is compounded quarterly, there will be 4 compounding periods per year, so n = 4. Plugging the values into the formula, we have:
Future Value = $500 × (1 + 0.05/4)^(4 x 2) = $536.69
If the interest is compounded monthly, there will be 12 compounding periods per year, so n = 12. Plugging the values into the formula, we have:
Future Value = $500 × (1 + 0.05/12)^(12 x 2) = $537.18