Final answer:
The future value of a $27,500 investment at a 9% interest rate after 6 periods is calculated using the compound interest formula: FV = P(1 + r)^n. In this case, the formula is 27,500(1 + 0.09)^6, and calculating it will provide the final value.
Step-by-step explanation:
The student asked about the future value of an initial investment of $27,500 placed into a high yield savings account with a 9% interest rate after 6 periods. This involves the concept of compound interest, which is a crucial part of financial mathematics. To calculate the future value (FV) of this investment, one can use the compound interest formula: FV = P(1 + r)n, where P is the principal amount, r is the annual interest rate (expressed as a decimal), and n is the number of compounding periods.
Step-by-Step Calculation
- Identify the principal amount, which is $27,500.
- Convert the interest rate from a percentage to a decimal by dividing by 100: 9% / 100 = 0.09.
- Determine the number of periods, which is 6.
- Plug the values into the compound interest formula: FV = 27,500(1 + 0.09)6.
- Calculate the value using a calculator or software.
The formula shows how compound interest can significantly increase the value of savings over time, demonstrating the power of investing early and allowing investments to grow.